Health monitoring of a Brayton 
cycle-based power conversion unit 
Thesis submitted for the degree Doctor of Philosophy 
at the Potchefstroom Campus of the 
North-West University 
Carel P. du Rand 
Promoter: Prof. G. van Schoor 
December 2007 
Abstract 
The next generation nuclear power plants like the Pebble Bed Modular Reactor (PBMR) 
permit for the design of advanced health monitoring (fault diagnosis) systems to improve 
safety, system reliability and operational performance. Traditionally, fault diagnosis has 
been performed by applying limit value checking techniques. Although simple, the 
inability of these techniques to model parameter dependencies and detect incipient fault 
behaviour renders them unfavourable. More recent approaches to fault diagnosis can be 
attributed to the advances in computational intelligence. Data driven methods like 
artificial neural networks are more widely used when modelling complex nonlinear 
systems, using only historical plant data. These methods are however dependent on the 
quality and amount of data used for model development. 
The key to developing an advanced fault diagnosis system is to adopt an integrated 
approach for monitoring the different aspects of the total process. Within this context, this 
goal is realized by presenting a new integrated architecture for sensor fault diagnosis in 
addition to the enthalpy-entropy graph approach for process fault diagnosis. The 
integrated architecture for sensor fault diagnosis named SENSE, exploits the strengths of 
several existing techniques whilst reducing their individual shortcomings. A novel 
approach for process fault diagnosis is proposed based on the characteristics inherent in 
the design of the PBMR. Power control by means of an inventory control system and no 
bypass valve operation facilitates a reference model that remains invariant over the power 
range. Consequently, the devised reference fault signatures remain static during steady 
state and transient variations of the normal process. 
In the thesis, both single and multiple fault conditions are considered during steady 
state and transient variations of the normal process. It is demonstrated that by applying 
SENSE, the fused variable estimates are consistent and more accurate than the individual 
sensor readings. Test cases corresponding to 32 single and multiple fault conditions 
confirmed that it is possible to use the enthalpy-entropy graph approach for process fault 
diagnosis. In addition, the proposed fault diagnosis approach is validated through an 
application to real data from the prototype Pebble Bed Micro Model (PBMM) plant. This 
application demonstrated that the proposed approach is ideally suited for early detection 
of faults and greatly reduces the amount of plant data required for model development. 
Acknowledgements 
To God with Love 
I would like to extend my sincere gratitude to everybody that helped me to complete the 
work presented in the thesis: 
To my supervisor, Prof. George van Schoor for his persistent guidance and valuable 
inputs. 
I would like to thank MTech Industrial (Pty.) Ltd. for the use of the simulation software 
Flownex. 
I greatly appreciate the assistance from the PBMR (Pty.) Ltd. team for all the resources 
they made available to me. 
Furthermore, I am deeply grateful to Chris Nieuwoudt for all his valuable remarks, 
suggestions and the long discussions. 
To all my colleagues at the McTronX Research Group who contributed in various 
degrees. 
The financial support of THRIP and MTech Industrial is gratefully acknowledged. 
Lastly, I would like to thank my family and all my friends for their constant support, 
encouragement and inspiration. 
Contents 
List of figures iv 
List of tables vii 
Notation and symbols ix 
Acronyms x
1. Introduction 1 
1.1 Motivation
1.2 Problem description 2 
1.3 Thesis objectives
1.4 The diagnostic methodology 3 
1.5 Thesis layout 4 
1.6 Original contributions 5 
1.7 Publications
2. Fault detection and isolation 7 
2.1 Introduction
2.2 The scope of health monitoring 8 
2.2.1 Fault classification
2.2.2 The health monitoring tasks
2.2.3 The health monitoring method 9 
2.3 Sensor fault detection and isolation 10 
2.3.1 Independent component analysis 1 
2.3.2 Instrumentation and calibration monitoring program 1
2.3.3 Nonlinear partial least squares 12 
2.3.4 Multivariate state estimation
2.3.5 Auto-associative neural networks 3 
2.3.6 Comparisons and limitations 1
2.3.7 Uncertainty analysis 5 
2.3.8 Conclusions 1
i 
2.4 Process fault detection and isolation 16 
2.4.1 Model-based methods 17 
2.4.2 Process history based methods 8 
2.4.3 Desirable qualities of the fault diagnosis approach 1
2.4.4 The proposed process fault diagnosis approach 9 
2.4.5 Conclusions 20 
2.5 Component and system degradation in HTGRs 2
2.6 Summary and conclusions 22 
3. The plant model and reference system faults 23 
3.1 Introduction 2
3.2 Theoretical analysis of the PBMR plant model 4 
3.3 Sensitivity analysis of the PBMR MPS 29 
3.3.1 The component and system performance parameters 2
3.3.2 Simplified simulation model of the Brayton cycle 30 
3.4 Fault classification in the PBMR MPS 33 
3.4.1 Fault class 1: Flow bypass
3.4.2 Fault class 2: Main flow resistance (resistive losses) 34 
3.4.3 Fault class 3: Effectiveness or efficiency 3
3.5 The PBMR simulation model 36 
3.6 Summary and conclusions 9 
4. Sensor fault detection and isolation 40 
4.1 Introduction 4
4.2 Sensor malfunctions 1 
4.3 Sensor validation
4.3.1 Measurement redundancy 42 
4.3.2 Non-temporal parity space analysis 4
4.3.3 Statistical shape analysis 4 
4.3.4 Maximum process change 6 
4.3.5 Principle component analysis 47 
4.4 Sensor fusion 53 
4.5 Sensor validation and fusion module architecture 55 
4.6 Application of sensor FDI in the PBMM and PBMR 60 
4.6.1 Case study 1 6
4.6.2 Case study 2 4 
4.7 Summary and conclusions 7 
5. Application of traditional fault detection techniques 70 
5.1 Introduction 7
5.2 Model-free methods - Limit value checking 7
5.3 Model-based methods - Mathematical models 3 
5.3.1 Model development and assumptions
5.3.2 The linear turbine model 74 
5.4 Summary and conclusions 8
n 
6. Implementation of the h-s graph approach for FDI 84 
6.1 Introduction 8
6.2 Enthalpy and entropy - An overview 85 
6.3 Attributes and construction of the h-s graph 87 
6.4 Effect of faults on the h-s graph 9 
6.5 Creating reference fault signatures with the h-s graph 95 
6.5.1 The error method 9
6.5.2 The area error method 6 
6.6 Fault detection and isolation with the h-s graph approach 99 
6.6.1 Noise properties 101 
6.6.2 Fault detection
6.6.3 Fault isolation 2 
6.6.4 Single fault extraction method 104 
6.6.5 The h-s graph and reference fault signatures at different power levels 105 
6.7 Process variations and the reference h-s graph 108 
6.8 Application of the h-s graph approach in the PBMR MPS 113 
6.8.1 Fault conditions during steady state operation of the plant 11
6.8.2 Fault conditions during load following of the plant 116 
6.9 Summary and conclusions 120 
7. Validation of the h-s graph approach for FDI 122 
7.1 Introduction 12
7.2 Differences between the PBMR models and the PBMM 123 
7.3 Modelling the PBMM plant in Flownex 126 
7.4 The PBMM data used for fault emulation 8 
7.5 Simulation of the emulated faults in Flownex 132 
7.6 Fault detection in the PBMM 135 
7.7 The T-P and h-s models applied to the PBMM 137 
7.8 Summary and conclusions 8 
8. Conclusions and recommendations 140 
8.1 Introduction 14
8.2 Conclusions 1 
8.2.1 Component degradation and suitable fault classes 14
8.2.2 Sensor fault diagnosis 14
8.2.3 Process fault diagnosis 2 
8.2.4 Validation of the process fault diagnosis approach 144 
8.3 Original contributions 145 
8.4 Recommendations for future research 14
Bibliography 147 
Appendices 153 
A. Normal distribution and the central limit theorem 15
B. The temperature-pressure versus enthalpy-entropy graphs 154 
B.l The h-s graph shape at different power levels 155 
B.2 The T-P and h-s models applied to the PBMR 6 
in 
List of figures 
Fig. 2.2.1 The health monitoring system 10 
Fig. 2.3.1 A simple sensor monitoring system
Fig. 2.3.2 The structure of a NLPLS 2 
Fig. 2.3.3 The structure of an AANN 4 
Fig. 3.2.1 PBMR MPS layout 2
Fig. 3.2.2 Solid model of the PBMR MPS 25 
Fig. 3.2.3 Modes and states for normal operation of the PBMR 28 
Fig. 3.3.1 A network diagram of a simplified Brayton cycle-based MPS 31 
Fig. 3.5.1 A network diagram of the PBMR Flownex model 37 
Fig. 4.2.1 Sensor malfunctions 4
Fig. 4.3.1 Probability density function for the normal distribution 45 
Fig. 4.3.2 Varying the maximum process change 46 
Fig. 4.3.3 Measured and PCA reconstructed values for T and P sensors 50 
Fig. 4.3.4 The data segments used for training and testing the PCA models 51 
Fig. 4.3.5 The SPE index for the pressure PCA model 5
Fig. 4.3.6 The SPE indices for fault detection together with the reconstructed sensors... 52 
Fig. 4.4.1 Fusion algorithm applied to random measurements 55 
Fig. 4.5.1 A flow chart illustrating the SENSE architecture 6 
Fig. 4.5.2 A reasoning map illustrating the SENSE architecture 57 
Fig. 4.5.3 Sensor configurations based on the amount of faulty sensors 58 
Fig. 4.5.4 Decision-tree illustrating the expert system reasoning 59 
Fig. 4.6.1 Sensor notation utilized in the two case studies 60 
Fig. 4.6.2 The SPE index for the temperature PCA model 1 
Fig. 4.6.3 The SPE index for the healthy sensor configurations 62 
Fig. 4.6.4 The sensor residuals for the eight measurement channels 63 
Fig. 4.6.5 Fused estimates for the PBMM temperature measurements 4 
Fig. 4.6.6 The PBMR sensor data 65 
Fig. 4.6.7 The SPE index for the healthy sensor configuration 6
Fig. 4.6.8 The sensor residuals for the eight measurement channels 66 
Fig. 4.6.9 Fused estimates for the PBMR pressure measurements 68 
IV 
Fig. 5.2.1 Plant measurements at different nodes during normal fault free conditions.... 72 
Fig. 5.3.1 Turbine efficiency and pressure ratio to non dimensional mass flow 75 
Fig. 5.3.2 The input-output measurements of the turbine model 7
Fig. 5.3.3 Inlet pressure transient for the turbine 80 
Fig. 5.3.4 Flownex and the linear turbine model response for an inlet pressure transient 81 
Fig. 5.3.5 Diagram illustrating the interaction between the individual turbine models.... 82 
Fig. 6.2.1 Conversion of enthalpy for a steady flow turbine 86 
Fig. 6.3.1 The h-s graphs of a closed Brayton cycle 88 
Fig. 6.3.2 Theoretical h-s graph of the Brayton cycle for full as well as reduced power. 88 
Fig. 6.3.3 The h-s graph for the PBMR, shown at full and reduced power 89 
Fig. 6.4.1 The h-s graphs for normal power operation 91 
Fig. 6.4.2 The h-s graphs for normal power operation 2 
Fig. 6.4.3 The h-s graphs for normal power operation 3 
Fig. 6.4.4 The h-s graphs for normal power operation 94 
Fig. 6.5.1 Fault signatures for fault 23 for different fault magnitudes 96 
Fig. 6.5.2 The normalized error signatures for the PBMR for normal power operation.. 97 
Fig. 6.5.3 Defining the areas between the reference and fault h-s graphs 98 
Fig. 6.5.4 Deriving h and s fault signatures with the area error method 9 
Fig. 6.5.5 The normalized area error signatures for the PBMR 100 
Fig. 6.6.1 Flow diagram of the single fault extraction method 4 
Fig. 6.6.2 The extracted h and s error signatures for the two single faults 106 
Fig. 6.6.3 The normalized signatures for a 1 % and 10 % change at 40/100 % MCR... 107 
Fig. 6.6.4 The reference h-s graph 108 
Fig. 6.7.1 The h-s graph for GBPC valve operation at different power levels 109 
Fig. 6.7.2 Variation surface for valve operation 110 
Fig. 6.7.3 The normalized signatures at 100 % MCR for GBPC valve operation 112 
Fig. 6.8.1 The isolated faults during steady state operation of the PBMR 114 
Fig. 6.8.2 Load following transient during normal power operation of the PBMR 117 
Fig. 6.8.3 Single fault detection during load following 11
Fig. 6.8.4 The normalized signatures for fault 18 during load following 119 
Fig. 6.8.5 Multiple fault detection during load following 11
Fig. 7.2.1 Schematic showing the three-shaft MPS of the first PBMR configuration.... 123 
Fig. 7.2.2 Gas flow path through the three-shaft MPS 124 
Fig. 7.2.3 The theoretical h-s graph for the three-shaft PBMR model 12
Fig. 7.2.4 Simplified schematic showing the PBMM three-shaft MPS 125 
Fig. 7.2.5 Solid model of the PBMM 126 
Fig. 7.3.1 Schematic diagram showing the PBMM Flownex model 127 
Fig. 7.3.2 The practical h-s graphs for the PBMM steady state simulation at 95 kPa.... 128 
Fig. 7.4.1 Turbo machinery parameters for bearing failure 130 
Fig. 7.4.2 Turbo machinery parameters for thrust test 131 
Fig. 7.5.1 The h-s graphs for the steady state PBMM datasets 133 
Fig. 7.5.2 Normalized fault signatures for the 6 PBMM faults 4 
Fig. 7.6.1 Normal probability plots for measurements in the PBMM 135 
Fig. 7.6.2 FII for the emulated faults in the PBMM after fault detection 137 
v 
Fig. 7.7.1 Practical graphs of the Brayton cycle for full and reduced power 138 
Fig. B.l.l Theoretical and practical graphs of the Brayton cycle 154 
Fig. B.2.1 Normalized error signatures for fault 15 157 
vi 
List of tables 
Table 3.2.1 Typical parameters of the PBMR MPS for normal operation at full power.. 25 
Table 3.3.1 Simplified Flownex model reference values 31 
Table 3.3.2 Summary of sensitivity analysis results 2 
Table 3.4.1 Summary of faults in the PBMR MPS 5 
Table 3.5.1 Summary of the Flownex model results for normal power operation 38 
Table 4.4.1 MSE results obtained for the sensor fusion algorithm 55 
Table 4.6.1 Summary of PBMM temperature sensor faults: Case study 1 61 
Table 4.6.2 MSE results obtained for sensor fusion with no faults present 62 
Table 4.6.3 MSE results obtained for sensor fusion with the eight faults present 62 
Table 4.6.4 Summary of PBMR pressure sensor faults: Case study 2 65 
Table 4.6.5 MSE results obtained for sensor fusion with no faults present 67 
Table 4.6.6 MSE results obtained for sensor fusion with the eight faults present 67 
Table 5.2.1 Fault alarms for the 25 single faults in the PBMR 72 
Table 5.3.1 Summary of turbine model variables 76 
Table 5.3.2 Summary of turbine model coefficients 9 
Table 6.2.1 Relationships for h and s in open systems 86 
Table 6.4.1 Flownex results for fault 23 90 
Table 6.6.1 Classification results with the FII for multiple faults 105 
Table 6.7.1 Results for the h and s calculations Ill 
Table 6.8.1 Summary of isolated faults during steady state 114 
Table 6.8.2 Average (A) and maximum (M) isolation percentage for 3000 samples .... 115 
Table 6.8.3 The isolation (I) and rejection (R) averages of the FII for multiple faults.. 116 
Table 6.8.4 Summary of isolated faults (fl|f2) during load following 118 
Table 7.3.1 PBMM steady state conditions 126 
Table 7.3.2 Steady state values for the two operating points 127 
Table 7.3.3 Results for the two operating points 129 
Table 7.5.1 Parameters for the two steady state simulations 132 
Table 7.5.2 Steady state results for the two PBMM datasets 3 
Table 7.5.3 PBMM emulated fault conditions modelled in Flownex 13
vii 
Table 7.5.4 Flownex results for the six emulated fault conditions 134 
Table 7.6.1 Statistical properties of the PBMM measurement noise 136 
Table 7.6.2 Alarms during fault detection for the PBMM datasets 13
Table 7.6.3 Average FII for the PBMM fault conditions after fault detection 137 
Table 7.7.1 Results for the reference models (PBMM operating at 40 % MCR) 139 
Table B.2.1 Temperature and pressure results for the Flownex and reference models.. 156 
Table B.2.2 Enthalpy and entropy results for the Flownex and reference models 157 
viii 
Notation and symbols 
General notation 
PBMR PBMR (Pty) Ltd. 
Flownex Flownex® 
Simulink Simulink® 
Matlab Matlab® 
List of symbols 
I Unit matrix 
v(t) Noise vector 
O(T) Correlation matrix 
E expectation ofx(t) 
t discrete time 
T discrete time shift 
QPT work deliverd by turbine 
QHPC work absorbed by HPC 
QLPC work absorbed by LPC 
QRU heat supplied by reactor 
T]cyck cycle efficiency 
rjsy switchyard efficiency 
r]m mechanical efficiency 
rjgen generator efficiency 
Phouse house load power 
Pgnd grid power 
mRu reactor mass flow 
cp constant pressure specific heat 
R gas constant 
h enthalpy 
ix 
s entropy 
T temperature 
P pressure 
M normal distribution mean 
a standard deviation 
J normal distribution variance 
y normal distribution skew 
Ax maximum process change 
T normal distribution confidence value 
Xf fused estimate 
Sc sensor configuration matrix 
S fault signature 
Pref reference parameter value 
P measured parameter value 
Snorm normalized fault signature 
r Euclidean distance 
r error vector 
TN noise vector 
Sarea Area error signature 
¥ covariance matrix 
AtCC 
hypothesis threshold 
A^o pipeline pressure drop 
£ heat exchanger effectiveness 
n turbo machinery efficiency 
AU product of the heat transfer area and the overall heat transfer coefficient 
PR turbo machinery pressure ratio 
P parity vector 
V projection matrix 
X measurement matrix 
E residual space matrix 
P principles components vector 
c2 
°SPE SPE threshold 
h fault direction vector 
X 
Acronyms 
AANN Auto-associative neural network 
CBCS Core barrel conditioning system 
CC Correlation coefficient 
CFD Computational fluid dynamics 
CWT Cooling water temperature 
EPRI Electric power research institute 
FDI Fault detection and isolation 
FII Fault isolation index 
GBPC Gas cycle bypass control valve 
HP High pressure 
HPC High pressure compressor 
HTGR High-temperature gas-cooled reactor 
HV High voltage 
ICA Independent component analysis 
ICMP Instrument and calibration monitoring program 
ICS Inventory control system 
LP Low pressure 
LPC Low pressure compressor 
MCR Maximum continuous rating 
MCRI Maximum continuous rating inventory 
MPS Main power system 
MSET Multivariate state estimation 
NLPLS Nonlinear partial least squares 
NN Neural network 
NPP Nuclear power plant 
NRC National regulatory commission 
OLM On-line monitoring 
PBMM Pebble bed micro model 
PBMR Pebble bed modular reactor 
PCA Principle component analysis 
PCU Power conversion unit 
PLS Partial least squares 
PPB Primary pressure boundary 
XI 
PR Pressure ratio 
PT Power turbine 
RBP Recuperator bypass valve 
RMSE Root mean squared error 
ROT Reactor outlet temperature 
RSQ r-square statistic 
RU Reactor unit 
RUCS Reactor unit conditioning system 
SENSE Sensor validation and fusion module 
SPE Square prediction error 
VM Variance and mean index 
VRE Variance of the reconstruction error 
VS Variation surface 
Xll 
CHAPTER 1 
Introduction 
This chapter lists the primary objectives of the study together with an overview of the 
chapters presented. 
1.1 Motivation 
Advanced system diagnostics have been extensively researched the past few years to 
support nuclear power plant (NPP) utilities in plant supervision. The most important tasks 
of these diagnostic systems are fault detection and isolation. Even though research shows 
that these diagnostic systems are essential to prolong the lifespan of the plant, only a few 
real systems are actually installed in operating units [1], [2]. For the next generation type 
NPPs, it is expected that these diagnostic systems will become a necessity. 
From a theoretical point of view, fault diagnosis of nonlinear systems is particularly 
difficult [2]. In addition, obtaining a sufficient accurate analytical model for complex 
processes like NPPs could take years. Traditionally, limit value checking techniques have 
been proven to perform well if the plant operates close to steady state. However, 
implementing a diagnostic system that performs well only during steady state conditions 
is not a desirable trait. Another traditional approach to fault diagnosis is signal 
processing. The difficulties with these techniques are distinguishing between changes in 
the signal properties due to faults or transient variations of the process. 
More recent approaches to fault diagnosis can be attributed to the advances in 
computational intelligence [3]. The methods are however data-driven and dependent on 
the quality and amount of data used for model development. Acquiring such data for the 
entire operating range in the next generation NPPs will be very difficult due to 
economical impacts on normal operation. 
All these factors motivate the development of a new approach to NPP supervision. 
The goal is to realize a total health monitoring system that is simplistic, reliable and most 
important, accurate for different variations of the supervised process. 
1 
Introduction 
1.2 Problem description 
Given the preceding motivation, the goal of the study is to develop an advanced fault 
diagnosis approach for NPP supervision. The approach should facilitate a novel sensor 
and process fault diagnosis technique that functions independently. To address these 
problems, the following solutions are proposed: 
• The goal of advanced sensor fault diagnosis is realized by integrating existing 
techniques in a new way to reduce their individual shortcomings. Measurement 
redundancy is exploited to allow early detection of instrument drift. 
• A novel approach to process fault diagnosis is accomplished by developing a new 
method based on a graphical representation of the supervised process. This technique 
aims to minimize the amount of monitored variables necessary to quantify the overall 
health of the system without any knowledge of the mathematical structure of the 
nonlinear dynamic process. 
1.3 Thesis objectives 
The goal of the thesis is to develop a novel approach to fault diagnosis in a nonlinear 
high-temperature gas-cooled reactor (HTGR) NPP. To address the shortcomings of 
current fault diagnosis techniques, the main objectives of the study are: 
1. Determine the most relevant mechanisms for component degradation in an HTGR 
main power system (MPS) and formulate suitable fault classes. 
2. Develop and implement a comprehensive fault diagnosis approach for health 
monitoring in an HTGR MPS. The approach must comprise independent sensor and 
process fault diagnosis methods. Specifically, the following areas are addressed: 
2.1 Propose and implement a novel integrated architecture for sensor fault diagnosis 
to take advantage of the strengths of existing techniques. For this goal, the 
independent detection of instrument drift is emphasized. 
2.2 Propose and implement a novel approach for process fault diagnosis. The goal is 
to develop a method that adheres to the strengths of existing techniques without 
incorporating their general deficiencies. The following desirable qualities must 
be realized: 
2.2.1 Robustness with regard to fault propagation, noise and modelling errors. 
2.2.2 Model development and re-training should be simplistic. 
2.2.3 Early detection of small faults with incipient time behaviour. 
2 
Introduction 
2.2.4 Supervision of the process during transient variations of the normal 
process. 
2.2.5 Isolation of single faults for multiple fault symptoms. 
3. Validate the proposed process fault diagnosis approach through application in the 
Pebble Bed Micro Model (PBMM). Since there are many ambiguities inherent from 
directly inducing faults in the real system with regard to control and safety concerns, 
faults are only simulated. 
The following constraints are imposed on the simulated HTGR NPP: 
1. Since the HTGR NPP is mostly operated at full power, only normal power operation 
of the plant is investigated. This includes steady state operation and transient 
variations of the normal process. 
2. The number of system faults is limited. Also, critical system faults that cause mode 
and state transitions of the plant are not applicable (discussed in Chapter 3). These 
faults are accommodated in the automated plant protection systems. From this 
constraint, it is concluded that the faults will typically be characterized with incipient 
time behaviour caused by plant degradation. 
1.4 The diagnostic methodology 
The engineering aspects of the study commence in Chapter 3. Firstly, a simplified model 
of an HTGR is developed in Flownex® comprising the key MPS components. Through a 
sensitivity analysis of the model, the most relevant system faults are identified (caused by 
the component degradation mechanisms). The fault parameters are grouped with regard 
to cause and effect and the final listing of probable single system faults is summarized. 
The choices for the fault symptoms are motivated and their importance was confirmed 
with engineers at PBMR (Pty.) Ltd. Following this, an optimized design of the PBMR 
that includes the inventory control system (ICS) is modelled in Flownex which serves as 
the reference NPP. 
The sensor and process fault diagnosis system is developed using Matlab®, 
Simulink® and Flownex. By means of a Flownex and Simulink interface, data is 
collectively transferred between the Flownex and Simulink models. Firstly, random noise 
with different variance is added to the Flownex measurements, which is then passed 
through a filter model that infers the appropriate sensor malfunctions on the signals. Next, 
the signals are evaluated by SENSE (Simulink m-file) and the fused estimates are passed 
to the process fault diagnosis module (Simulink m-file). After signal transformation, the 
model residuals are checked for consistency. If a discrepancy is detected, fault signatures 
are extracted from the residuals and matched to the reference fault database with a 
statistical classifier. Finally, the relevant information regarding process status and sensor 
health is collectively displayed. 
3 
Introduction 
1.5 Thesis layout 
An overview of health monitoring techniques is presented in Chapter 2 together with 
some basic terminology. For the purpose of advanced sensor fault diagnosis and 
parameter estimation, two redundant and three non-redundant techniques are investigated. 
To incorporate techniques that will be readily acceptable to regulatory bodies, the 
Nuclear Regulatory Commission regulations pertaining to on-line monitoring techniques 
are examined. For the second part of the chapter, process monitoring methods are 
discussed with their advantages and shortcomings. Lastly, the overall structure of the 
proposed process fault diagnosis approach is presented. 
Chapter 3 describes the general topology of the PBMR MPS and stipulates the 
relevant operating conditions. Through a sensitivity analysis of a simplified PBMR 
model, the type and origin of the component performance parameters are identified that 
are synonymous to the probable fault parameters caused by the component degradation 
mechanisms. 
Chapter 4 describes the development of a comprehensive sensor fault diagnosis 
methodology. The relevant monitoring techniques identified in Chapter 2 are integrated 
to reduce their individual shortcomings and improve measurement integrity. The fault 
detection and isolation capabilities of the proposed methodology are demonstrated 
through application to PBMR and PBMM data. With regard to the latter, real plant data 
obtained from the PBMM prototype plant is used for the validation. 
Chapter 5 applies two traditional process fault diagnosis techniques to the PBMR. 
These methods are based on limit value checking of the monitored variables and 
mathematical modelling of the plant for the purpose of residual generation. The 
implementation of the methods in the PBMR highlights their general limitations. 
Chapter 6 derives the h-s graph approach for process fault diagnosis. Firstly, two 
analytical techniques are utilized to generate reference fault signatures (with Flownex) for 
the related fault symptoms; whereafter the correlation among the fault signatures is 
established. It is demonstrated that each of the different reference fault signatures are 
highly correlated during transient variations of the normal process with negligible 
variation. Following this, the fault detection and isolation tasks are developed by means 
of a statistical hypothesis test and classifier that decide whether a given set of process 
observations contains any faults. In the presence of multiple fault symptoms, a single 
fault subtraction procedure is formulated to extract and classify the contributing single 
faults. To incorporate normal process variations like valve changes into the reference 
system model, the variation surface is proposed. In the final part of the chapter, the 
proposed methodology is applied to the PBMR. Fault detection and isolation is 
demonstrated for both steady state and transient conditions. 
Chapter 7 validates the h-s graph approach for process fault diagnosis through 
application in the prototype PBMM plant. Firstly, plant measurements captured during 
test runs are used to validate the integrity of the FLOWNEX simulation model. Following 
this, a reference system model together with fault signatures is derived for two emulated 
fault conditions. Lastly, the h-s graph approach is utilized for process fault diagnosis to 
identify the emulated fault symptoms in the plant data. 
4 
Introduction 
Chapter 8 summarizes the most important conclusions reached in the thesis and 
documents the original scientific contributions of the study. Recommendations and 
suggestions for future research are also presented. 
Appendix A lists the central limit theorem. In the thesis, assumptions regarding the 
measurement noise are based on the theorem. 
In Appendix B, the prove for the constant shape of the h-s graph at different power 
levels (bounded by constraints) is derived. This idea forms the basis for the proposed 
methodology. Following this, the improvement in model prediction is demonstrated 
through transformation of the measured variables. 
1.6 Original contributions 
The main scientific contributions of the thesis are summarized as follows: 
• A novel approach is proposed for process fault diagnosis in an HTGR NPP. Plant 
supervision is realized with a graphical model-based process model (h-s graph) that 
remains invariant over the power range. The proposed error and area error methods 
provide static reference h-s fault signatures that remain invariant to operating point 
changes, transient variations of the normal process and changes in the fault 
magnitude. There was no reference found to such an approach for process fault 
diagnosis in an HTGR NPP. 
• In addition, a new integrated architecture is proposed for sensor fault diagnosis that 
forms a comprehensive methodology of existing techniques. In a multi-sensor 
environment, the unique reasoning structure of this approach produces more accurate 
and reliable estimates of the sensed variables. A literature survey revealed that this 
unique and integrated reasoning structure has not been developed for application in 
an HTGR NPP. 
1.7 Publications 
"Enthalpy-entropy graph approach for the classification of faults in the main power 
system of a closed Brayton cycle HTGR", Annals of Nuclear Energy, Article in press. 
Article abstract: 
An enthalpy-entropy (h-s) graph approach for the classification of faults in a new 
generation type high temperature gas-cooled reactor (HTGR) is presented. The study is 
performed on a 165 MW model of the main power system (MPS) of the pebble bed 
modular reactor (PBMR) that is based on a single closed-loop Brayton thermodynamic 
cycle. In general, the h-s graph is a useful tool in order to understand and characterise a 
thermodynamic process. It follows that it could be used to classify system malfunctions 
from fault patterns (signatures) based on a comparison between actual plant graphs and 
reference graphs. It is demonstrated that by applying the h-s graph approach, different 
5 
Introduction 
fault signatures are derived for the examined fault conditions. The fault conditions that 
are considered for the MPS are categorized in three fault classes and comprise the main 
flow bypass of the working fluid, an increase in main flow resistance, and a decrease in 
component effectiveness or efficiency. The proposed approach is specifically illustrated 
for four single and two multiple fault conditions during normal power operation of the 
plant. The simulation of the faults suggests that it is possible to classify all of the 
examined system malfunctions correctly with the h-s graph approach, using only single 
reference fault signatures. 
6 
CHAPTER 2 
Fault detection and isolation 
This chapter gives a comprehensive review of advanced health monitoring techniques 
used in NPPs. In addition, the mechanisms for component degradation in HTGRs are 
discussed. 
2.1 Introduction 
Health monitoring is an important component in any large scale engineering plant to 
improve safety, reliability and overall plant performance. With this in mind, the next 
generation HTGR NPPs offer more complex challenges for advanced system diagnostics. 
This chapter gives a summary of the different health monitoring techniques that are 
currently either implemented or proposed for implementation in NPPs. 
In section 2.2, the fundamental concepts and basic terminology of health monitoring 
are introduced together with the total health monitoring framework. The framework 
includes several different tasks and comprises fault detection, fault isolation and fault 
identification. 
Section 2.3 presents an overview of different techniques that are applicable to NPP 
sensor fault diagnosis and process state estimation. Furthermore, the motivations for the 
techniques used in the thesis are also discussed. 
Section 2.4 summarizes some of the most relevant process fault diagnosis 
techniques. These techniques are mainly model-and process history based methods, each 
with their own unique strengths and weaknesses. In the final part of this section, the 
desirable qualities of an advanced fault diagnostic approach are presented, together with 
the general framework of the proposed approach. 
In order to determine the specific fault classes in the PBMR, section 2.5 presents an 
outline of the most relevant mechanisms for component degradation in HTGRs. These 
mechanisms include component corrosion, erosion, fouling and leakage. 
A summary of this chapter is presented in section 2.6. 
7 
Fault detection and isolation 
2.2 The scope of health monitoring 
In modern NPPs, information about the current health of the system is essential to 
improve plant safety and operational levels [4]. Therefore, it is important to detect 
component faults and irregular system operation promptly. 
2.2.1 Fault classification 
In general, unpermitted deviations from the normal behavior of the components or 
process are termed faults or failures. Faults are caused by physical defects or 
imperfections that occur within the component, whilst a failure suggest complete 
breakdown of the component [5]. The faults that are applicable for this investigation can 
be divided into the following categories [6]: 
• Additive process faults: These faults are caused by unknown inputs acting on the 
plant, which results in a shift in the plant outputs, independent of the measured 
inputs. A plant leak is a typical example of an additive fault. 
• Multiplicative process faults: These faults result in system parameter changes, where 
the outputs are dependent on the magnitude of the inputs. Such faults are mostly 
associated with component degradation and include fouling and efficiency changes. 
• Sensor faults: Any discrepancies between the measured and the expected values of 
the process variables are considered to be sensor malfunctions. 
• Actuator faults: These faults are described by discrepancies between the intended 
control actions and the actual realization of these commands by the actuators. 
2.2.2 The health monitoring tasks 
In order to identify and characterize the faults, the health monitoring system should 
comprise the following tasks [6]: 
• Fault detection: The identification of an irregularity in the monitored system. 
• Fault isolation!classification: The origin and the type of fault are determined. 
• Fault identification: The magnitude of the fault is established. 
The fault identification phase generally does not justify the additional computation it 
requires, and for this reason, most monitoring systems only comprise the fault detection 
and isolation (FDI) phases [6]. For the proposed diagnostic system, real-time 
computational complexity is reduced by implementing only the fault detection and 
8 
Fault detection and isolation 
isolation tasks. The drawback from this restriction is that the fault magnitude will not be 
directly calculated, but rather estimated from the fault signature magnitude before 
normalization. 
With the help of early fault detection and accurate fault isolation, process and 
component malfunctions can therefore be identified at an early stage to reduce the risk of 
sudden failure as well as allow enough time for maintenance or repair. Given the complex 
and safety critical nature of NPPs, the advanced FDI tasks should adhere to the following 
requirements [7]: 
• Reduce the occurrence of false alarms during operation due to normal transient 
variations of the process. 
• Original fault detection in the event of multiple fault conditions and propagation 
across subsystems. 
• Early detection of small faults with abrupt or incipient time behavior. 
• Reducing misdiagnosed faults due to modelling uncertainties and noise. 
2.2.3 The health monitoring method 
Designing a system for advanced fault diagnosis is a challenging engineering task, 
particularly in fields related to nuclear processes, owing to the stringent safety and 
environmental regulations. For these reasons, it is important that the diagnostic method 
meet the following performance requirements [6]: 
• Fault detection: 
- Fault sensitivity: The method must detect incipient faults with a small magnitude. 
- Detection time: The method must be able to detect faults with the smallest time 
delay after induction. 
- Robustness: The method must be able to function in the presence of noise, 
modelling uncertainties and disturbances, with minimal false alarms. 
• Fault isolation: The method must be able to distinguish between the different types 
of faults (single or multiple simultaneous faults) in the presence of noise and 
modelling errors. It is important to note that some faults, single or multiple, might be 
non-isolable, since their influence on the system is undistinguishable [6]. 
The health monitoring system, which constitutes sensor and process FDI, is illustrated 
in Fig. 2.2.1. 
9 
Fault detection and isolation 
System information: 
Control information: 
Plant 
System inputs 
raw 
data 
3.L.. 
Sensor FDI 
Validation 
and flision 
II 
3i 
Process FDI 
features Advanced 
diagnosis 
Monitoring and diagnosis 
Alarms 
Fault location 
Fault cause 
Corrective actions 
System outputs 
Fig. 2.2.1 The health monitoring system. 
2.3 Sensor fault detection and isolation 
This section reviews current sensor fault diagnosis techniques ranging from basic, well 
established methods to the latest reported advanced strategies. Throughout the literature, 
various methods are proposed by the industry and academia [8] - [15]. Advanced in this 
context signifies methods that will allow nuclear power utilities to diverge from utilizing 
a periodic based maintenance approach to condition based strategies. In general, these 
advanced methods aim at describing the sensors health whilst the plant is operational. A 
simple block diagram illustrating a sensor monitoring system is depicted in Fig. 2.3.1. 
Based on research applications, the most relevant techniques used in NPPs include 
the parity space method, principle component analysis (PCA), independent component 
analysis (ICA), instrumentation and calibration monitoring program (ICMP), nonlinear 
partial least squares (NLPLS), multivariate state estimation (MSET) and auto-associative 
neural networks (AANN) [16]. These techniques can roughly be classified into two 
categories: techniques that model a redundant group of sensors to obtain the estimate 
(first four) and models that include non-redundant measurements that are correlated, but 
not redundant (last three). 
A study conducted by [16] concluded that the simplicity of redundant techniques and 
the tractability of their uncertainty calculations could favour them for acceptance by 
regulatory bodies. For this reason, the non-temporal parity space and PCA techniques are 
adopted for sensor fault diagnosis based on their relative simplicity and individual strong 
points (discussed in Chapter 4). 
? ? 
Model Comparison Decision 
h t 
Xl 
—? : 
Xn 
Sensed inputs Model estimates Residuals Status 
Fig. 2.3.1 A simple sensor monitoring system [16]. 
10 
Fault detection and isolation 
The following sections discuss and compare the applicability of the remaining techniques 
for sensor fault diagnosis and highlight their general limitations. 
In this thesis, it is important to note that only a general overview of each technique is 
presented together with the basic notation. For the complete mathematical formulations, 
the reader is referred to the literature referenced. 
2.3.1 Independent component analysis 
In ICA, the sensed variables are described by means of a linear transformation of 
independent components that is maximally non-Gaussian (normally) distributed [16]. An 
important characteristic of this technique is its ability to separate the true signal (includes 
process noise) from the independent measurement noise [17]. This makes ICA a notable 
candidate for signal pre-processing and filtering. The ICA model is given by (2.3.1) 
X = AS (2.3.1) 
with X the observed data of n samples from m sensors, S is the matrix of m independent 
components and A the mixing matrix. The linear transformation of the observed data into 
non-Gaussian distributed components Y is 
Y = WX (2.3.2) 
where W is the weight matrix. The parameter estimate, which denotes the true signal with 
process noise, is then given by one of the independent components. 
2.3.2 Instrumentation and calibration monitoring program 
The ICMP was developed by the Electric Power Research Institute (EPRI). The ICMP 
algorithm is based on a weighted average of each sensor, which is denoted by consistency 
values c, [16]. The consistency values signify how much a sensor reading contributes to 
the final estimate. If the value correlates within the defined limits to another, they are 
consistent. The consistency value c, of the z'-th sensor is calculated with 
\x, -Xj\<^ + dt, then c, = c, +1 (2.3.3) 
with x» Xj the values of the z-th and j-th sensors and d,-, d j the consistency check 
allowance for sensor z and j respectively. The values are checked for consistency in an 
iterative way against the remaining sensors. The ICMP parameter estimated is calculated 
with 
n 
x = ^-n (2.3.4) 
11 
Fault detection and isolation 
where Wi is the weight related to the z'-th sensor. The influence of more reliable sensors 
within a redundant group can therefore be increased by varying their weights. If there is 
no preference between the sensors, the weights are set to 1. Following this, the 
performance of each sensor is determined in relation to x through an acceptance criterion 
|*-*,|<a, (2.3.5) 
where at is the acceptance criterion of the z'-th sensor. If the condition stipulated by (2.3.5) 
is not met, JC, has potentially drifted beyond the acceptable limits and its value is not 
considered. 
2.3.3 Nonlinear partial least squares 
The NLPLS technique is an extended nonlinear version of the partial least squares 
method (PLS) [18], [19]. For a theoretical overview of the PLS algorithm, the reader is 
referred to [20]. In NLPLS, the linear regression between pairs of score vectors is 
substituted by a single input single output neural network (NN). Each NN constitute a 
single hidden layer with a single output neuron. The number of NNs required is 
equivalent to the number of orthogonal input score vectors retained in the model. 
Moreover, the amount of NNs is considerably smaller than the number of input sensors. 
The NLPLS structure, together with the inner workings of one of the NNs, is illustrated in 
Fig. 2.3.2. The notation and complete structure is documented in [18]. 
2.3.4 Multivariate state estimation 
MSET is a non-parametric kernel regression technique, which utilizes a similarity 
operator to compare new observations with stored measurements [16]. Unlike neural 
networks, the optimal weights are not determined a priori. Through comparison, a weight 
vector is determined to compute a weighted sum of the stored measurements. This is done 
to generate an estimate for the sensor value. 
*& ...•?? tanh(a°+!<„,,, 6°) 
Inputs ^^^\ y 
Fig. 2.3.2 The structure of aNLPLS [18]. 
12 
Fault detection and isolation 
The MSET technique is based on linear regression [21], with the estimated equal to the 
product of a reduced measurement matrix A (prototype matrix) and weight vector w 
x = Aw = A '(A'A)V) (2.3.6) 
where x is the observed state, the left factor of the matrix product is the recognition 
matrix and A is reduced to only include the variations in the measured data. In (2.3.6), the 
linear relations in A results in conditioning problems related with the inversion of the 
recognition matrix. 
In contrast to linear regression, MSET introduces nonlinear operators and 
consequently, the recognition matrix is better conditioned. The estimate x is given by 
x = Aw = A (AT©A)"1(AT®x) (2.3.7) 
with <8> and © representing nonlinear similarity operators termed kernel operators. A 
typical similarity operator is the Gaussian operator [22] 
(x-Xj)2 
k,(x,Xi) = -_e 2s2 (2-3-8) 
V27ts 
with s the smoothing parameter, x the data point that is being compared to x;, and x; the 
data point around which the kernel is placed. 
2.3.5 Auto-associative neural networks 
The AANN structure utilizes an input layer, three hidden layers and an output layer [23], 
[24] and is illustrated in Fig. 2.3.3. The hidden layers comprise a mapping layer, 
bottleneck layer and de-mapping layer. The number of neurons in the mapping and de-
mapping layers is always greater than the input/output layers, whilst the bottleneck layer 
has the least amount of neurons in the structure. 
Basically, the reduction of the data from input to output is similar to PCA. The 
mapping layer compresses the data in a more compact representation of the training data 
by eliminating any redundancies whilst extracting the dominating features (principle 
components). The data is then recovered via the de-mapping layer from the principle 
components. Therefore, if a measurement is corrupted, it can be substituted with an 
estimate from the remaining valid sensors. 
2.3.6 Comparisons and limitations 
This section documents some of the shortcomings and desirable qualities of the advanced 
OLM techniques discussed [16]. Firstly, although most of the techniques are very little 
13 
Fault detection and isolation 
Mapping De-mapping 
layer layer 
Fig. 2.3.3 The structure of an AANN. 
affected by spillover, non-redundant techniques perform better in this situation. Spillover 
is a measure of how a drifting sensor input affects the predictions of the remaining 
sensors. A technique that is resistant to spillover will not be influenced by a drifting 
sensor, i.e. the other sensor estimates will not be degraded. 
The ICA technique has the ability to separate the true signal from channel noise, 
which renders it as a filtering technique also. Nevertheless, some of the ambiguities of 
ICA are that neither the variances nor the order of the independent components can be 
determined. This can be problematic when performing OLM since the component 
containing the estimate needs to be selected and scaled back to its original units. 
Furthermore, ICA is based on the assumption that the measurement data is time invariant, 
which does not hold when the plant undertakes a significant transient. During the 
transient, the data becomes nonstationary and the ICA method fails. 
The ICMP technique delivers excellent results overall. Some of its shortcomings are 
that the failed sensor (acceptance criterion exceeded) value can still influence the ICMP 
estimate. The failed sensor is only excluded form the estimate once the consistency check 
factor is also exceeded. Also, ICMP is unable to detect common mode failure (all the 
redundant sensor values drift in the same direction at the same rate). 
It is well established in the industry that all of the non-redundant OLM techniques 
discussed perform well. Some of the notable differences are: 
• MSET is easier to implement and requires no training. The model is extended to 
include new operating conditions by simply adding the new data vector to the 
prototype matrix. 
• NLPLS techniques inherently produce more consistent estimates and are quicker to 
train with regard to AANN models. 
However, many aspects may limit the usefulness of these techniques. One limitation is 
that the model can only make confident predictions in the region of the training data. 
For inputs outside this space, there will be no confidence associated with the model's 
prediction. Also, the uncertainty inherent in the model predictions must be correctly 
calculated. This factor is of main concern with regard to applicability and is discussed in 
the following section. 
14 
Fault detection and isolation 
2.3.7 Uncertainty analysis 
Uncertainty analysis refers to the quantification of the prediction uncertainty associated 
with the model estimate when safety-critical parameters are being monitored. This is a 
prerequisite by regulatory bodies for approval of the OLM technique [25], [26]. The 
requirement stated in the Nuclear Regulatory Commission (NRC) safety evaluation reads 
as follows: 
7726 submittal for implementation of the on-line monitoring technique must confirm that 
the impact of the deficiencies inherent in the on-line monitoring technique (inaccuracy in 
process parameter estimate single-point monitoring and untraceability of accuracy to 
standards) on plant safety be insignificant, and that all uncertainties associated with the 
process parameter estimate have been quantitatively bounded and accounted for either in 
the on-line monitoring acceptance criteria or in the applicable set point and uncertainty 
calculations. 
The various methods of uncertainty analysis belong to either analytical or Monte Carlo 
based algorithms, each of which constitutes different assumptions. The analytical based 
methods comprise analyses for NLPLS, MSET and AANN, whilst Monte Carlo based 
analysis are conducted for ICMP and ICA [16]. A detailed technical description of each 
algorithm is given in [27]. 
Factors that contribute to prediction uncertainty are model structure including 
complexity and misspecification, accuracy and selection of training data, the selected 
predictor variables, and noise. Over complex models will tend to fit the noise in the 
training data, while models without flexibility will bias the predictions. Also, improper 
model specification will result in a biased estimate. Different training data sets will 
produce different models, which results in a distribution of estimates for a given 
observation. In addition, selecting unrelated predictor variables increase the solution 
variance. 
Therefore, to demonstrate to validity of the uncertainty for an OLM technique, the 
prediction uncertainty must be lower than the allowable drift for each parameter to ensure 
the sensor is operating in its normal range. To date, the techniques that have undergone a 
full uncertainty analysis are MSET, ICMP, ICA, PCA [16], [28], [29]. 
2.3.8 Conclusions 
The following conclusions are formulated from the literature reviewed: 
• While many of the complex non-redundant OLM techniques deliver accurate 
estimates together with acceptable uncertainty analyses, it is concluded that the 
uncertainty associated with redundant techniques and their relative simplicity makes 
them more readily acceptable by nuclear regulatory bodies [16]. 
15 
Fault detection and isolation 
• Neural networks are generally excluded from consideration as state predictors for 
OLM applications in NPPs [16]. However, they are well suited for fault pattern 
recognition in process fault diagnosis systems [1], [4], [31]-[34]. 
For these reasons, redundant techniques will be applied for sensor fault diagnosis. These 
techniques will be applied in an original integrated way to form a comprehensive sensor 
diagnostic system which aims to minimize their individual shortcomings. The redundant 
techniques considered are: 
• The non-temporal parity space (NTPS) algorithm: NTPS is utilized for consistency 
analysis of similar measurements [30]. The consistent measurements are fused 
together to reduce the size of the measurement matrix. 
• The PCA algorithm: PCA is employed for state prediction [8]-[10], [29]. Although 
ICA has some advantages over PCA (does not assume the principle components are 
orthogonal), it does not perform well during significant transients of the process. 
2.4 Process fault detection and isolation 
Objective two of the study listed the desirable qualities of advanced process fault 
diagnosis techniques in NPPs. With this in mind, current well established techniques are 
evaluated in this section to determine their strong points and shortcomings, i.e. techniques 
incorporating artificial intelligence [31]-[39] and traditional model-based techniques 
[40]-[44]. The proposed approach will aim to incorporate these strong points whilst 
minimizing their individual shortcomings. 
Process fault diagnosis techniques can be broadly classified as model-or process 
history based. Model-based techniques rely on a fundamental understanding of the 
process using mathematical relations or first principle knowledge [7]. These methods are 
further classified as either quantitative, which includes parity equations, state and 
parameter estimation, or qualitative methods, which include digraphs and fault trees [40]. 
When information about the complex process is not available, qualitative methods are 
used to build constrained models that describe how parameters are related to each other. 
Limitations of qualitative methods include generation of a large number of hypotheses 
which makes the decision process uncertain, computational intense and complex. 
Process history based methods on the other hand rely on an abundance of process 
data. These methods can also be classified as quantitative methods, which includes NNs 
and PLS, or qualitative methods which include expert systems and qualitative trend 
analysis. Although qualitative methods are good at representing heuristic knowledge 
(provided by experts, operators etc.), they are hard to verify, are not good at representing 
time-varying phenomena, and their accuracy is difficult to prove. 
In contrast, the majority of quantitative model-or history based techniques offer 
some strong points for application in NPPs. To incorporate these qualities in the proposed 
approach, their characteristics are summarized next. 
16 
Fault detection and isolation 
2.4.1 Model-based methods 
Process model-based fault detection methods [7], [40]-[44] use residuals which indicate 
any discrepancies between the model and the monitored process. A basic scheme of 
process model-based FDI is depicted in Fig. 2.4.1. One drawback of these FDI methods is 
that they rely on an explicit mathematical model of the monitored process. This model 
may be representative of a state space representation, steady state balance equations, first 
principles modelling, partial differential equations or a transfer function. Any 
inconsistencies in the residuals can then be used for fault diagnosis. To test the residuals 
for abnormal behaviour, a statistical test is usually implemented as a decision rule or 
hypothesis. 
In a practical application, all the model-based methods perform differently. Parity 
equations are typically limited to faults that do not include large process parameter drifts. 
Parameter estimation on the other hand is computationally intensive for complex 
nonlinear processes, therefore not favouring a real-time solution. Although the latter does 
not require a precise model a priori, this approach to FDI is one of complexity 
throughout. State estimators in contrast require a precise dynamic process model and can 
mostly only detect large abrupt faults. This is due to the fact that the state variables are 
not so often directly affected by multiplicative process faults (changes in fluid resistance, 
heat exchanger coefficients etc.). 
In conclusion, the desirable characteristics of model-based methods are that potential 
faults are directly reflected in the residuals, which functions as the fault detection task. 
One major disadvantage of these methods is their applicability to nonlinear applications. 
For a nonlinear process, a linear transformation is usually required which may be very 
difficult to obtain [40]. 
faults 
inputs actuators process 
process 
model 
feature 
generation 
outputs 
fault detection 
features 
change 
detection 
symptoms 
fault 
isolation 
faults 
Fig. 2.4.1 A basic process model-based fault FDI scheme [41]. 
17 
Fault detection and isolation 
2.4.2 Process history based methods 
In the case of a complex nonlinear process, where mathematical models are hard to 
develop, NNs emerged as a suitable solution in NPPs [1], [3]-[4], [31]-[34]. The 
processing elements of a NN are similar to those depicted in figures 2.3.2 and 2.3.3. The 
appropriate training of such a network forms input-output relations into a 'black box' 
model which is difficult to comprehend. This unknown internal reasoning structure of the 
network is inherent one of its drawbacks. 
For the task of fault isolation, the success of this approach is highly dependent on the 
amount and quality of the training data, i.e. examples from which it will infer a decision. 
In addition, the data must cover operating conditions that is representative of all the 
transient variations of the monitored process, including the faulty ones. Acquiring such 
data for a safety critical process is unrealistic and therefore, the NN may be used as a 
model-based predictor instead. 
In conclusion, one of the main drawbacks of NNs is the lack of knowledge about the 
internal reasoning process. Consequently, the accuracy of the results is uncertain for 
unknown process variations or new operating conditions. Additionally, NNs require large 
amounts of quality training data that covers the entire range of process operation. 
Nevertheless, they are especially suitable for nonlinear model development since an 
explicit mathematical model of the process is not required. 
2.4.3 Desirable qualities of the fault diagnosis approach 
The desirable qualities and general shortcomings of current process fault diagnosis 
techniques are listed in the previous section. In view of these characteristics, the 
following desirable qualities should be adopted for advanced process fault diagnosis in 
addition to section 2.2.3 [40]: 
• Adaptability: The process generally changes or evolves during the lifespan of the 
plant due to normal component ageing. The diagnostic approach should adapt to 
these changes. 
• Modelling requirements: 
- The modelling effort should be minimal. 
- Knowledge about the mathematical structure should not be a prerequisite. 
- The reasoning structure must be clearly understood. 
- A relative small dataset must quantify the entire range of operation. 
• Storage/computational requirements: The approach should be computationally 
noncomplex and require the least amount of storage space. 
18 
Fault detection and isolation 
2.4.4 The proposed process fault diagnosis approach 
In the thesis, a novel process fault diagnosis approach is proposed comprising the 
following characteristics: 
• The overall approach is model-based, realized by a graphical reference process 
model. This incorporates the 'no mathematical model' advantage of process history 
based methods into a model-based approach. 
• The model-based approach is utilized to monitor the model residuals for any 
discrepancies. 
• The proposed graphical process model is representative of a nonlinear dynamic 
process. 
• Unlike process history based methods, the graphical process model is trained with a 
minimal amount of steady state data. 
• Graphical fault signatures (patterns) are derived from the model residuals. 
• A statistical classifier is employed for fault pattern recognition. 
The proposed approach is shown schematically in Fig. 2.4.2. The objective of this 
approach is to decide if a given set of process measurements contains any faults and to 
isolate them. In order to achieve this goal, reference fault signature patterns are utilized 
which are derived by means of simulations of the process in Flownex. The residuals 
features are extracted and a reference fault signature database is generated. Once the 
database is developed, the proposed approach can be used to classify system faults. The 
FDI procedure is as follows: for a given time instant, the graphical process model shifts 
inputs actuators process 
operating point 
definition 
model-based 
fault detection 
process 
model n 
feature 
generation 
3 | fault detection 
signature 
generation 
data 
transformation 
? outputs 
reference 
faults 
fault 
isolation pattern recognition 
6 1 decision 
Fig. 2.4.2 The proposed novel process FDI scheme. 
19 
Fault detection and isolation 
to the operating point defined whereafter a residual is generated between the transformed 
measurements and the graphical reference model. In order to detect a fault, the residuals 
are evaluated with a statistical hypothesis test. If the thresholds are exceeded, a fault 
signature is generated and compared to the reference fault database using a statistical 
classifier (fault pattern recognition). 
2.4.5 Conclusions 
The following conclusions are formulated regarding the proposed process fault diagnosis 
approach: 
• The tasks of fault detection and isolation are achieved by applying a graphical 
model-based approach for the dynamic nonlinear process. 
• By applying a graphical model-based approach, the mathematical model of the plant 
is not required. 
• The process model is developed with minimal training data. 
2.5 Component and system degradation in HTGRs 
In HTGRs, the mechanisms of component degradation include corrosion, erosion, fouling 
and leakage. It must be noted that the objective of the thesis is to determine the most 
relevant fault symptoms in HTGRs (Chapter 3) and therefore, the chemical reactions that 
cause these symptoms are not discussed. 
During the past few decades, material behaviour in HTGRs has been mainly focused 
on steam-cycle and process-nuclear-heat based applications. In this time period, very 
little knowledge was developed with the emphasis on direct-cycle gas-turbine-based 
HTGRs [45]. 
Helium, because of its chemical inertness and attractive thermal properties, is used 
as primary coolant (working fluid) in gas-turbine-based HTGRs. Although helium by 
itself is inert to the materials it is exposed to, small amounts of gaseous impurities such as 
H2, H20, CH4, CO, C02 and 02 contaminate the coolant. Within the MPS, structural 
alloys of components and pipelines can be significantly corroded by these gaseous 
impurities at high temperatures [45]. Corrosion of heat resistant materials include 
oxidation, carburization and decarburization, which are dynamic in nature, i.e. the 
corrosion process is a function of exposure time, gas chemistry variations and the 
presence of particulates in the gas phase. Carburization and decarburization are 
determined by the amount of carbon activity in the gas relative to the exposed metal 
surface. In addition, the effects of these impurities on the mechanical properties of the 
structural alloys include fatigue, fracture and rupture. 
Material degradation in particle laded-gases (hard particles suspended in the gas 
stream) also needs consideration and is called erosion. Erosion is a complex phenomenon 
because of the dynamic changes that occur on the eroding surface [45]. The main cause 
20 
Fault detection and isolation 
of erosion in HTGRs is carbon dust particles originating from the fuel spheres in the 
nuclear reactor. One study conducted on an HTGR (reactor contained ± 100 000 fuel 
spheres) showed that some components were significantly degraded, with the cause 
unknown [45]. At the end of the reactor's lifespan, 60 kg of carbon dust was collected. 
Since the PBMR contains in the order of 450 000 fuel spheres, this form of degradation is 
important. Factors that influence erosion degradation include particle size, hardness and 
velocity. 
The next type of system degradation is fouling. Fouling is characterized by any 
deposit or extraneous material that appears on the surface of the structural alloys and 
results in an increase in thermal resistance, fluid flow resistance and pressure drop. 
Fouling is produced by different mechanisms and depends on several conditions and 
variables. The following mechanisms apply: 
• Particulate/Sedimentation: Many cooling streams contain deposits or particles that 
settle on the heat transfer surface of the heat exchangers. This type of fouling is 
strongly dependant on the velocity of the steams and less by the wall temperature. 
However, some particles can 'bake' on to the hot wall and can be very difficult to 
remove. 
• Chemical reaction: This type of fouling involves physical changes that are the result 
of a chemical reaction that produce a solid phase near the surface. For example, the 
hot temperatures may cause thermal degradation of the components that result in 
carbon deposits on the surface. 
• Corrosion fouling: This type of fouling is associated with the corrosion of the heat 
transfer surface by one of the streams which increase the thermal resistance and 
surface roughness. 
• Biological: Cooling streams (usually seawater) contain organisms that will attach to 
surfaces and grow. 
• Inverse solubility: Certain salts are less soluble in warm water than in cold. If the 
stream encounters a temperature above saturation for the dissolved salt, the salt will 
crystallize on the surface. 
The last degradation mechanism is leakage. A leakage is an undesired and unintended 
opening through which the coolant of the enclosed system passes. In HTGRs, leakage 
occurs between two streams and includes transfer of coolant between gas-gas, gas-fluid 
or fluid-fluid streams. Leakage occurs due to improper welding, sealing or joining of 
components, damage (fractures, rapture or cracks) and deterioration of materials from 
wear and fatigue such as corrosion, erosion and rusting. The pressure difference between 
the two streams and the size of the opening are important factors that influence the mass 
flow rate of the leakage. 
In conclusion, these four mechanisms are deemed to be the most relevant factors in 
HTGR component and system degradation. The fault symptoms associated with these 
mechanisms will typically be characterized by incipient time behaviour. 
21 
Fault detection and isolation 
2.6 Summary and conclusions 
This chapter summarized the various methods proposed or implemented for sensor and 
process fault diagnosis in NPPs together with the component degradation mechanisms in 
HTGRs. 
Section 2.2 lists the concepts and basic requirements for an advanced health 
monitoring system. The fault detection and isolation tasks are identified as the most 
crucial components in these diagnostic frameworks. Consequently, these tasks will be 
applied in the study for sensor and process fault diagnosis. 
Section 2.3 discussed the redundant and non-redundant techniques that are 
applicable to NPP sensor fault diagnosis. It is concluded that an uncertainty analysis is an 
important factor for acceptance of an OLM technique. Redundant techniques emerged as 
the most favourable for OLM, and accordingly, redundant techniques will be applied in 
the thesis for consistency analysis and state estimation of critical system variables. In 
order to establish a reliable framework for sensor fault diagnosis, a novel integrated 
approach is proposed and is presented in Chapter 4. 
Section 2.4 summarizes the most relevant techniques for process fault diagnosis. The 
different model-and process history based techniques each offer some desirable qualities 
for application in NPPs and are discussed. In order to incorporate these qualities into a 
FDI system, the structure of the proposed process fault diagnosis approach is presented. 
In section 2.5, the most relevant mechanisms for component degradation in HTGRs 
are discussed and comprise component corrosion, erosion, fouling and leakage. 
The following chapter discusses the topology of the reference HTGR NPP together 
with the fault symptoms and component performance parameters associated with the 
degradation mechanisms. 
22 
CHAPTER 3 
The plant model and examined system faults 
This chapter focuses on the PBMR plant model comprising the MPS andlCS. Three main 
fault classes are identified for the MPS through a sensitivity analysis and include the 
main flow bypass of the working fluid, an increase in main flow resistance, and a 
decrease in component efficiency or effectiveness. 
3.1 Introduction 
In this chapter, the theory regarding the thermodynamic Brayton cycle, the components 
comprising the PBMR plant and the Flownex simulation model are discussed. In 
addition, a sensitivity analysis of the system is performed to identify the fault parameters 
and classify the different fault classes. 
Firstly, section 3.2 describes the thermodynamic system applicable for the 
investigation. The PBMR, which is a Brayton cycle-based modular nuclear gas power 
plant, is analyzed and the eight sub-processes together with the system components are 
discussed. In addition, plant mode and state transitions are examined to define normal 
power operation and to classify critical system faults. These faults are accommodated in 
the automated plant protection systems and are for this reason not applicable to the 
investigation. 
In section 3.3, a sensitivity analysis of the main power system (MPS) is performed to 
determine the influence of system/component parameters on system performance and to 
identify the fault parameters that are synonymous with the degradation mechanisms. 
Three main fault classes are identified in the MPS and are discussed in section 3.4. A 
motivation is formulated for the probable fault causes and their degrading effect on 
system performance is demonstrated. In total, 25 single and 7 multiple faults conditions 
are investigated in the study. 
Section 3.5 describes the Flownex MPS plant model comprising the reactor unit 
(RU), the power conversion unit (PCU) and the inventory control system (ICS). The basic 
control structures are discussed together with critical model parameters. 
Lastly, some conclusions are summarized in section 3.6. 
23 
The plant model and reference system faults 
3.2 Theoretical analysis of the PBMR plant model 
The PBMR MPS utilizes a closed direct Brayton cycle with helium (He) gas as the 
working fluid and a graphite-moderated nuclear core as heat source. Helium is chosen as 
coolant since it is chemically inert and has a high thermal conductivity. The MPS is 
divided into two main subsystems, the RU and the PCU. The helium gas transfers thermal 
energy generated by a nuclear reaction in the RU to the PCU, which consists of gas turbo-
machinery and heat exchangers. The resultant thermal energy is converted into electrical 
energy by an electric generator connected to the gas power turbine. Figures 3.2.1 and 
3.2.2 shows the layout and solid model of the PBMR MPS respectively. 
The numbers depicted in Fig. 3.2.1 correspond to the eight sub-processes employed 
in the Brayton cycle. Starting at (1), helium at low pressure and temperature is 
compressed by the low-pressure compressor (LPC) to an intermediate pressure (2) and 
then cooled in the intercooler (3). Next, the helium is compressed to a higher pressure (4) 
by the high-pressure compressor (HPC) and preheated in the recuperator (5) before 
entering the RU. After the process in the reactor (6), high pressure and temperature 
helium is expanded in the gas power turbine (PT) (7), which in turn drives the electrical 
generator. The low pressure hot helium is then cooled at constant pressure in the 
recuperator (8) and further cooled in the pre-cooler to state 1. This completes the 
thermodynamic cycle [46]. Table 3.2.1 shows the typical parameters of the PBMR MPS 
for normal operation at full power. 
PCU 
HI 
J-^rVOD-j—* HV Breaker Generator Breaker 
CRB 
(ZZ) 
OM0> 
-&r 
LPB - Low Pressure Compressor Bypass Valve 
GBP - Gas Cyda Bypass Valve 
GBPC - Gas Cycla Bypass control vulva 
LCV - Low Pressure Coolant Valve 
RBP • Recuperator Bypass Valve 
HPC 
Fig. 3.2.1 PBMR MPS layout. 
24 
The plant model and reference system faults 
REACTOR 
RECUPERATOR 
COMPRESSOR 
TURBINE GENERATOR 
GEARBOX 
COS &CBCS 
SYSTEMS MAINTENANCE 
SHUT-OFF DISC 
INTER-COOLER 
Fig. 3.2.2 Solid model of the PBMR MPS. 
OIL LUBE SYSTEM 
The PBMR MPS comprises the follovving components: Reactor, HPC, LPC, PT with 
electric generator, recuperator, pre-cooler, intercooler, pipelines and valve systems. The 
functions of the components in the sub-processes are [46]: 
• Reactor unit 
The reactor provides the heat energy required for conversion into electrical energy. 
The RU consists of the reactor pressure vessel, the nuclear core containing the fuel 
spheres and the core structures. Since the RU is an absolute safety critical component 
Component 
(at inlet) 
Cycle parameters 
Efficiency (%)/ 
effectiveness 
T 
(°C) 
P 
(MPa) 
m 
(kg/s) 
1. LPC 89 22 2.9 201 
2. Intercooler 0.82 109 5.0 201 
3. HPC 89 22 5.0 201 
4. Recuperalor HP 
5. Reactor 
0.97 106 
500 
8.9 
8.9 
190 
190 
6. Turbine 91 900 8.6 190 
7, Recuperator LP 
8. Pre-cooler 
0.97 
0.84 
510 
140 
2.9 
2.9 
201 
201 
Performance parameters 
Cycle efficiency (%) 
Reactor thermal power (MWt) 
Generator output (MWe) 
Helium mass in PPB (kg) 
46 
400 
165 
5800 
Table 3.2.1 Typical parameters of the PBMR MPS for normal operation at full power. 
25 
The plant model and reference system faults 
with integrated protection systems, no internal reactor faults are examined. However, 
faults that influence system performance (e.g. gas leakage) are examined. 
• Turbo units 
The HPC and LPC provide the pressure in the Brayton cycle to drive the PT. The 
compressors use simple dump diffusers instead of complex inlet/outlet volutes and 
the blades adjust with a ±15 ° angle for the purpose of plant control. 
• PT and electric generator 
The PT absorbs the energy from the high pressure and temperature helium to drive 
the electrical generator. In turn, the generator supplies the high voltage (HV) 
electrical network with power. 
• 
• 
Recuperator 
The recuperator returns heat downstream of the PT back to the flow path ahead of the 
reactor to raise the gas temperature, thus reducing the heating demand on the reactor. 
This exchange of thermal energy improves the efficiency of the Brayton cycle. 
Heat exchangers 
Within the closed Brayton cycle, the pre-cooler anchors the temperature of the low 
pressure line. The function of the intercooler is to reduce the volume flow to the 
HPC, causing a reduction of compressive work. This multistage compression with 
intercooling improves the efficiency of the Brayton cycle. The heat exchangers 
utilized in the PBMR are compact counter flow, finned-tubed heat exchangers. 
• Pipelines 
Helium and secondary coolant is transported via the pipelines between the MPS 
components and the auxiliary systems. 
• Valves 
The valves are mainly used to manipulate helium flow for inventory control and 
several MPS safety features. 
The controllability and response of the PBMR MPS is determined by the dynamic 
characteristics of the PCU and the reactor. Two system characteristics are highlighted to 
better comprehend the fault simulation responses [47]: 
• Since the PBMR utilizes a closed direct Brayton cycle, all the dynamics are 
interlinked. The time constant for the gas cycle is approximately 5 seconds, i.e. the 
time it takes for an operational disturbance like a fault to propagate throughout the 
system. 
• The nuclear core has a large thermal capacity. Since the temperature coefficient of the reactor is negative, the reactivity and neutronic power changes to counteract 
temperature variations. As a result, the reactor is nearly self-regulating and minimal 
26 
The plant model and reference system faults 
control is required to maintain the reactor outlet temperature (ROT) at a given set 
point. 
The main advantage of the slow thermal response of the reactor is to allow fast load 
changes without requiring a fast response from the core. During normal power operation, 
the ROT is controlled at 900 °C by means of the control rods (reactivity control). This 
average ROT results in the highest cycle efficiency. The other contributing factor that 
influences cycle efficiency during normal power operation is the type of load/power 
control. 
The primary power control of the MPS is achieved by adding or removing helium 
inventory from the primary pressure boundary (PPB) with the ICS. By using inventory 
control, the cycle temperatures and pressure ratios stay the same whilst only the gas 
density and mass flow rates change. The change in mass flow rates in turn varies the 
power output of the gas turbine and electrical generator. This method allows high 
efficiency at all power levels above 40 % of the maximum continuous rating (MCR). 
Transport of helium mass between the MPS and ICS is realized by means of pressure 
differential. Helium is extracted at the HPC outlet (highest pressure point in the MPS) 
and injected at the pre-cooler inlet. 
Alternatively, the gas cycle bypass (GBPC) valves are used in combination with the 
ICS to realize faster load changes and accurate set point tracking. By opening the valves, 
the mass flow through the reactor and turbine is reduced, thus decreasing the output 
power of the electrical generator. The drawback of this method is lower cycle efficiencies 
and changes in the cycle temperatures. 
Although the PBMR plant encompasses several additional subsystems, e.g. systems 
for cooling, purification, shutdown, pressure relief etc., the plant model used in the study 
comprises only the MPS (includes RUCS and CBCS conditioning/cooling systems) and 
the ICS. Additionally, since the MPS is mostly operated at full power, the study mainly 
focuses on normal power operation of the plant. The modes and operational states of the 
PBMR are illustrated in Fig. 3.2.3. In the normal power mode (mode 5b), the Brayton 
cycle is self-sustaining and the generator is synchronized with the power grid (generator 
and HV breakers are closed). The ROT is controlled at 900 °C (reactor critical) and the 
power delivered to the grid varies between 40 % MCR and 100 % MCR. Power control is 
realized by means of the ICS and manipulation of the GBPC valves. 
Fig. 3.2.3 shows that four critical fault transients are incorporated in the automated 
plant safety systems. These transients comprise a PCU trip, reactor or control rod 
SCRAM (emergency shutdown procedure of the reactor) and loss of load. In all these 
cases, the Brayton cycle stops functioning and the plant protection systems initiate mode 
and state transitions to ensure the plant is kept within defined limits. As a result, these 
faults are not investigated in the study and not included in the proposed fault diagnosis 
scheme. The system faults include electrical malfunctions, turbo machinery over speed, 
compressor surge, excessive vibration, electro-magnetic bearing failure, loss of cooling, 
power oscillations, manifold over pressurization, increase in reactor outlet/differential 
temperature, and unexpected reactor neutron flux variations. 
27 
The plant model and reference system faults 
Reactor 
SCRAM 
PCU Trip 
Synchronized / 
Control rod 
SCRAM/ 
Reverse 
Defuelled 
Maintenance (0) 
Fig. 3.2.3 Modes and states for normal operation of the PBMR [47]. 
28 
The plant model and reference system faults 
3.3 Sensitivity analysis of the PBMR MPS 
In this section, a simplified simulation model of the PBMR MPS is used to determine the 
influence of certain component parameters on system/cycle performance [48]. This is 
done to identify the probable fault parameters that are associated with degrading 
component and system performance. 
Firstly, the type and origin of the component performance parameters are identified 
that are synonymous to the degradation mechanisms. These parameters are varied 
between upper and lower limits to determine the influence on system performance. The 
performance of the MPS is calculated by means of three parameters that serve as 
reference for normal power operation. 
3.3.1 The component and system performance parameters 
This section elaborates on the chosen component parameters that are varied for the 
sensitivity analysis. The influence of the following component parameters is considered: 
• Loss factors/resistive losses 
The secondary loss coefficients are varied in the equivalent intake pipe models to 
emulate a variation in resistive losses. This in turn varies the pressure losses around 
the circuit. 
• Leakage flows 
Unavoidable leakage flows occur between the manifold and the turbo machinery 
inlets and outlets, between the recuperator high pressure and low pressure streams 
and the reactor inlet and outlet plenums. 
• Turbo machine isentropic efficiency 
The isentropic efficiencies of all the turbo machines are essential to achieve a high 
efficiency MPS. The HPC, LPC and PT efficiencies are adjusted. 
• Turbo machine pressure ratio 
Since the cycle efficiency is a function of the overall pressure ratio, the pressure ratio 
of the HPC, LPC and PT are varied. 
• Heat exchanger effectiveness 
To vary the effectiveness of the pre-cooler, intercooler and recuperator, the heat 
transfer area of the specific component are changed. 
• Minimum cycle temperature 
This is one of the critical parameters in the PBMR to achieve the highest possible 
cycle efficiency. The minimum gas temperatures are located directly after the pre-
and intercoolers and vary with variations in ultimate heat sink (cooling towers, 
seawater) temperature. 
29 
The plant model and reference system faults 
Two additional parameters that influence system performance are the maximum cycle 
pressure (manifold) and temperature (ROT). Since both parameters are controlled within 
predefined limits and integrated in the automated protection systems, they are not 
considered as potential fault parameters. 
The system performance is measured in terms of power delivered to the grid, cycle 
efficiency and mass flow through the reactor. The cycle efficiency is a function of the net 
work and the heat added to the process and is defined by (3.3.1) 
%de = QpT~Q"PC~QLPC (3.3.1) 
with QPT, QHPC, QLPC the work delivered or absorbed by the turbo machinery and QRU the 
heat supplied by the reactor. The power delivered to the grid is given by 
Pgrid = % {"nPgenPpT ~ Phouse ) (3 -3.2) 
where ijsy, f]m and T]ge„ are the switchyard, mechanical and generator efficiencies 
respectively and Phouse is the house load (power supplied to the installation). The mass 
flow through the reactor is calculated as follows 
QRU 
cp{T0Ut-Tin) (3.3.3) 
with cp the constant pressure specific heat and Tout, T„ the reactor outlet and inlet 
temperatures respectively. 
3.3.2 Simplified simulation model of the Brayton cycle 
The simplified model of the PBMR MPS is constructed in Flownex and is given in Fig. 
3.3.1. The following settings apply to the model: 
• The reactor is modelled as a simple pipe element with a fixed exit temperature of 
900 °C. 
• The manifold pressure is fixed at 7 MPa. 
• All the flow resistances in the system are negligibly small. 
• The speed of the shaft connecting the turbo machinery is fixed at 6000 rpm. 
• The cooling water temperature (CWT) is set at 18 °C. 
• In (3.3.2), PPT corresponds to the excess shaft power. 
To conduct the sensitivity analysis of the MPS, the system performance parameters are 
firstly calculated. This is done to establish the baseline values for the component 
parameters that result in the best realistic cycle efficiency. 
30 
The plant model and reference system faults 
Fig. 3.3.1 A network diagram of a simplified Brayton cycle-based MPS. 
The baseline values for the component and system parameters are listed in Table 3.3.1. 
The table shows that the highest realistic cycle efficiency obtained for the Brayton cycle 
is 45.7 %. Realistic in this context signifies component baseline values that can be 
realized, i.e. component geometry and performance are limited. 
The sensitivity analysis is performed by setting the component parameters equal to 
the baseline values and varying the appropriate parameters as defined in section 3.3.1. 
Table 3.3.2 summarizes the results obtained with the sensitivity analysis. 
Cycle parameters 
Component Efficiency (%)/ 
effectiveness Pressure ratio 
LPC 90.5 1.69 
Intercooler 0.956 
HPC 89.8 1.64 
Recuperator 0.976 
Power turbine 89.6 2.68 
Pre-cooler 0.957 
Performance parameters 
Cycle efficiency (%) 45.7 
Grid power (MW) 123.8 
Reactor mass flow (kg/s) 130.6 
Shaft power (MW) 132.5 
Reactor thermal power (MW) 295.0 
Total pressure losses (kPa) 184.1 
Total leakage mass flows (kg/s) 11.3 
Minimum cycle temperature (°C) 21.5 
Table 3.3.1 Simplified Flownex model reference values. 
31 
The plant model and reference system faults 
Change in system performance parameters 
Component Change Grid Cycle Reactor mass 
parameters power efficiency flow rate 
(MW) (%) (kg/s) 
Pressure losses (kPa) +10 % -1.1 -0.4 -0.3 
PT inlet leakage (kg/s) +10 % -0.9 -0.4 -0.6 
PT outlet leakage (kg/s) +10 % -4.8 -1.7 -0.5 
Recuperator leakage (kg/s) +10 % -0.1 -0.2 0 
Core bypass leakage (kg/s) +10 % -0.1 -0.1 -2.5 
All leakages (kg/s) +10 % -5.6 -2 -3.5 
All efficiencies (%) -1% -3.5 -1.3 0 
LPC efficiency (%) -1% -0.6 -0.3 0 
HPC efficiency (%) -1% -0.6 -0.2 0 
PT efficiency (%) -1% -2.4 -1.0 0 
All pressure ratios -1% -0.8 -0.3 -0.7 
LPC pressure ratio -1% -0.6 -0.2 -0.2 
HPC pressure ratio -1% -0.1 -0.1 -0.1 
PT pressure ratio -1% -0.3 -0.1 -0.4 
Minimum cycle temperature (°C) +1°C -0.3 -0.3 -0.1 
Pre-cooler effectiveness -1% -0.1 -0.1 0 
Intercooler effectiveness -1% -0.1 -0.1 0 
Recuperator effectiveness -1% -0.6 -0.1 0 
All effectivenesses -1% -0.8 -0.3 -0.1 
Table 3.3.2 Summary of sensitivity analysis results. 
Table 3.3.2 shows that changes in leakage flows and turbo machinery efficiencies have a 
profound effect on the cycle efficiency as well as the power delivered to the grid. The 
most noticeable contributors are the leakage flow between the manifold and the PT outlet, 
and the PT efficiency. A ten percent increase in the outlet leakage flow of the PT results 
in a mass flow of approximately 4.5 kg/s and a decrease in cycle efficiency and grid 
power of 1.7 % and 4.8 MW respectively. Furthermore, a 1 % percent decrease in PT 
efficiency results in a reduction in grid power and cycle efficiency of 2.8 MW and 1 %. 
The system pressure losses, turbo machinery pressure ratios and the heat exchanger 
effectivenesses are also important and show a decrease in system performance for a small 
change in component parameters. 
It is evident from the table that the core bypass leakage has a major effect on the 
mass flow through the reactor. A ten percent increase results in a leakage flow of 
approximately 12 kg/s, and a reduction in mass flow through the reactor of 2.5 kg/s. 
Overall, the sensitivity analysis shows that the effects of all the selected component 
parameters are detrimental on the Brayton cycle. In reality, this will be associated with 
degraded components due to normal wear or system faults. Table 3.3.2 shows that a small 
change in some component characteristics result in an indistinguishable change in system 
performance. Accordingly, incipient fault behaviour will be very difficult to detect at an 
early stage and can result in component failure. 
The following section describes the correlation between the chosen component 
parameters and probable fault causes as well as the PBMR MPS fault classes. 
32 
The plant model and reference system faults 
3.4 Fault classification in the PBMR MPS 
As demonstrated in section 3.3, changes in certain component parameters influence the 
performance of the Brayton cycle. During normal power operation of the plant, these 
changes are associated with known fault conditions and may be attributed to normal 
component wear, ageing effects, material defects or operation of the plant beyond the 
defined limits. 
In the thesis, faults in the MPS are defined as any malfunction or abnormal 
behaviour of the components or the process. By means of the sensitivity analysis, three 
different fault classes are identified. The fault classes characterize or group the individual 
faults according to cause and effect, and include: 
• Changes in bypass flows. 
• Changes in the main flow resistance. 
• Changes in efficiency or effectiveness. 
Firstly, flow bypass faults disturb the natural flow path of the working fluid and are 
mainly caused by leakage flows between components or nodes. The second fault class is 
defined as faults that increase the resistance of fluid flow and is the result of fouling, 
erosion, corrosion and surface roughness. The increase in resistive losses, in turn 
increases the pressure losses around the system. Lastly, the third fault class is described 
as faults that influence the efficiency or effectiveness of the components. 
The following paragraph elaborates on the selected component parameters that are 
varied to reflect the appropriate fault conditions. In total, 25 component parameters are 
varied in the MPS to denote the most likely single and multiple (combination of single 
faults) fault conditions. 
3.4.1 Fault class 1: Flow bypass 
This fault class results in helium gas that bypasses components or whole parts of the 
process. In the MPS, these alternative paths are modelled by parallel 'equivalent' 
resistive elements. The mass flow through the element is given by [49] (3.4.1) 
m = MACjP, *-
l> (3.4.1) 
with Mthe mach number and A the area in the throat, Cd the discharge coefficient, po\ and 
7bI the total upstream pressure and temperature, and y the ratio of specific heats. The 
faults considered are the leak flows between the HP manifold and the turbine inlet and 
outlet respectively, the recuperator HP and LP streams, and the reactor core bypass leak 
(between inlet and outlet plenums). By varying the resistance of the element, any change 
33 
The plant model and reference system faults 
in the leakage mass flow can be simulated. It is expected that the leakage flows would 
increase over time in the MPS. 
3.4.2 Fault class 2: Main flow resistance (resistive losses) 
An important quantity of interest is the pressure losses Ap in the MPS since it directly 
relates to the power required to maintain the flow. The secondary loss coefficients of the 
main components' intake pipe models are used to vary the pressure losses around the 
circuit. It is important to note that the objective is to create a change in Ap between the 
eight sub-processes of the Brayton-cycle and not in a single specific component. In the 
MPS, the pressure drop across an intake pipe with variable inlet and outlet areas is 
defined by [49] (3.4.2) 
Ap0 = ^ P 
VZ K^Hm *0 ) Z Z 
(3.4.2) 
with po and p the mean and static pressures, V, F, and Ve the mean, inlet and outlet 
velocities. /, Az and p are the friction factor, inlet/outlet height difference and mean 
density. L and Dnm represent the length and mean hydraulic diameter, and K,, Ke, Ks the 
inlet, outlet and secondary loss coefficients. In the MPS, the loss coefficients are varied to 
an upper limit since it is expected that Ap would more likely increase than decrease. 
3.4.3 Fault class 3: Effectiveness or efficiency 
As illustrated in section 3.3, the effectiveness of the heat exchangers (e) and efficiency of 
the turbo machinery (n) are important to maximize the efficiency of the cycle. The 
effectiveness of a heat exchanger (intercooler, pre-cooler, and recuperator) is a function 
of the AU value and the primary and secondary mass flow rates. The AU value is the 
product of the heat transfer area and the overall heat transfer coefficient. The 
effectiveness of the heat exchangers is defined by [50] (3.4.3) 
ApUp\ 1 C' min/ / ^max ) 
l-e 
APUPV-
l__^min_e 
cmin/ 1 (3.4.3) 7c
maJ 
c 
max 
with Ap the primary side heat transfer area, Up the overall heat transfer coefficient and 
Cmin, Cmax the minimum and maximum values of the heat capacity rates. A lower limit 
was chosen for the variation in heat transfer area (A) since a lower effectiveness is 
expected during fault conditions. 
34 
The plant model and reference system faults 
The performance of the turbo machines (LPC, HPC, and turbine) is a function of the 
pressure ratio (PR), isentropic efficiency, corrected mass flow rate and corrected speed 
[51]. The function is given by (3.4.4) 
r \ 
with pot and 7o, the inlet total pressure and temperature, Toe the exit total temperature and 
TV the speed. For the variables defined in (3.4.4), the performance of the turbo machines is 
given by two curves namely pressure ratio and isentropic efficiency as a function of 
corrected mass flow rate for various corrected speed curves. To vary the performance of 
the turbo machines, scaling factors are used to change the performance characteristics of 
the two curves. The pressure ratio and efficiency scaling factors are varied between upper 
and lower limits to simulate the different fault conditions. 
Table 3.4.1 summarizes the faults in the PBMR MPS together with the selected 
component parameter variations. 
Component Fault description Mechanism Class Direction Parameter 
1. Pre-cooler Heat transfer area fouling 3 decrease a(m2) 
2. Intercooler Heat transfer area fouling 3 decrease a(m2) 
3. Recuperator Heat transfer area fouling 3 decrease a(m2) 
4. HP to LP leakage leakage 1 increase d(m) 
5. LPC Pressure ratio combined 3 increase scaling factor 
6. Pressure ratio combined 3 decrease scaling factor 
7. Efficiency combined 3 decrease scaling factor 
8. HPC Pressure ratio combined 3 increase scaling factor 
9. Pressure ratio combined 3 decrease scaling factor 
10. Efficiency combined 3 decrease scaling factor 
11. Turbine Pressure ratio combined 3 increase scaling factor 
12. Pressure ratio combined 3 decrease scaling factor 
13. Efficiency combined 3 decrease scaling factor 
14. Manifold leakage to outlet leakage 1 increase d(m) 
15. Manifold leakage to inlet leakage 1 increase d(m) 
16. Pipelines LPC inlet combined 2 increase k 
17. Intercooler inlet combined 2 increase k 
18. HPC inlet combined 2 increase k 
19. Recuperator HP inlet combined 2 increase k 
20. Reactor inlet combined 2 increase k 
21. Turbine inlet combined 2 increase k 
22. Recuperator LP inlet combined 2 increase k 
23. Pre-cooler inlet combined 2 increase k 
24. Reactor Reactor bypass leakage leakage 1 increase aim2) 
25. Reactor pressure drop combined 2 increase /(m) 
26. Multiple LPC efficiency + fault 2 combined combined 
27. LPC efficiency + fault 3 combined combined 
28. LPC efficiency + fault 22 combined combined 
29. LPC efficiency + fault 10 combined combined 
30. LPC efficiency + fault 15 combined combined 
31. LPC efficiency + fault 23 combined combined 
32. LPC efficiency + fault 24 combined combined 
Table 3.4.1 Summary of faults in the PBMR MPS. 
35 
The plant model and reference system faults 
Faults 1 to 25 correspond to single faults and faults 26 to 32 denote multiple fault 
conditions. To demonstrate multiple fault symptoms in the MPS, the LPC efficiency fault 
is used in combination with a single fault from each of the three fault classes. 
These 32 faults form the basis for the fault study in the PBMR MPS. As discussed, 
the sensitivity analysis indicated that certain faults will be difficult to detect at an early 
stage. The task at hand is therefore to devise an advanced fault diagnosis method that will 
be able to detect and isolate all the faults within a given fault magnitude. This will not 
only promote early FDI, but reduce the risk of unexpected component failure and allow 
enough time for planned maintenance or repair. 
In order to investigate the responses of the MPS and the fault diagnosis method to 
incipient and abrupt faults, a maximum fault magnitude of 10 % (referenced to the 
baseline values) is deemed sufficient. In the thesis, the objective of early FDI is achieved 
if a fault condition with a magnitude of < 1 % is correctly identified. 
Since the prototype PBMR plant is not operational at the time of the investigation, a 
complex simulation model of the plant is used as substitute, and is discussed in the 
following section. 
3.5 The PBMR simulation model 
The system CFD (Computational Fluid Dynamics) code named Flownex [49] is used for 
the development and optimization of the PBMR plant. The Flownex model comprising 
the MPS, ICS, and various conditioning subsystems, serves as an evaluation and testing 
platform for the complex dynamic behaviour of the PBMR design. Some of the unique 
features of Flownex are steady state and transient solutions of the system as well as its 
ability to incorporate control strategies. The network diagram of the Flownex model is 
illustrated in Fig. 3.5.1. 
In order to maintain stable Brayton operation in the PBMR, several control 
objectives are achieved with different control mechanisms. Three of these controlled 
variables, together with a non-controlled parameter, determine the operating point of the 
Flownex model. The controlled variables are the ROT, the pressure in the HP manifold 
and the position of the bypass valves. The fourth parameter, the CWT, is a function of the 
site location, type of main heat sink used and the time of the year. 
As discussed, during normal power operation of the plant, the ROT is controlled by 
means of the control rods. Calculations for the reactivity controller include the ROT, 
reactor neutronic power and the reactor fluidic power. In the Flownex model, the ROT is 
controlled by varying the cooling flow area over the control rods. 
The pressure in the HP manifold is controlled by changing the gas inventory in the 
PPB, which in turns varies the output power of the plant. In the Flownex model, the ICS 
isolation valves together with the ICS flow control valve are used for injection, extraction 
and flow control of helium between the ICS and MPS. The ICS controller selects the 
correct tank during helium mass transfer and normally switches if the mass flow 
decreases below 75 % of the setpoint value. 
To obtain the required setpoint mass flows through the MPS and ICS control valves, 
the valve openings are corrected using valve controllers. 
36 
The plant model and reference system faults 
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37 
The plant model and reference system faults 
Lastly, the CWT changes the operating point of the plant since it directly influences the 
minimum cycle temperature. The CWT, which is the inlet water temperature of the 
pre-and intercoolers, varies with ambient conditions during the year and is usually taken 
as an average. Therefore, to vary the heat transfer through the heat exchangers, the mass 
flow rate of the cooling water is adjusted accordingly. 
In general, Flownex requires detailed input data for all the components and fluid 
parameters to simulate a model that is highly accurate. Although the objective of the 
study is to show a general implementation of the proposed fault diagnosis method in a 
thermodynamic system, the Flownex model employed comprises a detailed and optimised 
design of the PBMR. The normal expected operating conditions applied in Flownex 
include the following assumptions and parameters: 
• The ROT is controlled at 900 °C and the HP manifold pressure is limited to 9 MPa. 
• The average CWT is taken as 18 °C. This is derived from an average seawater 
temperature at Koeberg2 of 13 °C. 
• The generator is synchronized to the power grid with the turbine-compressor shaft 
speed fixed at 6000 rpm. 
To construct the h-s graph (discussed in Chapter 5), the eight sub-processes depicted in 
Fig. 3.2.1 are monitored. The Flownex model illustrated in Fig. 3.5.1 shows the location 
of the monitoring points (green nodes). The system variables, which comprise only the 
pressures and temperatures, are measured at each of the eight nodes. Table 3.5.1 
summarizes the average Flownex measurements for normal power operation. 
Node Operating point (% MCR) 100 90 80 70 60 50 40 
71 22.873 22.973 22.664 22.456 22.679 22.805 22.791 
72 109.001 109.256 109.080 109.011 109.245 109.427 109.752 
73 21.829 21.936 21.695 21.548 21.270 21.046 21.610 
74 106.316 106.689 106.758 106.910 106.982 106.99 107.01 
T5 499.086 499.845 499.340 499.628 499.632 499.989 499.99 
78 899.521 899.638 899.448 899.488 899.517 899.737 899.786 
TJ 510.499 510.458 509.865 509.519 509.469 509.498 509.607 
T& 139.867 139.415 139.312 138.783 138.736 138.774 139.002 
PI 2909.802 2602.754 2292.503 1999.661 1709.241 1418.262 1127.775 
PI 5089.092 4552.149 4011.535 3500.618 2988.692 2478.153 1973.505 
P3 5058.270 4524.604 3987.247 3479.414 2970.566 2463.100 1961.520 
PA 8978.038 8030.415 7082.779 6185.007 5287.228 4389.433 3491.609 
P5 8896.449 7957.271 7018.225 6128.523 5238.921 4349.278 3459.601 
P6 8551.313 7646.421 6741.859 5884.966 5028.497 4172.210 3316.354 
PI 2970.539 2657.920 2342.031 2043.584 1747.386 1450.423 1153.770 
P8 2928.874 2619.873 2307.673 2012.974 1720.691 1427.837 1135.455 
Table 3.5.1 Summary of the Flownex model results for normal power operation. 
2The prototype demonstration plant of the PBMR will be constructed at Koeberg. Koeberg is currently the 
only nuclear power station in South Africa comprising two uranium pressurized water reactors. 
38 
The plant model and reference system faults 
3.6 Summary and conclusions 
In this chapter, the PBMR plant model together with probable component and system 
malfunctions are discussed. The plant model is developed in Flownex, which serves as 
evaluation and testing platform for the performance of the proposed fault diagnosis 
method. 
In section 3.2, the operation of the MPS comprising the PCU and RU are described. 
The PBMR utilizes a recuperative, pre-and intercooled topology that includes eight 
sub-processes. Following this discussion, the conditions for normal power operation are 
defined. During this state of operation, a number of critical system faults may put the 
plant at risk. These faults are integrated in the automated protection systems and are for 
this reason not included in the proposed fault diagnosis scheme. 
In section 3.3, probable component and system faults are identified by means of a 
sensitivity analysis of a simplified MPS. These faults are normally associated with 
degraded components and can be attributed to the degradation mechanisms. The results 
showed that variations in the selected component parameters have a detrimental effect on 
system performance. 
By grouping the fault parameters with regard to cause and effect, three fault classes 
are identified and are motivated in section 3.4. The three fault classes comprise changes 
in main flow bypass, main flow resistance and component efficiency or effectiveness. 
The mathematical descriptions that describe the behaviour of the specific components and 
consequently the fault classes are also discussed. In total, 32 single and multiple fault 
conditions in the PBMR MPS are selected for the study. 
The PBMR MPS is realized in section 3.5 with a simulation model in Flownex. 
Several plant control objectives are implemented in Flownex using different control 
mechanisms and include pressure, temperature and mass flow control. Lastly, section 3.5 
describes the selected measurements and the monitoring points in the PBMR MPS. The 
proposed fault diagnosis scheme monitors only temperature and pressure measurements, 
captured at the inlets of the eight sub-processes. The total amount of measurements 
required to monitor the health of the MPS is therefore limited to 16. 
To provide the process fault diagnosis scheme with accurate plant measurements, 
sensor fault diagnosis is formulated in the next chapter. 
39 
CHAPTER 4 
Sensor fault detection and isolation 
This chapter presents an integrated framework for intelligent sensor validation and 
fusion in the PBMR MPS. The comprehensive sensor fault diagnosis scheme includes a 
validation procedure comprising a signal pre-processing, non-temporal parity space, and 
principle component and shape statistical analyses. These, together with the data fusion 
procedure, provide consistent and accurate information for the process FDI scheme. 
4.1 Introduction 
In this chapter, an integrated framework for intelligent sensor fault diagnosis is proposed. 
The methodology uses a combination of analytical techniques to reduce their individual 
shortcomings. 
The sensor malfunctions that are considered for the study are discussed in section 
4.2. The sensor faults include dead, bias, drift, excessive noise and random spikes. 
Section 4.3 explains the individual monitoring and conditioning techniques 
employed for measurement validation. Firstly, section 4.3.1 discusses the use of 
redundant measurements in a critical process plant, which is checked for consistency 
with the non-temporal parity space algorithm. To condition the signals before the 
consistency check, a signal pre-processing procedure validates the absolute limits of the 
measurement intervals and the maximum acceptable variable change per time step. 
Data reconstruction is an important part of the sensor validation system and is 
described in section 4.4. To compensate for erroneous measurements, the sensor 
configuration is validated with a principle component analysis (PCA) model together 
with the squared prediction error (SPE) index. Moreover, once the SPE threshold is 
exceeded, the PCA model can reconstruct the faulty measurement from the remaining 
healthy ones. The validated variables are then combined with a fusion technique based on 
a confidence level associated with each sensor's residual distribution. 
In section 4.5, the proposed sensor validation and fusion module (SENSE) is 
discussed. The basic steps and detailed reasoning structure of the methodology are 
explained together with the rules employed for the statistical expert system. The proposed 
methodology is applied to data from the PBMM and PBMR and is presented in section 
4.6. The chapter is summarized in section 4.7. 
40 
Sensor fault detection and isolation 
4.2 Sensor malfunctions 
In general, sensor malfunctions are roughly classified into two types of fault classes, 
abrupt sensor faults or sensor degradation. Abrupt sensor faults result in either complete 
failure or erroneous readings from the sensor, whilst sensor degradation changes the 
performance of the sensor. Abrupt faults are due to power failures, corroded or loose 
contacts and mechanical failure. Sensor degradation on the other hand is the result of a 
variety of circumstances and includes incorrect calibration, fouling and electrical or 
mechanical malfunction. 
For the investigation, both types of fault classes are considered, although the primary 
goal is to identify and correct the latter. Sensor degradation normally exhibits incipient 
fault behaviour, and is for this reason more difficult to detect. The following faults are 
examined given the common sensor malfunctions [52]: dead/stuck, bias/offset, drift, 
noisy and random spikes. Figure 4.2.1 illustrates the different sensor malfunctions. 
4.3 Sensor validation 
In a sensor network, the validation of sensor readings entails the verification regarding 
the integrity of the measurements. This is crucial in plants comprising safety critical 
processes since plant performance and stability may be adversely affected by erroneous 
measurements. It is therefore important to determine if a sensor reading is a true 
representation of the measured quantity. 
Time [s] 
(a) 
Time [s] 
(b) (c) 
0 200 400 600 800 1000 0 200 400 600 800 1000 0 200 400 600 800 1000 
Time [s] Time [s] Time [s] 
(d) (e) (f) 
Fig. 4.2.1 Sensor malfunctions: (a) normal; (b) dead/stuck; (c) bias/offset; (d) drift; (e) noisy; (f) spikes. 
41 
Sensor fault detection and isolation 
The sensor validation scheme must accomplish the following two tasks: detection of 
sensor malfunctions and isolation of the faulty sensors [53]. These tasks become difficult 
if a large number of different sensors and configurations are used. Therefore, the 
validation module must be flexible and include different methods to accommodate sensor 
configurations that constantly change due to faulty sensors. The following sections 
motivate and describe the methods used in the thesis and discuss the complete 
architecture of the validation module. 
4.3.1 Measurement redundancy 
The most commonly used technique for measurement validation is the comparison of a 
set of redundant measurements. Measurement redundancy is divided into two groups, i.e. 
spatial and temporal redundancy. The former is realized by means of multiple sensors or 
functional relationships among different measurements. Functional relationships are also 
referred to as analytical redundancy where the process is described by a mathematical 
model. Temporal redundancy is achieved by means of repetitive measurements of the 
sensor values at regular time intervals. 
As discussed in Chapter 2, quantities that are of great importance to the safety of the 
plant are measured by multiple sensors and named 'hardware redundant'. In addition, the 
nuclear power industry requires that safety critical parameters be monitored by several 
redundant sensors [1], [16], [54]. Consequently, the inlet parameters of the main 
components in the PBMR MPS are monitored with 3 redundant sensors, i.e. 48 
temperature and pressure sensors in total. 
One concern of hardware redundant measurements is common mode failure among 
sensors. Although this condition is extremely uncommon [16], the integrity of each 
redundant measurement set in the PBMR is increased by shielded and physically isolated 
channels. The assumption is therefore made that not all of the three sensors may fail 
simultaneously in each measurement set/channel. Common mode failure is generally 
corrected and replaced with a sensor estimate, i.e. the unavailable information is 
predicted using the remaining valid measurements. In the study, the PCA technique is 
used to predict sensor estimates. 
Given that the measurements in the PBMR MPS are hardware redundant, the 
non-temporal parity space algorithm is first applied to the measurements and is discussed 
next. 
4.3.2 Non-temporal parity space analysis 
To check the hardware redundant measurements for consistency, the non-temporal parity 
space technique is applied [30]. The non-temporal algorithm allows the system to be 
described by the actual time instant, i.e. the measurements are time-independent and 
therefore the process history is not applicable. 
Consider a measurement set comprising n redundant measurements mi, all 
representing the scalar quantity x, are corrupted by sensor errors e; 
42 
Sensor fault detection and isolation 
m = Hx + e (4.3.1) 
with H = [1, 1,..., 1]T. Since the correct value of the measurement is not known, x is 
removed by projecting the n-dimensional measurement space to the n-1-dimensional 
parity space 
p = Vm (4.3.2) 
The (n-1) x n projection matrix V has the following properties: 
• VH = On_, 
• WT = In_! 
• WT = In -H(HTH) 'H1 
where I represents the unity matrix and 0 the null vector. The residual vector is defined 
by 
r = VTp (4.3.3) 
with rTr = pTp and r = m - H(u). (u) denotes the mean of all n measurements. The n 
redundant measurements m, are inconsistent if the parity vector p exceeds a threshold 
PTP = (lP,2|^n (4.3.4) 
Assuming that the magnitudes of all sensor errors are uniformly limited by b, i.e. |ej| < b, 
the threshold 5n is determined by 
8 = 
nb2 n even 
n2-l, 2 (4.3.5) b nodd 
To isolate the faulty sensor, the direction of the parity vector is examined. The magnitude 
of the parity vector's projection orthogonal to the direction of the i-th sensor is given by 
,2 U2 n .2 PL=P —^tf (4-3.6) 
n-1 
In the fault free case, the projection must be lower than 8n-i. 
Although the consistency of redundant measurements is easily validated with this 
technique, one limitation is that isolation is impossible if more than one sensor fails. For 
this reason, additional methods are used if the measurements are inconsistent and 
multiple sensors are erroneous. 
43 
Sensor fault detection and isolation 
4.3.3 Statistical shape analysis 
Even though the parity space technique is an uncomplicated yet effective way of 
checking measurement consistency, it cannot classify the type of sensor fault. To classify 
the faults depicted in Fig. 4.2.1, some features regarding the measurement distribution are 
evaluated. First, a motivation for the use of the normal distribution is presented. 
In the proposed process fault diagnosis approach, noise originating from the sensors 
is assumed to be Gaussian or normally distributed. This statement is justified by [6], [16] 
and verified in section 7.6 with real measurement data from the PBMM. Gertler [6], using 
the central limit theorem, states that many random processes can be approximated by the 
normal distribution. In addition, [16] states that research has shown that nuclear power 
plant data normally has a Gaussian distribution 
The central limit theorem states that the distribution of the average of random 
variables (measurements) tends to be normally distributed as the number of observations 
approaches infinity. The basic form of the central limit theorem is given in Appendix A. 
Although the theorem states exact equality in the limit (n-»oo), any limited number of 
variables (sample window) can be fairly accurately characterized by the standard normal 
distribution, given an approximation error. However, the choice of sample window size 
versus approximation error is dependent on the type of implementation and the sampling 
time. The choice of sample size for the PBMR is discussed in section 4.5. 
In order to classify sensor faults, some characteristic features regarding the sensor's 
distribution are evaluated. These features include the mean, standard deviation/variance, 
and skewness. Another important feature is the minimum and maximum values of the 
variable. These values are used to identify the absolute limits of the measured quantity. 
To illustrate the different features, the normal distribution is firstly calculated by 
computing the mean and standard deviation of the variable. The mean is the arithmetic 
average of the measurements, and is given by 
» = -t,\ (4-3.7) 
n i=1 
where n is the number of measurements and x; is the i-th measurement. The standard 
deviation is a measure of the dispersion of the measurements, and is defined by 
V n i=l 
The probability density function of the normally distributed measurement is 
i (x->1)2 
f(x) = —^=e 2°2 (4.3.9) 
In (4.3.9), a2 is also known as the variance. The bell-shaped probability density function 
of the normal distribution is shown in Fig. 4.3.1. 
44 
Sensor fault detection and isolation 
Fig. 4.3.1 Probability density function for the normal distribution. 
In probability theory, the skewness is a measure of the asymmetry of the measurements 
around the mean. For the normal distribution, the skewness is zero and defined by 
Y = -
^E(xi-^)3 
i=l  
Efr-n)2 \Yi 
(4.3.10) 
To realize the design objective of simplicity with high interpretability, an uncomplicated 
rule-based expert system is used for fault classification and is based on the behaviour of 
the distribution features. The following mechanisms are utilized for sensor FDI: 
• The absolute limits of the variables are set that approximately 95 % of the 
measurements lie between them. For the normal distribution, this corresponds to 
approximately ± 2a. These limits are used to identify outliers in the measurements 
caused by spikes, missing data or dead sensors (zero value). In addition, sensor bias 
and excessive noise can be detected if the variable surpasses the limits for an 
extensive time period. 
• To classify bias and drift faults, the distributions of the sensor residues are examined. 
Since these faults manifest themselves as changes in the mean or variance, a change 
in the mean is associated with sensor bias and changes in the variance an indication 
of excessive noise. 
• As discussed, the skewness is a measure of the asymmetry of the probability 
distribution. Therefore, for either positive or negative skew, an uneven distribution is 
an indication of sensor degradation. 
Given that the distributions of the sensor residues are evaluated for changes, an 
approximation of the sensor values is needed. To perform this task, a principle 
component analysis is applied to the measurements and is discussed in section 4.3.5. 
45 
Sensor fault detection and isolation 
4.3.4 Maximum process change 
In order to detect an unexpected abrupt step in a sensor value, a maximum process 
change parameter is defined. For any process variation, the maximum process change 
signifies a theoretical limit for change per time instant, and is determined by means of the 
system characteristics. The maximum change parameter for any two consecutive samples 
is defined as 
AXi = Xi(k)-Xi(k-l) (4.3.11) 
where x; denotes the i-th variable. As discussed in Chapter 3, the different variations for 
normal power operation include injection, extraction, valve manipulation and normal 
steady state operation. 
By applying the maximum process limit, any large deviation can be detected and 
isolated at the specific time instant. Normal statistical methods will however only identify 
the deviation after the mean of the sample window changes. One of the main drawbacks 
of the method is that incipient faults are only detected once the limit is surpassed. 
The implementation of a maximum process change parameter is demonstrated in 
Fig. 4.3.2. A good first choice of the parameter during normal steady state conditions is 
the standard deviation of the measurements. 
80 100 
Fig. 4.3.2 Varying the maximum process change: (a) 0.05; (b) 0.2; (c) 0.5; (d) 1. 
46 
Sensor fault detection and isolation 
Fig. 4.3.2 shows that the filtered signal (blue) approaches the original (red) if the 
maximum step increases. As a result, the maximum step minimizes the effects of noise 
and produces a 'smoother' signal. For implementation in the PBMR MPS, the maximum 
process parameter will be determined by the characteristics of the measurement 
distributions. 
4.3.5 Principle component analysis 
The PCA method is employed to perform the tasks of sensor FDI and state prediction 
[8]-[10], [29]. The reasons for this choice are: 
• The method is applied independent of the mathematical model of the process. 
• A model of low dimensions can be realized with a small amount of process data. 
Given that the characteristics of the process may change, the principle components 
can simply be altered or new ones added. 
• The method is very successful if the process dynamics are relatively slow and sensor 
FDI is achieved faster than process feedback control. In this case, the feedback 
control system will not mask the effects of faults [55]. 
PCA is a statistical method that forms linear combinations of the original variables, 
which aims to account for all the variation in the data [56], [57]. The following notation 
is applied: 
Consider a measurement vector at time instant k, with m observed variables 
x(k) = [x1(k),x2(k),...,xm(k)]T (4.3.12) 
The measurement matrix comprising n samples (k = 1,..., n) and zero mean, is calculated 
with 
X = [x(l), x(2),...,x(n)] -[^i(l), n(2),...,n(n)] (4.3.13) 
with |x the matrix mean vector. The n x m measurement matrix X is decomposed as 
follows 
X = X+E (4.3.14) 
The matrices X and E signify the modelled (component space) and unmodelled (residual 
space) variations of X 
47 
Sensor fault detection and isolation 
X_TP
T (4.3.15) 
E = TPT 
where Te<Rnxl and PeST*1 are the score and loading matrices respectively, and 1 the 
number of principle components. Normally, the first few principle components can 
describe most of the variation in the data, and the original set of variables is reduced to 1. 
Therefore, the partition of the principle components and the principle vectors give 
P = P P 
r\ rm-l 
and T = T T (4.3.16) 
The original measurement matrix is projected onto the principle component space and the 
residual space, i.e. 
X = f1P1T + fm,PmT1 =C,X + Cm,X (4.3.17) 
A A A _ ~ A 
where the projection matrices C, = P^ and Cm., = Im - C,. 
After the PCA model is constructed, the model is used for fault detection. Consider a 
new sample vector x(k) that is scaled to zero mean and unit variance. Following the 
decomposition with (4.3.14) 
x(k) = x(k) + e(k) = C1x(k) + (lm-C1)x(k) (4.3.18) 
where x(k) and e(k) are the projection of the sample vector onto the principle component 
and residual space respectively. 
To perform sensor fault detection using PCA, the vector's projection on the residual 
space is monitored. For normal operating conditions, e(k) will be small due to estimation 
errors and noise. A statistic, called the squared prediction error (SPE), is a measure that 
indicates how good the fit of the PCA model is. The SPE is monitored at every time 
instant k and is defined as 
SPE(k) = |e(k)|2=|(lin-C1)x(k)|2 (4.3.19) 
For normal operation, the SPE is lower than a threshold S2 [58] 
SPE(k) = £s2PE (4.3.20) 
The test suggests an abnormal condition if the SPE surpasses the selected threshold. For 
the investigation, the SPE is estimated empirically using simulation data. 
After a fault condition is detected, the faulty sensor must be isolated. An iterative 
variable reconstruction method is proposed by [59]. This method is based on the 
following procedure: 
48 
Sensor fault detection and isolation 
• Suppose the i-th sensor in the measurement vector x(k) is faulty. 
• For m sensors, assume one is faulty and reconstruct the variable using the PCA 
model and the remaining m-1 healthy sensors. 
• Recalculate the SPE after reconstruction. 
Therefore, if the i-th sensor is reconstructed, the SPE will decrease below the threshold 
since the fault is corrected. However, if a non faulty sensor is reconstructed, the SPE will 
stay approximately the same. 
Next, the variable reconstruction method is presented. The estimation of the i-th 
variable from the x(k) measurement vector is expressed by (4.3.21) 
xi(k) = x(k)ci =[cl 0 cl,]x(k) + ciixi(k) (4.3.21) 
with [c, c2 ...cm] = P,P,T and c^ = [ci; c2i ...c^] = [c* cu c^l. The subscripts -i and +i 
denote a new vector formed by the first (i-1) and last (m-i) elements of the sample vector 
respectively. 
From (4.3.21), it can be seen that the value of the faulty sensor is included in the 
estimate of the reconstructed sensor. Therefore, the i-th variable Xj(k) is fed back to the 
input of (4.3.21) and iterated until it converges. The converged value of Xj(k) for 
Cn < 1 is approximately 
TcT o £l 
*.(k)- ! - J*(k) (4-3-22) 
Dunia et al. [59] states that the iteration will always converge. 
An important feature that influences the accuracy of reconstruction is the number of 
principle components. As shown in (4.3.16), the principle components are split into 
separate matrices to allow projection onto the component space and the residual space. 
To determine the optimal number of components for the component space, the variance 
of the reconstruction error is used (VRE) [60]. The proposed index has a minimum 
corresponding to the best reconstruction. The variance of the reconstruction error, in the 
direction £;, is 
VREi ES var(£(x(k)-Xi(k))) (4.3.23) 
where ^ = [0...1j...0]T is the fault direction vector. To determine the optimal number of 
principle components 1, the following objective is minimized 
m 
min^qiVREj (4.3.24) 
49 
Sensor fault detection and isolation 
where q; denotes positive weights (can be chosen identical to equalize the reconstruction 
errors). 
To illustrate the application of the PCA method for sensor FDI, an example is 
presented next. Real noisy sensor data from the prototype PBMM plant (discussed in 
Chapter 7) is used and include the following process variations: MPS start-up, normal 
power operation, injection and extraction together with valve operation, and MPS shut 
down. 
In this example, measurements from 16 pressure and temperature sensors are 
considered. The measurements correspond with the eight inlet monitoring locations 
identified for the PBMR MPS and are shown in Fig. 4.3.3 (a) and (b). Since the variables 
are of different units (kPa and °C), the data can be either standardized by dividing each 
column with its standard deviation or separate models can be constructed for each 
variable type. The latter is selected and two PCA models are trained for the pressures and 
temperatures respectively. The data is divided that approximately 90 % is used for 
training the PCA models and 10 % for testing the various indices. The different data 
segments are illustrated in Fig. 4.3.4. Figures 4.3.3 and 4.3.4 show that the data segment 
used for testing (800 samples) includes steady state operation, injection and extraction. 
2000 4000 6000 8000 
Time (s) 
(a) 
350 
300 
O u
„ 250 -
G 200 -
01 
Q. 
is 150 ,-.--""" . 
1- r /* 
100 1 / 
/ 50 T5 original / - T5 reconstructed 
/ T8 original , % 
2000 4000 6000 8000 
Time (s) 
(d) 
Fig. 4.3.3 Measured and PCA reconstructed values for T and P sensors: (a) measured P; (b) measured T; 
(c) reconstructed P5 and PS; (d) reconstructed T5 and TS. 
50 
Sensor fault detection and isolation 
start-up \ normal power operation shut down 1 
'. : * * : 1 6349 6350 7150 7151 8300 9250 | 
^ 
training 
-> y ^-
testing 
Y 
training 
; 
Fig. 4.3.4 The data segments used for training and testing the PCA models. 
An initial requirement for the PCA models is the determination of the optimal number of 
principle components. The first step is to calculate the minimum VRE by reconstructing 
each sensor from the remaining whilst varying the number of principle components. The 
optimal number of principle components in the PBMM corresponds to 3 and 4 for the 
pressure and temperature models respectively. Figure 4.3.3 (c) and (d) illustrate the 
measurements and reconstruction estimates for the turbine (5) and pre-cooler (8) sensors. 
By taking into account the nonlinear nature of the process, the estimations are 
acceptable. To verify that the proposed PCA models are sufficient for FDI, the four 
sensor faults depicted in Fig. 4.2.1 (b) - (d) are introduced in the data. Since the pressure 
data clearly shows when injection and extraction commences, the pressure model is used 
as an example. Figure 4.3.5 illustrates the calculated SPE index for the fault free 
measurements. The figure shows that for the fault free case, a threshold of §\m = 0.5 is 
selected. In addition, Fig. 4.3.5 (b) shows that the SPE remains below the threshold if a 
sensor is estimated. 
The four sensor faults are introduced in the HPC pressure data P3 at t = 200 seconds 
(6550 seconds in Fig. 4.3.3 (a)). The fault magnitudes are as follows: bias fault of 1 kPa, 
drift fault of 0.005 kPa/s, sensor noise with a = 1 and a complete failure resulting in a 
reading of 0 kPa. Accordingly, the SPE is used for fault detection and the faulty sensor is 
reconstructed. The SPE indices and the reconstruction estimates for the four faults are 
illustrated in Fig. 4.3.6 (a) - (h). 
0 100 200 300 400 500 600 700 800 
Time (s) 
0 100 200 300 400 500 600 700 800 
Time (s) 
(a) (b) 
Fig. 4.3.5 The SPE index for the pressure PCA model: (a) without a sensor fault; (b) HPC pressure (P3) 
estimated. 
51 
Sensor fault detection and isolation 
100 200 300 400 500 600 700 800 
Time (s) 
100 200 300 400 500 600 700 800 
Time (s) 
(a) (b) 
100 200 300 400 500 600 700 800 
Time (s) 
100 200 300 400 500 600 700 800 
Time (s) 
(c) (d) 
100 200 300 400 500 600 700 800 
Time (s) 
(e) 
100 200 300 400 500 600 700 800 
Time <s) 
190 
185 
180 Jr *-
•n 175 
*170 
0) 
m 165 en 
g> 
0. 160 
155 
150 ffi I measured I 
| reconstructoq 
I46 100 200 300 400 500 600 700 8 10 
Time (s) 
(f) 
200 
180 
160 
„ 140 
to 
^ 120 
% 100 
in 
S 80 
L 60 
40 
20 I measured 
, | racmslmcled 0 0 100 200 300 400 500 600 700 8 00 
Time (s) 
(g) (h) 
Fig. 4.3.6 The SPE indices for fault detection together with the reconstructed sensors. 
52 
Sensor fault detection and isolation 
The left column in Fig. 4.3.6 illustrates the variation in the SPE index during fault 
induction, whilst the right column shows the estimation of the faulty sensor. Although 
reconstruction normally commences after the SPE threshold is exceeded, P3 is estimated 
for the entire test set in this example. 
Fig. 4.3.6 shows that the SPE index is below the selected threshold prior to induction 
of the different faults. In Fig 4.3.6 (a), the SPE index surpasses the threshold without any 
time delay after a bias fault is induced. Therefore, by comparing the SPE indices before 
and after reconstruction, i.e. Fig. 4.3.5 (b) and Fig. 4.3.6 (a), P3 can be isolated. 
The figure shows that for the drift fault, the SPE index surpasses the threshold only 
after some time delay. This is expected since the sensor bias is relatively small for this 
period. The results therefore indicate that the time delay before fault detection is a 
function of the magnitude of the drifting sensor and the threshold of the SPE. In Fig. 
4.3.6 (d), the SPE index is actually only surpassed at approximately 280 seconds when 
reconstruction commences. 
Fig. 4.3.6 (e) shows that the SPE index fluctuates repeatedly for a noisy or degraded 
sensor. Therefore, it is concluded that larger values for the SPE index at irregular time 
intervals can be an indication of a noisy sensor. To identify spikes in the sensed values, 
the large SPE index will normally appear less frequently. In general, all the reconstructed 
sensor estimates are in good agreement with the original measured values before fault 
induction. 
In conclusion, the PCA model was able to reduce the high redundancy among the 
process variables. Although the PBMM plant represents a nonlinear process, most of the 
variation in the data was captured by forming linear relations between the various sensed 
values. Also, by using the SPE index for fault detection, the induced faults are detected 
promptly without uncertainty. The major disadvantage of this method is that multiple 
sensed variables cannot be corrupted simultaneously, since the reconstruction procedure 
assumes that (m-1) sensors are healthy. However, for the PBMR MPS, the assumption is 
made that at any time instant, (m-1) measurement sets will be available with at least one 
healthy sensor out of three. Therefore, the difficult task is to identify a minimum of 7 
healthy pressure and temperature sensors in different measurement sets out of a total of 
48. 
In the following section, sensor fusion is discussed. In hardware redundant sensor 
networks, sensor fusion gives a more reliable variable estimate if more than one healthy 
measurement is available. 
4.4 Sensor fusion 
In hardware redundant sensor networks, several concurrent values are normally available 
for each measured variable. Since these values are unavoidably corrupted with random 
noise, no single sensor can be relied on to give a truthful reading. Also, two sensor 
readings may be within their operational limits, but lie at different ends of the valid 
measurement region, resulting in a distribution for each measurement. Consequently, 
multiple sensor information is combined to provide more reliable and consistent readings 
for the sensed variables. 
53 
Sensor fault detection and isolation 
In the thesis, the task of sensor data fusion is accomplished by taking the average of the 
measured quantity weighted by the corresponding confidence values. A fuzzy validation 
curve is proposed by [61] and is based on fuzzy rules that define the centre of the 
validation curve. Since the statistical properties of each measurement distribution 
(residuals) are estimated off-line, these properties are utilized to assign a confidence 
value for the new measurement. In the investigation, the residual mean (ideally zero) is 
used to centre the validation gate. 
Firstly, the curve is normalized to scale the confidence values between 0 and 1. As 
discussed in section 4.3.3, the absolute limits of the sensed variable are defined as ± 2a, 
and accordingly, the borders of the validation gate are set to these values. For the normal 
probability density function, the confidence values are computed as follows 
x = 4 
0 
l-e "right 
x, < -2a 
(Vn? |V(-2a)V 
e { "left J _g{ "left J 
-2a < xi < \x 
\x<Xj <2a 
l_e{ *left J 
fx,-n? fxs-(2a)f 
UrightJ _g{ bright J 
rx,-(2a)f 
(4.4.1) 
X: >2a 
where x is the confidence value for the sensor, xj is the sensor value, u. and a are the mean 
and standard deviation of the normal distribution (residuals), and aieft, ar;ght are 
modification parameters for the left and right sides of the validation gate. These 
parameters determine the width of the curve to compensate for external effects such as 
temperature changes. The fused estimate is calculated by 
5>iT(xi) 
— izL 
5M*) 
(4.4.2) 
with Xf the fused estimate and Xj the i-th sensor reading. In order to demonstrate the 
importance of the fusion algorithm, an illustrative example is shown in Fig. 4.4.1. A 
simple sine wave is measured with three sensors and corrupted with random noise. The 
original signal is then compared with the fused estimate, and the residuals are calculated 
for each sensor accordingly. Consequently, u. and a are approximately 0.0001 and 0.5 for 
54 
Sensor fault detection and isolation 
~ 14 
100 
Time (s) 
(a) (b) 
Fig. 4.4.1 Fusion algorithm applied to random measurements: (a) 3 sensors with noise; (b) fused estimate. 
each sensor. The validation gate is therefore centred on zero mean and the limits are set to 
± 1 kPa. Fig. 4.4.1 (b) depicts the fused estimate obtained with (4.4.1) and (4.4.2). The 
figure shows that the fused estimate closely follows the original signal. 
To show the improvement in measurement accuracy, the mean squared errors (MSE) 
of the original and fused measurements are computed and the results are summarized in 
Table 4.4.1. The table shows that the fused estimate of the sensors produce a better 
approximation of the original signal than the sensors' mean. Also, it is observed that the 
MSE decreases with an increase in the amount of sensors utilized for a measured 
variable. 
In conclusion, it is demonstrated that the sensor fusion algorithm produces a better 
estimate of the measured variable compared to the mean of the sensors. In addition, it is 
observed that variable estimation is more accurate if measurement redundancy increases. 
4.5 Sensor validation and fusion module architecture 
This section discusses a comprehensive methodology for intelligent sensor validation and 
fusion based on the PBMR MPS. By applying an integrated architecture of the methods 
discussed, the uncertainty inherent in single sensor information is minimized. The 
Simulink® SEnsor validatioN and fuSion module, SENSE, intelligently combine 
information from different sources to increase the accuracy and integrity of the 
measurements. 
SENSE exploits the redundant sensor information by analyzing data from sensors 
independently, sensors in a measurement group, the immediate history of the previous 
sample window, and functional redundant sensor estimates. Consequently, the 
methodology is more robust than any single technique in the sense that different fault 
sensitivities can be incorporated into each. 
Combination Sensor 1 Sensor 2 Sensor 3 Mean (2)* Mean (3)* Fused (2)* Fused (3)* 
MSE 0.11533 0.12131 0.10307 0.06327 0.05304 0.02195 0.01192 
Table 4.4.1 MSE results obtained for the sensor fusion algorithm. * () denotes the amount of sensors. 
55 
Sensor fault detection and isolation 
The SENSE methodology comprises the following steps: 
• Sensor signal pre-processing. 
• Consistency analysis among each redundant measurement set. 
• Fusion- 1st layer. 
• Sensor configuration selection. 
• PCA model analysis, fault isolation and sensor reconstruction. 
• Fusion - 2nd layer. 
• Residual statistical evaluation, fault detection and isolation. 
• Fusion - 3rd layer. 
The basic steps of the methodology are depicted in Fig. 4.5.1 and a more detailed 
reasoning structure of SENSE is illustrated in Fig. 4.5.2. 
First, the information from the eight measurement channels/sets comprising 3 
sensors per channel is pre-processed by means of the absolute limit and maximum 
process change indices. The obvious false readings are filtered out based on the absolute 
limit index. Following this, the maximum process step is checked for the remaining 
variables and adjusted accordingly. Initially, a large index is chosen to allow the filtered 
signal to follow the sensed values exactly. Systematically, the index is lowered to filter 
out the effects of noise and large measurement variations. 
Sensor channels 
Pre-processing 
Consistency 
analysis 
Fusion - Is1 
Sensor 
configuration 
PCA 
*? Fault isolation < 
Residuals Statistical analysis 
Fusion - 2n' 
Reconstruction 
Fusion - 3rd 
Fig. 4.5.1 A flow chart illustrating the SENSE architecture. 
56 
Sensor fault detection and isolation 
min(cri,ju) 
Sensor channels 
rp 
r(k) = x,(k)-xni(k) 
x,{k) < 2<T 
Pre-processing Fault 
isolation 
Axik) < os x,{k) = x,{k-\) + dir{x,(k)}.<js 
'p=Ep:k 
Consistency analysis ] 
2 I |2 " 2 
«-i 
Fusion - Is 
median 
.(*)=zzzzzzzzM.-.*r 
Configuration 
<* 
1=1 c=l rf=l «=1 /=1 g=l A=l 
jc(jt) = i(jt) + e(jt) 
Z*/T(*«) 
^/3/ — ' 
Z^U) 
I Fusion - 3rd 
! Healthy */« 
median 
! Fusion - 2ni 
SPE(/fc)< S' 
Principle component analysis 
i(*) = 
c_T 0 cl, 
l-c„ <k) 
Fig. 4.5.2 A reasoning map illustrating the SENSE architecture. 
Next, the filtered signals are validated for consistency using the non-temporal parity 
space algorithm. As discussed, isolation is not possible during this phase for multiple 
failures in a measurement channel. Therefore, the inconsistent signals are not combined 
before PCA analysis. If a single fault occurs, the faulty sensor is isolated and the 
remaining consistent signals are transferred to the first fusion layer. 
Since the residual estimates are not available at this stage, consistent signals are 
fused based on the median of the readings. Computing the median rather than the mean 
eliminates any bias induced by outliers within the absolute limits of the sensor. 
Alternatively, sensor confidence values can be determined based on the previous sample 
window (residuals). By providing the PCA model with a fused estimate, the uncertainty 
in each measurement channel (single sensors) is minimized. 
57 
Sensor fault detection and isolation 
Following this, an intelligent search algorithm determines the total number of unique 
sensor configurations and organizes them with a decrease in the likelihood of failure 
according to a variance and mean (VM) index. The VM index is determined based on the 
minimum variance and mean of the (t-l)-th sample. Each configuration includes eight 
sensor channels with at least one sensor or fused estimate per channel. The total number 
of unique sensor configurations is given by sc 
s t u v w x y z 
Sc(k) = IIIIIIXShb,..,h]T (4.5.1) 
a=l b=l c=l d=l e=l f=l g=l h=l 
with s, t,..., z the number of sensors available in each channel or fused estimate. The 
impact of the number of faulty sensor configurations on the PCA model is depicted in 
Fig. 4.5.3. The following constraints are applicable to the figure: 
• At any given time, a maximum of 16 sensors may fail. This constraint is based on the 
assumption that there is always one healthy sensor per measurement channel in the 
PBMR MPS. 
• Sensor configurations must include at least 7 healthy ones to be functional; the eighth 
can be reconstructed (PCA algorithm requires m-1 healthy sensors). 
The figure shows that the number of functional sensor configurations (red) decreases 
sharply if the number of faulty sensors increases. Therefore, more configurations will be 
tested by the PCA model before a functional configuration is found. However, this 
procedure is greatly reduced by means of selecting the most likely functional sensor 
configurations using the VM index. 
Subsequently, each sensor configuration is projected onto the component and 
residual space by means of the PCA model. The squared prediction error is computed and 
the process is repeated until a functional sensor configuration is established (SPE < 52). 
To establish functional redundancy, each of the healthy sensors is set to zero and the 
signal reconstructed utilizing the remaining measurements. By providing functional 
redundant estimates, the uncertainty in each measurement channel is also decreased. 
Fig. 4.5.3 Sensor configurations based on the number of faulty sensors. 
58 
Sensor fault detection and isolation 
Next, the PCA model estimates and the first fusion layer are fused (also based on the 
median) to combine all the redundant sensor information. The fused estimate serves as 
the expected value for each individual measurement channel. 
To compute the sensor residuals, the original sensor values are subtracted from the 
fused estimate. Since the sensor residuals are assumed to be normally distributed for 
normal operation, their statistical properties (mean and variance) are monitored for any 
changes. Any variation in these properties will firstly identify and isolate a faulty sensor 
and secondly, characterize the type of sensor fault. It must be noted that since the residual 
distributions are applied, the trade-off is between sample window size and approximation 
error. A smaller sample size will promote early detection but also increase the 
approximation error. 
To isolate the sensor faults, a simple rule-based expert system is devised and is 
illustrated in Fig. 4.5.4. The expert system consists of if-then statements and the ruling is 
based on the characteristics of the residuals. The list of rules is given below: 
• If ju = N and o2 = S and skew = S, then sensor = normal. 
• If ju = N and o2 = L and skew = S or L, then sensor = noise. 
• If ju = L and o2 = N and skew = S, then sensor = dead. 
• If ju = N and o2 = N and skew = S, then sensor = stuck. 
• If ju = S and o2 = S and skew = S and {bias(/) - bias (t-l)} ~ c, then sensor = bias. 
• If ju = S and o2 = S and skew = S and {bias(/) - bias (t-l)} # c, then sensor = drift. 
with N, S and L indicating negligible, small and large values. The thresholds for each of 
these values are selected based on the specific application. Also, it is important to note 
that the methodology do not only rely on statistical residual evaluation to isolate faulty 
sensors. During each phase, sensors that do not comply with the given technique's criteria 
for normal operation are isolated and excluded from the estimates. 
The final step is to calculate confidence values for each healthy sensor based on the 
sensor's residual distribution. To compute the values of the third fusion layer, the healthy 
sensors are fused together using the proposed method described in section 4.4. This 
produces the final estimate for each measurement channel. 
To evaluate the fault detection and isolation capabilities of SENSE, the methodology 
is applied to a practical system next. 
7N o
2 Skew 
negligible small large negligible small large 
Normal Bias| *C » Drift 
Fig. 4.5.4 Decision-tree illustrating the expert system reasoning. 
59 
Sensor fault detection and isolation 
4.6 Application of sensor FDI in the PBMM and PBMR 
This section discusses the implementation of the sensor fault diagnosis methodology in a 
Brayton cycle-based PCU. Two case studies are presented and comprise applications in 
the PBMR and PBMM. In both case studies, random noise with different variances is 
added to the plant data. As a result, three different signals are generated for each 
measurement channel. The corresponding notation employed to identify the 24 pressure 
or temperature sensors are illustrated in Fig. 4.6.1. In each of the case studies, eight out of 
a maximum of 16 sensor malfunctions are introduced and include, noise, spikes, dead 
sensors, bias and measurement drift. 
The a priori information of the validation and fusion methodology comprises the 
following parameters: 
• Noise properties of the measured variables/sensors. 
• The absolute limits 2a of the sensor distributions. 
• The maximum process change index Ax; per time step. 
• The parity vector threshold 8n. 
• The PCA model together with the number of principle components. 
• The SPE threshold 5 2SpE-
• The fusion modification indices aieft, aright. 
• The thresholds that define the fault range indices N, S and L. 
It is important to note that some of the parameters must be defined for different process 
variations, for example, a valve change or operating point change (injection/extraction) 
requires a larger maximum process step. As discussed, this step will typically be small 
during steady state to minimize the effects of random noise. 
4.6.1 Case study 1 
In the first case study, the PBMM temperature data (normal power operation) depicted in 
Fig. 4.3.3 (b) is used. A preliminary step is to analyze the noise properties of each sensor 
distribution during fault free operation. From the data, the absolute limit for each variable 
is calculated (approximately 1.2) and the maximum process step is selected. Following 
this, the PCA model is trained with approximately 90 % of the sensor data, i.e. trained 
with the median of the three noisy sensor values. To determine the optimal number of 
principle components, the variance of the reconstruction error is used. The minimum 
VRE is obtained utilizing a PCA model with four principle components. Lastly, the SPE 
Sensor 
channel 
Sensor 
channel 
sc2 
Sensor 
channel 
5C3 
Sensor 
channel 
5C4 
Fig. 4.6.1 Sensor notation utilized in the two case studies. 
60 
Sensor fault detection and isolation 
1 ?-
0.9-
0.8-
0.7-
2550 3550 4550 5550 6550 7550 
Time (s) 
Fig. 4.6.2 The SPE index for the temperature PCA model (normal power operation). 
threshold is calculated for the entire dataset (single sensors) during fault free operation 
and is shown in Fig. 4.6.2. The figure shows that the minimum SPE threshold can be 
selected as 0.6. For this case study, eight faults are induced in the PBMM sensor data and 
are listed in Table 4.6.1. The table shows that for two measurement channels, multiple 
sensor failures occur. 
Following the pre-processing algorithm, each of the measurement channels is 
checked for consistency and the parity space method promptly identifies non-consistent 
measurements. In the case of faults 3/4, and 6/7, no unique fault isolation is observed 
after 5500 and 7500 seconds respectively. Therefore, the redundant signals are not fused 
in the respective measurement channels after these time intervals. 
During each sample interval, a healthy sensor configuration is quickly identified by 
means of the minimum VM index and the PCA model. The SPE index calculated for each 
of these sensor configurations is shown in Fig. 4.6.3. The figure indicates that the average 
SPE index is lower than the index observed in Fig. 4.6.2. The reason for this is that the 
fused estimates for the different measurement channels provide a better approximation of 
the sensed variable than any single sensor. 
Next, the healthy sensor estimates are calculated using the PCA model and fused 
with the original sensor configurations. These values serve as the expected estimates for 
each measurement channel. The residuals are determined for all the sensors and are 
illustrated in Fig. 4.6.4. In the figure, the three redundant measurements are depicted by 
different colours. 
Sensor Time (s) Type Magnitude 
1. ?Sll 3000 Noise CT = 1 
2. ?S23 Random Spikes Random 
3. *31 5500 Dead 0 
4. S33 4100 Bias + 1°C 
5. ?S52 6200 Drift + 0.005 °C/s 
6. ?S61 7500 Bias + 1.5 °C 
7. ?S62 4800 Noise CT = 1 
8. ?S83 3800 Dead 0 
Table 4.6.1 Summary of PBMM temperature sensor faults: Case study 1. 
61 
Sensor fault detection and isolation 
:.j 
0.8 
0.7 
0.6 
0.4 
2550 3550 6550 7550 4550 5550 
Time (S) 
Fig. 4.6.3 The SPE index for the healthy sensor configurations selected for each sample interval. 
The figure shows that the different faults can be detected and isolated by means of the 
sensor residuals. Moreover, since the sensor residuals are computed independently, the 
isolation of multiple simultaneous sensor failures is possible. By applying the rule based 
expert system with a sample size of 10, each of the faults is correctly isolated. An 
important observation is that the residual distributions are centred on zero mean, which 
indicates that sensor malfunctions can be detected during variations of the normal 
process. For the healthy sensors, the variations in the residuals are mainly caused by 
measurement noise. 
To emphasize the improvement in measurement accuracy, the MSE of the residuals 
is computed and the results are summarized in Tables 4.6.2 and 4.6.3 respectively. 
Channel Sensor 1 Sensor 2 Sensor 3 Mean Fused 
1 0.09685 0.09536 0.09610 0.06265 0.02628 
2 0.09523 0.09591 0.09860 0.07145 0.02880 
3 0.09923 0.09278 0.09517 0.06651 0.02976 
4 0.09339 0.09635 0.09847 0.06682 0.02870 
5 0.09979 0.09660 0.09747 0.06682 0.02719 
6 0.09616 0.09468 0.09666 0.06452 0.02819 
7 0.09716 0.09321 0.09641 0.06610 0.02836 
8 0.09641 0.09376 0.09797 0.06457 0.02693 
Table 4.6.2 MSE results obtained for sensor fusion with no faults present (case study 1). 
Channel Sensor 1 Sensor 2 Sensor 3 Mean Fused 
1 0.27826 0.09678 0.09357 0.07773 0.03211 
2 0.09376 0.09747 0.09904 0.07285 0.02976 
3 49.8407 0.09376 0.65675 5.16653 0.03553 
4 0.09309 0.09511 0.09716 0.06656 0.02897 
5 0.09803 4.21563 0.09536 0.61043 0.02989 
6 0.21492 0.21632 0.09591 0.09236 0.03460 
7 0.09653 0.09666 0.09523 0.06595 0.02853 
8 0.09853 0.09691 17309.5 1924.68 0.03276 
Table 4.6.3 MSE results obtained for sensor fusion with the eight faults present (case study 1). 
62 
ON U> 
4^ 
H 
sr 
3 
3 
3 
00 
Residuals 
p- /—N 3 
w ^ 1 
<JQ° *~^ 3 
5 o> w 
o s* 
o 
a 
o 
s 
o 
Ol 
o 
OD 
o 
^1 
o 
Residuals Residuals 
f>. 
Residuals 
6 o P - Residuals k ~ ° 
as 
S-
*-* 3' 
a a 
a a. 
o 
o a 
Sensor fault detection and isolation 
For the eight measurement channels, the MSE is calculated over the entire dataset for: the 
single redundant sensors, the mean of the redundant sensors, and the fused estimate 
obtained with the proposed methodology. 
Table 4.6.2 lists the results obtained for the fault free measurements. The table 
shows that even though the mean of the sensors generates a better approximation for each 
measurement channel, the fused estimate is much lower. Table 4.6.3 shows that if sensors 
fail in a measurement channel, the mean is not an accurate approximation for the sensed 
variable. Also, the results show that even though multiple sensor failures occur, the 
methodology still gives an accurate estimate although slightly poorer than for a single 
failure. Therefore, the conclusion is drawn that the methodology gives a better estimate if 
the number of healthy sensors increases. 
Figure 4.6.5 illustrates the fused estimates for each of the measurement channels. 
The figure shows that the fused values produce much 'smoother' signals. As a result, the 
final estimates correspond to values that are less corrupted with sensor noise. 
4.6.2 Case study 2 
In the second case study, data is generated by means of the PBMR Flownex model that is 
discussed in Chapter 3. The simulation starts at steady state 100 % MCR with all the 
bypass valves fully closed. The following process variations commence after this: valve 
operation between 100 and 250 seconds, extraction between 500 and 950 seconds, 
injection between 1300 and 2650 seconds, extraction between 4200 and 6200 seconds 
and lastly injection between 7500 and 8000 seconds. In order to evaluate sensor FDI 
during normal variations of the process, the pressure measurements are considered 
(temperature stays approximately constant). The pressure data for the eight measurement 
channels are illustrated in Fig. 4.6.6 (a). 
In this case study, the same procedure is followed as discussed for case study 1 and 
is therefore not explained in detail again. The SPE index for the fault free measurements 
is depicted in Fig. 4.6.6 (b) (single sensors). The figure shows that the minimum 
threshold can be selected as 0.6. 
2550 3550 4550 5550 6550 7550 
Time (s) 
Fig. 4.6.5 Fused estimates for the PBMM temperature measurements after sensor validation. 
64 
Sensor fault detection and isolation 
2000 4000 6000 
Time (s) 
2000 4000 6000 
Time (s) 
(a) (b) 
Fig. 4.6.6 The PBMR sensor data: (a) measured P; (b) SPE index for PCA model. 
The eight faults considered for the pressure sensors are listed in Table 4.6.4. In this case 
study, multiple sensor failures occur in measurement channel 2. The parity space 
algorithm will therefore not be able to isolate the faults after 3600 seconds. The 
calculated SPE index for each of the selected healthy sensor configurations is illustrated 
in Fig. 4.6.7. The figure shows that the average SPE index for the fused estimates (first 
fusion layer) is lower than the index for single sensors. 
The sensor residuals for each measurement channel are depicted in Fig. 4.6.8 (a)-(h). 
Sensor Time (s) Type Magnitude 
1. Sn 2500 Dead 0 
2. s2l 1100 Bias + 1.5 kPa 
3. s22 3600 Noise CT=1 
4. 531 4700 Bias + lkPa 
5. 542 5300 Drift + 0.005 kPa 
6. 551 Random Spikes Random 
7. 563 6400 Noise <7 = 1 
8. s72 7800 Dead 0 
4 Summary of PBMR pressure sensor faults: C 
0.9 -
0.8 ? 
0.7 ? 
0.6 • 
LU a. 0.5 
in • 
0.4 -
0.3 -
0.2 ill!'Jill ml) IT 
0.1 
0^^^ 2000 4000 600C 8000 
Time (s) 
Fig. 4.6.7 The SPE index for the healthy sensor configuration selected for each sample interval. 
65 
Sensor fault detection and isolation 
4000 6000 
Time(s) 
(a) 
4000 6000 
Time(s) 
(c) 
2000 4000 6000 
Time(s) 
(e) 
4000 6000 
Time(s) 
4000 6000 
Time(s) 
(g) (h
Fig. 4.6.8 The sensor residuals for the eight measurement channels (a-h signifies channel 1-8). 
66 
Sensor fault detection and isolation 
As observed in case study 1, the changes in the residuals are characteristic of the specific 
types of sensor faults. Also, the figure shows that the proposed methodology can isolate 
multiple simultaneous sensor failures during different variations of the process. 
The results for the MSE of the residuals are summarized in Tables 4.6.5 and 4.6.6 
respectively. Similarly, the results are consistent with those observed in case study 1. In 
Table 4.6.6, the errors in the faulty sensors are large whilst the methodology generates 
accurate estimates of the sensed variables. Also, similar to case study 1, the fused 
estimates are slightly less accurate if more than one sensor fails. The final fused values 
for each measurement channel are illustrated in Fig. 4.6.9. 
In conclusion, the two case studies presented are indicative of real processes and 
demonstrate that the proposed methodology can promptly detect and isolate any of the 
sensor malfunctions during normal variations of the process. In addition, sensor fault 
diagnosis is possible for multiple simultaneous sensor failures. 
4.7 Summary and conclusions 
This chapter discussed an integrated framework for intelligent sensor validation and 
fusion in the PBMR MPS. The proposed methodology comprises a combination of 
techniques that exploits their individual strengths. 
Channel Sensor 1 Sensor 2 Sensor 3 Mean Fused 
1 0.07701 0.07563 0.07530 0.04627 0.02051 
2 0.07767 0.07728 0.07596 0.04558 0.02286 
3 0.07618 0.07574 0.07629 0.04635 0.02155 
4 0.07486 0.07701 0.07712 0.04657 0.02059 
5 0.07601 0.07486 0.07601 0.04584 0.02238 
6 0.07634 0.07612 0.07469 0.04580 0.02135 
7 0.07773 0.07629 0.07596 0.04644 0.02193 
8 0.07667 0.07773 0.07579 0.04631 0.02226 
Table 4.6.5 MSE results obtained for sensor fusion with no faults present (case study 2). 
Channel Sensor 1 Sensor 2 Sensor 3 Mean Fused 
1 0.07601 0.07612 2979538.5 331081.8 0.02512 
2 1.83846 0.21400 0.07579 0.22156 0.02859 
3 0.41152 0.07728 0.07491 0.07986 0.02515 
4 0.07667 23.0236 0.07767 2.68435 0.02509 
5 0.08049 0.07607 0.07524 0.04822 0.02187 
6 0.07546 0.07431 0.13587 0.05856 0.02292 
7 0.07535 306871.6 0.07773 34117.26 0.02347 
8 0.07640 0.07790 0.07740 0.04670 0.02235 
Table 4.6.6 MSE results obtained for sensor fusion with the eight faults present (case study 2). 
67 
Sensor fault detection and isolation 
9000 
8000 
—. 7000 
% 6000 
£ 
g 5000 
£ 4000 
3000 
2000 
1000 
0 2000 4000 6000 8000 
Time (s) 
Fig. 4.6.9 Fused estimates for the PBMR pressure measurements after sensor validation. 
Section 4.2 listed the most common faults that cause sensors to fail or give erroneous 
information. The following sensor malfunctions are investigated: sensor bias or offset, 
dead sensors, excessive noise, sensor drift and random spikes. 
The different measurement validation techniques are described in section 4.3. The 
first technique employed, the non-temporal parity space, checks for consistency among a 
set of redundant sensors. In the case of the PBMR, three hardware redundant sensors are 
employed to monitor critical process parameters. The measured signals are pre-processed 
to exclude or condition any obvious false readings prior to the consistency check. 
After the first fusion layer, sensor configurations that comprise inconsistent and 
fused measurement channels are validated with the PCA model. A healthy sensor 
configuration is characterized by a minimum of seven healthy or fused sensor estimates 
in different measurement channels. 
Following the second fusion layer, fault isolation is achieved by monitoring the 
sensor residual distributions with a set of statistical indices. Since each residual 
distribution is calculated independently, multiple simultaneous sensor faults can be 
detected and isolated. 
Section 4.4 discussed the fusion technique that is used to calculate the final sensor 
estimates. The technique is based on the average of the measured quantities weighted by 
corresponding confidence values. 
Section 4.5 described the structure of the proposed methodology SENSE, whereafter 
section 4.6 presented two case studies. The case studies confirmed that the methodology 
can be successfully applied to a practical Brayton cycle-based PCU. 
Some of the important conclusions reached in this chapter are: 
• Most of the process variations during normal power operation can be captured with 
a linear PCA model, and is for the investigation, sufficient for the task of sensor 
FDI. However, to model all the system characteristics and minimize the estimation 
error, a nonlinear PCA technique will ideally be employed. 
• To ensure that the methodology produces accurate sensor estimates, the different 
validation techniques must be used in combination. Some of the limitations of the 
individual methods are: 
68 
Sensor fault detection and isolation 
- No unique fault isolation is possible with the non-temporal parity space algorithm 
in the case of multiple sensor failures. 
- The PCA method requires that m-1 sensors are healthy. This makes the method 
highly likely to fail in the case of multiple sensor malfunctions. 
- Statistical evaluation of the redundant sensor signals alone will not be sufficient 
for sensor FDI. Since the mean of the sensor distributions constantly change due 
to process variations, fault isolation will be impossible in the case of multiple 
sensor failures. This is due to the fact that there will be no mechanism available 
for cross-reference among redundant measurements, i.e. all sensors will indicate 
different values. 
• To provide the PCA model with a healthy sensor configuration (in the case of 
multiple failures), an intelligent search algorithm determines the total number of 
unique sensor configurations and organizes them with a decrease in the likelihood 
of failure according to a VM index. By applying this algorithm, the PCA model can 
be used for sensor FDI even though multiple sensors fail. This conclusion is based 
on the assumption that not all the redundant sensors may fail in (m-1) measurement 
channels simultaneously. 
• An important attribute of the proposed methodology is that incipient faults (drift) 
can be identified and isolated in multiple sensors by means of evaluating the sensor 
residuals individually. 
In addition to the motivations presented in previous chapters, the sensor fault diagnosis 
approach is developed since the sensors that measure critical process variables are located 
within the PPB in the PBMR. This arrangement requires that sensors can only be 
removed or tested once the PPB is open for maintenance, which will normally only be 
once every fuel cycle. Therefore, by implementing the proposed approach on-line, sensor 
readings can be validated in real-time. 
Before the h-s graph approach for process fault diagnosis is presented in Chapter 6, 
two traditional methods of process FDI are applied to the PBMR MPS to emphasize their 
general shortcomings and the difficulties inherent in the implementation of the specific 
methods. 
69 
Application of traditional fault detection techniques 
CHAPTER 5 
Application of traditional fault detection techniques 
This chapter presents two traditional process FDI techniques that are more readily used 
for NPP monitoring. The two methods are limit value checking and residual monitoring 
using a mathematical model of the plant. In order to demonstrate their advantages and 
limitations, both techniques are applied to the PBMR MPS. 
5.1 Introduction 
To date, most NPPs use two traditional methods for the task of process supervision. 
These methods are based on either a model-based or model-free representation of the 
process. The main objective of this chapter is to show a general implementation of the 
two methods in the PBMR MPS and investigate the limitations and complexities of these 
methods. 
In section 5.2, the limit value checking approach is applied to the temperature and 
pressure measurements in the PBMR MPS. The 25 single faults listed in Chapter 3 are 
induced and the general limitations of this model-free method are illustrated. 
Section 5.3 emphasizes the complexities in obtaining an accurate mathematical 
model that captures all the system dynamics in the PBMR MPS during normal power 
operation. Although this goal is achievable, the result is a transfer function that is 
unwieldy and too computational complex for real-time fault diagnosis. In order to 
simplify the mathematical model structure, only the most dominating system dynamics 
are included. As a result, the accuracy of the mathematical model is compromised. The 
development of a linear turbine model for the PBMR MPS is used as an example. 
The chapter is summarized and concluded in section 5.4 
5.2 Model-free methods - Limit value checking 
This approach is widely used in practice because of its simplicity and reliability. Limit 
value checking performs well if the measurements are wide sense stationary and the 
system operates close to steady state. Their implementation however becomes more 
70 
Application of traditional fault detection techniques 
involved and nontrivial if plant variables vary widely due to transient variations of the 
process. The method is based on setting limits (thresholds) above and below the normal 
range of variation, and faults are indicated if the limits are surpassed. Setting the limits is 
crucial and is usually done by incorporating system operational knowledge or by 
trail-and-error. Whilst implementation and maintenance are simple, the limit checking 
approach has several serious limitations: 
• The fault detection sensitivity is highly dependent on the threshold width. Ideally, the 
limits are set around the normal variation of the fault free measurements. If the limits 
are set too wide apart, the fault detection scheme will be insensitive to incipient fault 
behaviour (a small deviation in the measurements will not exceed the thresholds). On 
the other hand, if the limits are too narrow, the number of false alarms will increase 
due to the normal variation of the process and noise. Also, if the mean of the 
measurements is not centred between the thresholds, false alarms may be generated 
due to normal plant variations. 
• Single faults may cause several measurements to exceed their limits due to fault 
propagation through the system. This will trigger numerous alarms which makes 
isolation of the original fault very difficult. 
• In a closed loop system like the PBMR, feedback systems may correct the effect of 
process faults to some extent, causing the measurements to remain within the normal 
limits. Detection of these faults will only be possible once the changes in the 
measurements are large enough (early detection not possible). 
• Faults may cause sporadic alarms, i.e. alarms are not generated throughout the 
duration of the fault condition, but only when the data exceeds the limits. An 
example is a heat transfer area fault in the heat exchangers. Although debris on the 
heat transfer area could trigger an alarm, fragmentation break off may cause the data 
to settle between the thresholds again. An alarm will only be triggered once the fault 
becomes large enough to surpass the thresholds again. This makes the decision 
between an ongoing fault condition and a transient effect very difficult. 
To demonstrate the performance of the method in a closed system, the 25 single faults are 
induced in the PBMR MPS. The eight temperature and pressure measurements are 
captured with the system operating at 100 % MCR. To simulate random noise with a = 2 
and zero mean, the steady state temperatures and pressures are varied by approximately 
± 2 °C and ± 2 kPa. To allow for the variation in magnitude, the thresholds are set to an 
upper limit of +3 °C or kPa and a lower limit of -3 °C or kPa from the mean. Also, due to 
normal variations of the process, the thresholds are adaptive (not stationary) and move 
with the varying signals. 
Figure 5.2.1 shows an example of the temperature and pressure measurements for 
the HPT inlet and the recuperator LP inlet respectively. The graphs illustrate the normal 
variation of the noisy signals (blue) and the centred fault free limits (red). With the limits 
set, the fault magnitudes are increased to 1 %. The results are listed in Table 5.2.1 for 
71 
Application of traditional fault detection techniques 
HPT temperature signal Recuperator LP pressure signal 
0 500 1000 1500 2000 2500 3000 3500 4000 
Time (s) 
(a) 
0 500 1000 1500 2000 2500 3000 3500 4000 
Time (s) 
(b) 
Fig. 5.2.1 Plant measurements at different nodes during normal fault free conditions: (a) HPT inlet 
temperature; (b) recuperator LP inlet pressure. 
each of the 25 fault conditions. An alarm is indicated by ' 1' if a measurement limit is 
exceeded. 
The following limitations of the method became apparent: by placing empirical 
thresholds on the measurements, some of the fault conditions can not be detected at an 
early stage. Faults 3, 7, and 25 did not surpass the thresholds for a small change in fault 
magnitude. In this case, the trade-off is between the threshold range and the false alarm 
Node Fault number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 
Tl 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
T2 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 
T3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
T4 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
T5 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 
T6 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 
T7 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 
T8 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 
PI 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 
P2 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 
P3 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 
P4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 
P5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 
P6 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 
P7 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 
P8 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 
Table 5.2.1 Fault alarms for the 25 single faults in the PBMR (alarm = 1, faulty component node = bold). 
72 
Application of traditional fault detection techniques 
rate. Reducing the thresholds will improve the missed detection rate of small faults with 
incipient fault behaviour, but will increase the number of false alarms due to the presence 
of measurement noise. 
The second drawback observed is the effect of fault propagation. Some fault 
conditions exceeded several thresholds, which will in reality set off a multitude of alarms. 
Also, it is important to note that the sequence of alarms is not unique, which will make 
fault isolation impossible. For example, faults 5, 6, 17 and 18 triggered the same set of 
alarms which makes the decision regarding fault isolation a nontrivial task. 
Although the implementation of the method is straightforward, it is evident that the 
limit value checking method has several shortcomings if applied to the PBMR MPS, and 
is therefore not recommended as a viable solution to process fault diagnosis in the next 
generation type nuclear power plants. 
5.3 Model-based methods - Mathematical models 
In model-based FDI systems, the measured variables are compared to model estimates 
and various techniques are used to evaluate the residuals. Mathematical models are 
usually developed to describe the dynamics of the physical system by means of 
differential or difference equations for a specific operating region [41]. The effectiveness 
of model-based methods, however, relies on an accurate mathematical model of the 
process, and building a nonlinear model of a complex plant is very difficult. In addition, 
priori knowledge about system behaviour is usually exploited in these models, which are 
limited in the next generation type nuclear power plants. 
To date, simulation software like Flownex are used to model thermodynamic 
processes, but results and system parameter dependencies can be difficult to interpret and 
identify. In addition, developing an accurate model of the system is the responsibility of 
the engineer, and it is usually not clear from the simulations what the important 
parameters are that drive the system dynamics. 
This section describes the development of a mathematical model (state equations) of 
the MPS power turbine, which can be used in model-based FDI techniques like state 
observers. Although the model gives insight into parameter dependencies and system 
dynamics, some drawbacks of this type of modelling are emphasized. 
5.3.1 Model development and assumptions 
In this section, a linear model of the turbine is developed and applied to the PBMR by 
means of a state observer. A linear model is developed since most model-based methods 
assume system linearity, and a nonlinear system requires linearization around an 
operating point or region [40]. The modelling method is discussed next. 
A simplified linear modelling method was developed by [62] for the purpose of plant 
control of a three-shaft Brayton cycle and is adapted for the investigation. This technique 
is suitable for the purpose of FDI seeing as the model is based on perturbed values that 
characterize system changes (representative of faults or process variations). 
73 
Application of traditional fault detection techniques 
The following assumptions are made regarding the linear model and modelling method: 
• The variations in state variables are the result of perturbations in some of the other 
state variables due to transients (process variations or faults). 
• The system operating point is the steady state values of the system prior to the 
system states being perturbed by a transient. 
• The change in system states is small enough for the system to be modelled by a 
linear approximation during the period of interest (normal power operation). 
Assume a system during steady state with no faults present, which is a function of other 
variables, is described by 
y = f{xl,x2) (5.3.1) 
If one or all of the variables are perturbed by a small change due to a fault, the result is 
y0 + Ay = f{xoi + Ax1,x02 + Ax2) (5.3.2) 
with: the subscript 0 representing the steady state values; 
Axi, Ax2 the changes in variables ;ci and X2, and 
Ay the resulting change in y due to the change in variables. 
Applying a first order Taylor expansion (motivated by the third assumption listed above) 
8y y
0 + by*>f(xn,x{a)+-2-
ox, 
Ax,+ dx
2 
Ax2 (5.3.3) 
The steady state term is removed since the partial derivatives are evaluated at the 
operating point, and as a result, (5.3.3) reduces to 
Ay*-^Axl+-^Ax2 (5.3.4) 
9*! dx2 
5.3.2 The linear turbine model 
The following section describes the development of the linear turbine model. The model 
is based on the following assumptions (assumptions are made to obtain a lower order 
dynamic model): 
• There is no significant volume inside the turbine (infinitely fast pressure transfer). 
74 
Application of traditional fault detection techniques 
e = Qft,/P, Q' = Q^T,/P, 
Fig. 5.3.1 Turbine efficiency and pressure ratio to non dimensional mass flow. 
• The turbine is described by two maps, i.e. the non dimensional mass flow and non 
dimensional speed versus pressure ratio and isentropic efficiency (see Fig. 5.3.1). 
• Apart from the gas flow and shaft, no energy flows occur across the boundaries of 
the turbine (e.g. heat losses). 
• The inlet and diffuser volumes are modelled by separate models. 
• There is no energy storage within the turbine itself and energy storage due to the 
shaft inertia and volumes (due to the pressure vessel) are modelled by separate 
models. 
• The steady state turbine maps are valid under transient conditions. 
Therefore, the turbine model is reduced to a system with four inputs and outputs 
respectively and is depicted in Fig. 5.3.2. Table 5.3.1 lists the variables and their 
nonlinear equations that are used in the development of the linear turbine model. 
Inputs 
Inlet pressure ^ 
Outlet pressure ? 
Inlet temperature ? 
Shaft speed *? 
Outputs 
-> Outlet temperature 
-> Mass flow 
?> Efficiency 
?> Shaft power 
Fig. 5.3.2 The input-output measurements of the turbine model, 
75 
Application of traditional fault detection techniques 
Variable Description Equation 
P\ Total inlet pressure 
P2 Total outlet pressure 
h Total inlet temperature 
h Total outlet temperature 
N Shaft speed 
N' Non dimensional speed N' = Nl4i[ 
Q Mass flow 
Q' Non dimensional mass flow Q = QjtJpl 
w Shaft output power W = Qcp{t,-t2) 
y Ratio of specific heats of the gas r = cpjcv 
Pr Pressure ratio Pr=P\IPl 
n Isentropic efficiency __ '2A-I 1
 p-(r-Vr)_i 
Table 5.3.1 Summary of turbine model variables. 
The linear model of the turbine uses the perturbed values as described above with the 
steady state terms removed. The linear pressure ratio approximation is given by 
Apr=^.Ap1+^.Ap2 (5.3.5) 
dp, dp2 
To determine the linear mass flow, it is seen in Fig. 5.3.1 that the pressure ratio is a 
function of the non dimensional mass flow and non dimensional speed, and hence it 
follows that 
Ap=^-A& + &-W (5.3.6) 
r dQ' 8N' 
Since the non dimensional mass flow and the non dimensional speed are calculated by the 
equations listed in Table 5.3.1, (5.3.6) can be expanded with the chain rule for derivatives 
and gives 
A 8P 
Apr = 
f*rt xnt xm \ dpJdN' .„ 8N' ^ 
dQ' 
dQ' ^ dQ' dQ' A 
dQ * dp, Fl dtx + -8N' -AN + At KdN a/, ', (5.3.7) 
From (5.3.7), the mass flow rate can be determined as 
76 
Application of traditional fault detection techniques 
AQ = 
rdp^
+dp^ Atx-^.AN 
1 57V 
dQ 
(5.3.8) 
The expansion of change in efficiency follows the same method as for the mass flow 
expansion. The isentropic efficiency is a function of the non dimensional mass flow and 
non dimensional speed, and hence it follows that 
dQ' dN' (5.3.9) 
Since the non dimensional mass flow and the non dimensional speed are given by the 
equations listed in Table 5.3.1, (5.3.9) can be expanded with the chain rule for derivatives 
and gives 
At] = drj dQ' dQ' A ^ dQ' A dQ' A 8Q * 8
Pl
 Fx 8t
x
 l 
\ drj r 
8N' 
dN' A Ar dN' A ?AN + At, 
dN dtx (5.3.10) 
Given the efficiency, the linear change in outlet temperature can be expressed as 
dL . dL A dL . At
2=^-Atl+^^-Apr + —
L-AT] 
dtx dpr df] (5.3.11) 
Assuming that the specific heat of the gas at constant pressure stays the same, the linear 
change in shaft power is given by 
dW dW AW= — -AQ + — -AT 
dQ dT 
(5.3.12) 
with the change in temperature given by AT= (t\-t2). 
It is important to note that the mechanical efficiency of the turbine must be included in 
the shaft model and is for this reason not accounted for in the turbine model itself. The 
turbine equations can now be written in matrix form as 
1 0 
-c5c9 1 
0 -c 
-~cn 0 
0 0" "A0" 
0 0 Af] 
1 0 At2 
1 
"12 1_ 
AW 
C\ C14 Si. _SL 
C« Cl3 c« 
c6cg 0 C7C10 
C1C18 C2C18 0 
0 0 0 
Cie. Ap, 
C13 Ap, 
C8C10 + C9C20 A7V 
Cl7 Af, 
C12 J 
(5.3.13) 
77 
Application of traditional fault detection techniques 
The descriptions and steady state values for the coefficients used in (5.3.13) are given in 
Table 5.3.2. 
Coefficient Description Steady state value 
C\ dp
l 
1 
P02 
Cl 9b. dp
2 
Poi 
„2 P02 
Cl 
dp, 
dQ' 
Slope of pressure ratio and obtained from pressure ratio map at operating point 
c4 dp, dN' 
Slope of pressure ratio to non dimensional mass flow and obtained from 
pressure ratio map at operating point 
Cs 
dQ' 
dQ 
Q'o 
Q0 
c6 
dQ' 
dp, Pm 
en dN' dN 
Ct 
dN' 
dt, 2'oi 
c9 dt] dQ' 
Slope of isentropic efficiency and obtained from efficiency map at operating 
point 
C\0 
dt] 
dN' 
Slope of isentropic efficiency to non dimensional mass flow and obtained from 
efficiency map at operating point 
Cll 
dW 
dQ 
w0 
Qo 
C\l 
dW 
dT Q0cP 
Cl3 
dp, 
dQ Qo 
C]4 
dp, 
dpx />01 
Cl5 dN C^ 
C\6 
dp, 
dt, c^-c^ 2r01 42r01 
CM 
dt2 
~dh ri(p^
r-l) + l 
78 
Application of traditional fault detection techniques 
Cl8 
dt2 
8Pr 
_ '0lA)2 
c17. 
An 
C19 
dt2 
dt] 
'01 
c17. 
>7o 
C20 dt
x 2^o. 
Table 5.3.2 Summary of turbine model coefficients. 
It is important to note that the shaft dynamics are not included in the turbine model since 
the perturbation in torque due to a change in shaft power or speed is given by the net 
torques acting on the shaft. Owing to the fact that the net torques is a function of the 
turbine and compressors torques (connected to a single shaft), the shaft model is devised 
separately. 
The turbine state space model equations, derived in explicit form, is given in matrix 
form by (5.3.14) as 
A0 
At] 
At2 
AW 
cr^u 
6 9 5^9 
q-C14 
^8 +C19 
^-^4 
V C13 J 
c6c9 + 
c c ——— 
V. ^ C13 )) 
\ 
( 
f 
<\9 
\ v 
C6^ + 
f 
<\~<\n 
V ^3 ))j 
C2^ + 
V 
^3 
ClC£<pY> 
<&u + CfifiPv} 
IV ^Xi J 
<\5 
C1C\0 ~*~C& 
' c > 
°\i) 
f 
C~f\d ~T~C5C9 
f f 
V °aJJ 
<\9 
V v 
^5 
YS 
c5c9 
\ °i3 JJ) 
<\6 
£^C[0 +C9C20 +C£9 
/ > 
u16 
f 
^7+^S 
f 
£^C[0 +C9C2o +C5C9 — 
°yi)) 
c]2+cn 
f \ 
^6 
V % <$J 
,+ 
^0 +t9C20 + 
V, V J) 
(5.3.14) 
4P2 
AY 
A?, 
with Q the mass flow, 77 the isentropic efficiency, t\ and ti the inlet and outlet 
temperatures respectively, N and W the shaft speed and output power, p\ and pi the total 
inlet and outlet pressures respectively. 
As discussed, the turbine model uses perturbed values and hence, cannot give a 
steady state solution, since by definition, all the states are zero for steady state (zero 
change). A precondition for model development is to obtain a steady state solution to 
determine the model coefficients listed in Table 5.3.2. This can be done by using 
simulation software or plant measurements. 
79 
Application of traditional fault detection techniques 
In order to validate the linear turbine model, the nonlinear PBMR Flownex model is 
firstly used to obtain a steady state solution to determine the model coefficients. 
Following this, the following inputs are varied around their steady state values: the inlet 
temperature 900 °C, the outlet pressure 2975 kPa and the turbine speed 6000 rpm. The 
inlet pressure is varied and depicted in Fig. 5.3.3. The perturbed transient values 
(Flownex minus the steady state solution) is entered into the linear model and the results 
are shown in Fig. 5.3.4 (a) to (d) for the turbine mass flow, efficiency, outlet temperature 
and output power. 
The results presented in Fig. 5.3.4 (a) to (d) show that the linear turbine model 
correlates well with Flownex, but showed some deviations for temperature and 
efficiency. This is an indication that not all the dynamics are included in the model. 
Next, the model is validated with a fault condition. A turbine pressure ratio fault, i.e. 
fault 12 described in Chapter 3, is induced. A scaling factor of 0.001 *t is subtracted from 
the turbine pressure ratio (starting at t = 100 seconds) in the nonlinear model to emulate 
an internal turbine fault. The outputs of the models are shown in Fig 5.3.4 (e) to (h). To 
detect the fault condition, a state observer is selected and is discussed next. 
Given the linear equations are in state space form and parameters A, B and C are 
known, a state observer can be designed [4] for fault detection as 
x = Ax(t) + Bu(t) + He(t) 
e(t) = y(t)-Cx(t) 
(5.3.15) 
with H the observer feedback and e(t) the output error. Since the fault acts as an output 
change Ay, the state estimation error is then given by 
x = [ A - HC] Ax (t) - HMfM (t) 
e(t) = Cx(t) + HfM(t) 
(5.3.16) 
with x(t) = x(t)-x(t) and fM the output fault acting through M. The output error e(t) 
can now be used as residual to detect the fault condition. 
9200 , 
9000 y/ / . 
^ 8800 - r^ ^ 
§ 8600 
jjj 8400 
-
Q. 
o 8200 
8000 
7800 
50 150 200 
Time [s] 
Fig. 5.3.3 Inlet pressure transient for the turbine. 
80 
Application of traditional fault detection techniques 
220 p 
215-
210-
. 205-
' 200-
I 195 
190-
i 
? 185 
180-
175 
17QL 
570 
580 
II 
Flownex 
' Linear model -
-
150 200 
Time [s] 
(a) 
520 
Flownex 
Linear model 
^ 
? 
0 50 100 150 200 250 300 350 
Time [s] 
(c) 
215p 
210-
205-
— 200-
gl95-
I 190-
5= 
8 185-
cn 
S 180-
175 
170-
I65J-
570 
560 
Flownex 
Linear model „ 
4/ 
K -
150 200 
Time [s] 
(e) 
II 
?3 520-
O 
510 ? 
50oL 
Flownex 
Lineer model 
? 
^tr" k; 
150 200 
Time [s] 
0.92 
0.918 
0.918 
0.914 
>. 0.912 
.2 0.91 u 
i£ 0.908 
0.906 
0.904 
0.902 
0.9 
Flownex 
Linear model 
? 
150 200 
Time [s] 
(b) 
4.6 
X10 
Flownex 
4.4 Linear model 
4.2 , 
I* ^/ 
H» 
? i: 
0 
32 
3 
100 150 200 
Time [s] 
(d) 
0.92 p 
0.918-
0.916-
0.914 
>. 0.912 
.2 0.91 -
£ 0.908 ? 
0.906 ? 
0.904 ? 
0.902 -
0.9 
Flownex 
' Linear model 
'i - -
150 200 250 300 350 
Time [s] 
(f) 
4.6 
x10 
Ftewnex 
4.4 Linear model 
4.2 „ s. 
I* 
^<> ^ f i: 
3.2 
3 
150 
Time 
200 250 
[s] 
(g) (h) 
Fig. 5.3.4 Flownex and the linear turbine model response for an inlet pressure transient: (a)-(d) fault free; 
(e)-(h) pressure ratio fault. 
81 
Application of traditional fault detection techniques 
With the linear turbine model developed, the model must be extended to incorporate the 
dynamics of the system. The system dynamics are illustrated in Fig. 5.3.5 and show the 
interactions between the individual models that will make up the total turbine model. The 
dynamics include: 
• Leak flows from the HP manifold to the turbine inlet and diffuser respectively. 
• The shaft dynamics. 
• Energy storage from the shaft inertia and the inlet and diffuser volumes. 
• Pressure losses and flow resistances in the turbine inlet and diffuser. 
• Gas momentum effects. 
The symbols depicted in Fig. 5.3.5 are as follows: V= gas velocity, x = torque, M= gas 
momentum, Q = mass flow, N = shaft speed, W = Power, p = pressure, / = temperature. 
With all the variables identified, it is now possible to determine the system equations 
for the total turbine model. Following this approach, the linear equations that describe the 
complete PBMR MPS can be formulated and must include: heat exchanger models, 
turbine model, compressor models, valve and pipe models, volume models, leak flow 
models, energy storage models (e.g. heat storage) and the reactor model. 
All these models must be included since [43] states that models of high accuracy are 
necessary for FDI and some models interact between system components. Looking at 
(5.3.14) describing a single model and figure 5.3.5 showing the total model, it is evident 
that combining all these models to obtain a state space model that captures all the 
nonlinear dynamics in the PBMR MPS, will be a burdensome task. This is not only a 
very complex process, but will result in symbolic state space equations that may become 
unwieldy and unmanageable in size. Additionally, several supporting measurements must 
be taken from the system to calculate the variables defined in these models. 
HP Manifold 
Model 
Volume 
Model 
&WHPC AW^c 
Fig. 5.3.5 Diagram illustrating the interaction between the individual models that make up the total turbine 
model in the PBMR. 
82 
Application of traditional fault detection techniques 
5.4 Summary and conclusions 
This chapter discussed the general implementation of two traditional methods for process 
fault diagnosis in the PBMR MPS. 
In section 5.2, the model-free limit value checking technique is examined. To date, a 
major problem in nuclear power plants is that of alarm flooding during transients due to 
fault propagation, even though this has been reduced to a certain degree by intelligent 
alarm handling systems [63]. This difficulty also became apparent during the 
investigation. Another drawback of the technique is that an in-depth diagnosis of the fault 
is generally not possible. Therefore, it is concluded that limit value checking is not a 
suitable solution for process FDI in a complex dynamic system like the PBMR. 
Section 5.3 discussed a linear mathematical modelling method for components in a 
complex dynamic system. Although the development of a linear model gives insight into 
the dynamic behaviour of the system, some drawbacks are identified if applied to the 
PBMR. The following can be concluded about mathematical modelling for the purpose of 
process fault diagnosis in the PBMR MPS: 
• The model structure that describes all the dynamics in the system must be known 
exactly, which is seldom true in practice, especially for a new generation type NPP 
like the PBMR. The result is modelling uncertainty and modelling errors. 
• The level of complexity is much higher due to the complex nonlinear dynamics of 
the system. 
• The amount of monitored system variables increases because of the input 
dependencies of the models. 
• Most model-based FDI techniques assume system linearity, and a linear 
transformation describing the system around the operating point or region is thus 
necessary. In addition, most techniques require a state space representation or 
transfer function of the system to evaluate the monitored residuals. 
All these difficulties motivated the development of the h-s graph approach for process 
fault diagnosis in the PBMR MPS. 
The following chapter presents the development of the h-s graph approach for 
process FDI in a Brayton cycle-based PCU. In this chapter, the Flownex measurements 
are corrupted with random measurement noise and NO signal conditioning (i.e. SENSE) 
is applied before process fault diagnosis. 
83 
CHAPTER 6 
Development of the h-s graph approach for process FDI 
This chapter discusses the development and implementation of the h-s graph approach 
for process FDI in a thermodynamic system. The approach is demonstrated by means of 
an implementation in the PBMR MPS. The single and multiple faults listed in chapter 3 
are induced in the system and the approach is applied to detect and isolate the fault 
conditions. 
6.1 Introduction 
In Chapter 3, the three main fault classes in the PBMR MPS were identified and 
discussed. In this chapter, the structure for developing the h-s graph approach for process 
FDI is firstly described. Following this, the method is applied to the PBMR MPS and the 
32 single and multiple faults are induced in the system. Lastly, a procedure is derived to 
detect and isolate the fault conditions. 
In section 6.2, the properties h and s are described and their importance in a 
thermodynamic system is explained, after which the construction of the h-s graph is 
illustrated in section 6.3. Following this, the effects of the different fault conditions are 
visualized on the h-s graph. Although the changes in system states are reflected on the h-s 
graph, the objective is to use the graph to derive uncorrelated static reference fault 
signatures. Two different methods are derived in section 6.5 and include the error and 
area error methods. 
In section 6.6, the properties of plant noise is firstly described after which the %2 
hypothesis test is presented for fault detection. Fault isolation is achieved by means of the 
h-s graph and the fault isolation index (FII) is defined for fault pattern recognition. To 
reduce the reference fault database to a minimum, a single fault extraction procedure is 
devised to isolate single faults from multiple fault conditions. The results show that the 
extraction procedure together with static reference h-s fault signatures reduces the fault 
database to a minimum. 
In order to shift the reference h-s graph to different operating points, a shape 
reconstruction technique is derived in section 6.7. The latter together with the variation 
surface, allows normal process variations to be characterized with only one reference 
model. 
In section 6.8, the h-s graph approach is implemented in the PBMR MPS with added 
measurement noise. Lastly, section 6.9 summarizes the chapter. 
84 
Development of the h-s graph approach for process FDI 
6.2 Enthalpy and entropy - An overview 
In a thermodynamic system, the closed cycle comprises several common open systems. 
For example, in an HTGR, open systems include turbines, compressors, heaters, heat 
exchangers, valves etc. These systems usually perform or require shaft work instead of 
boundary work. In order to solve these open systems, the first law of thermodynamics as 
developed for closed systems is usually applied. This can be a cumbersome task and gave 
rise to a new property enthalpy h. The property h is a combination of the internal energy 
(«) and the energy (Pv) necessary to get the working fluid flowing. 
For a closed system undergoing a constant pressure process, the heat transfer (Q) is 
calculated with the first law for steady state, open systems 
Q = m(u2-ul + P(v2-vl)) (6.2.1) 
with m the mass flow and v the specific volume. Substituting the u + Pv term, the heat 
transfer in terms of change in h gives 
Q = m(h2-hl)=mcp(T2-Tl) (6.2.2) 
The change in enthalpy [64] with constant pressure specific heat (cp) is thus calculated by 
means of (6.2.3) 
Ah=h2-hl = cp{T2-T1) (6.2.3) 
Equation (6.2.3) is valid since the specific heat of the working fluid, helium (He) is 
assumed to be independent of the temperature. According to (6.2.2), (6.2.3) and assuming 
the working fluid is heated without a change in pressure, the change in h will equal the 
heat transfer. Also, the first law states that the energy flowing into the system must equal 
the energy flowing out of the system (conservation of energy), therefore, consider a 
turbine losing heat and performing shaft work as an example. The amount of enthalpy 
converted into shaft work is decreased with heat loss. This concept is illustrated in Fig 
6.2.1 and is expressed as 
mhln = mhoul + W + Q (6.2.4) 
if the first law is applied. From the first law, it is derived that energy cannot be created or 
destroyed. It follows that energy can only be converted from one form to another, and the 
second law of thermodynamics and the property entropy s sets limits to this energy 
conversion. Also, s is a measure of the amount of internal energy not available to perform 
work. The change in specific entropy [65] in compressible gas flow undergoing a change 
in temperature is given by 
As = s2-s, =c An^-Rln^- (6.2.5) 
2 1 , j, j, 
85 
Development of the h-s graph approach for process FDI 
control surface 
Fig. 6.2.1 Conversion of enthalpy for a steady flow turbine. 
where T, R and P are the temperature, gas constant and pressure. Entropy is an abstract 
property and cannot be measured like T and P. For open systems, the entropy change is 
always positive except during heat rejection. Also, increasing the heat energy increases 
the entropy generation 
To sum up some common causes of entropy change or generation, the term 
"irreversibility" is firstly defined. In an irreversible process, everything (system and 
surroundings) cannot be reversed to the original condition without an input from the 
environment. Some factors that cause a thermodynamic system to be irreversible [65] 
include fluid flow with friction, mixing of gases which differ with regard to 
thermodynamic state, compression, expansion, and heat transfer across a finite 
temperature difference. The irreversibility of a system is important since entropy is 
generated in a real irreversible process which can be an indication of component or 
process faults. Table 6.2.1 summarizes the h and s relationships of the individual open 
systems in the PBMR MPS. In Table 6.2.1, the relatively small kinetic QAV2) and 
potential (gz) energies are not shown, but are modelled in Flownex [49] (conservation of 
energy of a control volume). 
Component H s 
Valve K = hou, 
Pipe K = K,„ P P =P -AP 
Turbine (adiabatic) minK = mouAu< + Khafl ^sin + Sgm = ms0Ut 
Compressor mJttn + w*4=m««h<»« ms,n = msoul+Sgen 
Heat exchanger (™,AL+(™,AL = KA,L>+KA,)ZP Sgen = mSHP + mSLp 
Reactor wA + fi^A* 
Table 6.2.1 Relationships for h and s in open systems. 
86 
Development of the h-s graph approach for process FDI 
In Table 6.2.1, Sge„ is the entropy generation term and not the entropy change As = s2 - s,. 
This term is dependent not only on the start and end states, but on the path of the process 
and hence not a thermodynamic property. The entropy generation term is given by [65] 
Sge„=s2-Si-j;f (6.2.6) 
with SQ/T the entropy transfer. From (6.2.6), it is evident that the change As can be 
rearranged to include the Sgen and entropy transfer terms. This form is convenient and can 
easily be calculated with (6.2.5). To summarize, a few properties regarding h and s are 
emphasized to show why these variables could be used to identify normal irreversibility 
or changes (fault conditions) in the thermodynamic state of a system [65]: 
• Enthalpy increases with fluid friction (more energy required to get the fluid flowing). 
• If the working fluid is heated at constant pressure, the change in enthalpy will equal 
the heat transfer. 
• The second law states that the entropy of a closed system can never spontaneously 
decrease. 
• The spontaneous flow of heat between bodies at different temperatures increases the 
entropy. 
• The entropy generated in a system is directly proportional to the decrease in turbine 
shaft work. 
• Entropy transfer accompanies heat transfer. 
• There is no entropy transfer associated with the transfer of energy as work or power. 
• If the turbine outlet temperature is constant, the decrease in shaft power is 
proportional to the rate of entropy generation. 
These properties are important and make h and s an ideal combination to analyze the 
thermodynamic state of the process. Since the normal system irreversibility can be 
calculated or approximated, any changes not associated with these conditions can thus be 
linked to a contributing fault condition. 
6.3 Attributes and construction of the h-s graph 
To visualize the state of the thermodynamic Brayton cycle, the properties h and s are 
plotted on an h-s graph, also called a Mollier diagram. The theoretical h-s graph 
comprising the eight sub-processes (nodes) is illustrated for a closed Brayton cycle in 
Fig. 6.3.1 (a). To construct the h-s graph, rand P are measured at the inlets of the eight 
sub-processes in the PBMR MPS. By applying (6.2.3), (6.2.5) and assuming the constant 
pressure specific heat is not dependent on the temperature, h and s are calculated for the 
eight nodes respectively. The transformation from T-P to h-s is important and is 
motivated in Appendix B. 
87 
Development of the h-s graph approach for process FDI 
i _ Constant pressure 
— Practical cycle /A 
i^L.. .I-' j^iS 
.]?&! 
T"7- —*TI ^f' g As 
3 1 
—? 
Practical cycle 
(a) (b) 
Fig. 6.3.1 The h-s graphs of a closed Brayton cycle: (a) theoretical; (b) simplified. 
In Fig. 6.3.1 (a), the curvature in the theoretical plot (nodes 2-3, 4-5-6 and 7-8-1) are 
due to a smaller step size for T and P. Since data for the PBMR MPS is only captured at 
the eight nodes, the graph reduces to a simplified form (straight lines between nodes) and 
is shown in Fig. 6.3.1 (b). The simplified h-s graph will be used in the calculations 
throughout the study to minimize computational complexity. 
As discussed in Chapter 3, the primary power control of the PBMR is achieved by 
adding or removing helium inventory from the PPB with the ICS. This type of control 
allows a constant shape of the h-s graph at all power levels above 40 % MCR. For 
reduced power levels, the graph shifts to a lower absolute pressure, but maintains the 
shape (proved in Appendix B). Fig. 6.3.2 depicts the shift direction as well as the shape 
of the h-s graph for a decrease in absolute pressure. The figure shows that the graph 
moves to the right for a decrease in power and to the left for an increase in power. The 
constant shape of the graph will therefore allow a reference model that remains invariant 
over the power range (subject to no bypass valve operation). Figure 6.3.3 shows the 
theoretical h-s graph (small step size) for the practical cycle of the PBMR MPS. The 
specific entropy is referenced to T0 = 0 °C and Po = 10 MPa. 
h 
Decrease in pressure 
Fig. 6.3.2 Theoretical h-s graph of the Brayton cycle for full as well as reduced power (ICS control). 
88 
Development of the h-s graph approach for process FDI 
5000 
4500 
4000 
3500 
* 3000 
£ 2500 
c 2000 LXJ 
1500 
1000 
500 
0 
123456789 10 11 
Entropy IkJZ(kg.K) 
Fig. 6.3.3 The h-s graph for the PBMR, shown at full and reduced power (ICS control). 
6.4 Effect of faults on the h-s graph 
This section illustrates the effects of the 32 faults on the h-s graph. It is important to note 
that the main objective of the study is to use the h-s graph for fault diagnosis and not to 
investigate the causes for the changes in h and s with regard to physics and 
thermodynamics . To show an example of a typical h-s cause-effect scenario, an increase 
in the pre-cooler inlet resistive losses (fault 23) is discussed for a 5 % change. 
The result of fault 23 is an increase in the main flow resistance (class 2) and is 
modelled in Flownex as a change in the resistive losses of the pre-cooler inlet pipe (nodes 
8-1). In order to compare the amount of entropy generated and the available work 
delivered for an equal amount of heat energy supplied, the reactor power for 100 % MCR 
is fixed and the recuperator bypass valves (RBP) controlled to ensure an inlet and outlet 
reactor temperature of 500 °C and 900 °C respectively. Table 6.4.1 lists the Flownex 
results and the h-s calculations for fault 23. 
The table shows that the fault condition results in higher cycle temperatures and an 
increase in pressure loss between the turbine and the LPC. Furthermore, a reduction in 
mass flow rate is observed throughout the system. The h-s calculations show that entropy 
generation increases, whereas the work delivered by the turbine is considerably less than 
for the fault free case. According to [65], entropy generation and pressure loss increase 
with frictional fluid flow whilst available work in the system is lost. In this case, it is 
evident that useful work must be invested to push the working fluid through the "faulty" 
pipe section and therefore, the net result is a reduction in available power. 
The remaining fault conditions in the PBMR MPS can be described with similar 
explanations regarding cause and system irreversibility. The main objective now is to 
investigate the effect of each fault on the shape of the h-s graph. 
3This is a specialized field of study and the reader is referred to [65] for further reading regarding 
entropy generation and causes of thermodynamic irreversibility in theory and real-world applications. 
89 
Development of the h-s graph approach for process FDI 
Node/ 
component 
Normal Fault 23 (5 % change) 
P AP m h s (kJ/ P AP m h s(kJ/ 
(kPa) (kPa) (kg/s) (kJ/kg) [kg.K]) (kPa) (kPa) (kg/s) (kJ/kg) [kg.K]) 
1-2 2909.80 2179.29 201.34 128.76 2.98 2864.82 2149.18 197.07 134.63 3.04 
2-3 5089.09 30.82 202.56 583.04 3.15 5014.00 29.97 198.29 590.91 3.20 
3-4 5058.27 3919.76 202.55 130.98 1.82 4984.03 3994.86 198.28 129.78 1.84 
4-5 8978.03 81.58 190.21 582.27 1.93 8978.89 72.85 186.00 592.41 1.96 
5-6 8896.44 345.13 190.08 2618.80 5.64 8906.04 328.73 185.87 2578.14 5.59 
6-7 8551.31 5580.78 190.08 4695.75 7.89 8577.31 5163.69 185.87 4701.04 7.89 
7-8 2970.53 41.66 201.19 2660.71 8.00 3413.62 284.97 196.88 2862.63 7.96 
8-1 2928.86 19.06 201.33 735.96 4.70 3128.65 263.83 197.06 986.92 5.14 
Heat transfer*/power (kW) 
LPC 91471.30 ! 59907.98 
HPC 91405.74 ( 51715.97 
Turbine 364027.61 317093.88 
Reactor* 395314.30 395200.00 
Recuperator* 387164.06 369220.46 
Pre-cooler* 122254.54 167957.9 
Intercooler* 91568.30 < 91436.43 
Table 6.4.1 Flownex results for fault 23. 
In Chapter 3, three fault classes comprising single and multiple fault conditions are 
identified for the PBMR MPS. To illustrate the effects of the faults on the h-s graph, the 
fault conditions are modelled in Flownex for normal power operation at 100 % MCR. In 
the simulations, the reactor outlet temperature and manifold pressure are controlled at 
900 °C and 9 MPa respectively. Figures 6.4.1 to 6.4.4 illustrate the shift of the h-s graph 
for each fault in addition to the fault-free reference graph. The figures show a 1 %, 5 % 
and 10 % change in the fault magnitude for single faults (1 to 25) and a 1 % and 5 % 
change for multiple fault conditions (26 to 32). 
The figures show that the fault conditions are reflected as a distinguished shift in the 
h-s graph with regard to direction and magnitude. This feature will be used as basis for 
the h-s graph approach for process fault diagnosis. Although the shift may appear to be 
similar for some fault conditions, the distinctive properties of the graph will become 
evident once the fault signatures are derived. In addition, the figures show that the 
combination of single faults also results in a distinguished shift in the h-s graph. Although 
this feature increases the isolation ability of the approach, the reference fault database 
will become unmanageable in size if all the fault combinations are modelled. Therefore, it 
would be favorable to classify any combination of faults with single reference faults only. 
To illustrate that the shift in the h-s graph itself also reflects the combination of 
single faults, the graphs of the multiple faults are compared to the graphs of the 
contributing single faults. The graphs of the multiple faults (Fig. 6.4.4 (b) - (h)) show that 
the single fault illustrated in Fig. 6.4.1 (g) is clearly one of the contributing faults. This 
observation is based on the shift direction of the h-s graphs between nodes 1 and 2. By 
repeating this principle and evaluating each section of the h-s graph, the second fault can 
also be identified. To simplify this process, the single fault extraction method is devised 
and is discussed in section 6.6.4. 
90 
Development of the h-s graph approach for process FDI 
4500 
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(h) fault 8 
Fig. 6.4.1 The h-s graphs for normal power operation: (a) fault 1 to (h) fault 8. 
91 
Development of the h-s graph approach for process FDI 
2 3 4 5 6 7 
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Fig. 6.4.2 The h-s graphs for normal power operation: (a) fault 9 to (h) fault 16. 
92 
Development of the h-s graph approach for process FDI 
4500 
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Fig. 6.4.3 The h-s graphs for normal power operation: (a) fault 17 to (h) fault 24. 
93 
Development of the h-s graph approach for process FDI 
4500 
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Fig. 6.4.4 The h-s graphs for normal power operation: (a) fault 25 to (h) fault 32. 
94 
Development of the h-s graph approach for process FDI 
Although the change in system state is reflected on the h-s graph, the goal is to utilize the 
graph to derive uncorrelated reference fault signatures for the faults. To construct the 
signatures, two different methods are used and are described next. 
6.5 Creating reference fault signatures with the h-s graph 
In order to classify fault conditions in the PBMR MPS, a reference fault signature 
database must first be established. The first step is to derive reference fault signatures 
from the h-s fault graphs based on some criteria. Two methods are chosen for the h-s 
graph approach and are based on the error between the reference and fault graphs for each 
node and the area covering the error between consecutive nodes. The latter is termed the 
'area error' method. 
6.5.1 The error method 
The first method is based on the error or shift between the fault and the reference h-s 
graphs and is calculated for each node. By applying this method, the corresponding fault 
signatures s(i) are determined by 
s(i)-P"f(l);P,(i) i-l,2....,n (6-5-1) 
Prcr(>) 
with pref(i) the reference parameter value, p(i) the value of the measured parameter (fault) 
and i the node number. For the PBM.R MPS, s(i) corresponds to the h and 5 errors. 
In (6.5.1), a fault condition with a varying fault magnitude will result in different 
signatures for the same fault condition. For this reason, it is necessary to normalize the 
fault signatures in order to obtain a signature independent of the fault magnitude. An 
important advantage of using the h-s graph is the fact that the fault directions stay the 
same for the different magnitudes of the fault symptoms. Therefore, each signature 
retains the fault direction for each node and consequently, simplifies fault isolation. An 
example is illustrated in Fig. 6.5.1 (a) for fault 23. The figure shows that the signatures 
stay the same for each node with regards to fault direction, but vary in magnitude. To 
obtain a normalized signature snorm(i) that is independent of the fault magnitude, the 
following equation is applied 
•?„M—^ i-l.2 „ (6-5-2) 
max^|s(i)| 
The normalized fault signature is shown in Fig. 6.5.1 (b). This figure shows that the 
signature is highly correlated with regard to fault direction and magnitude if (6.5.2) is 
applied. Therefore, the conclusion is drawn that the fault conditions can be characterized 
95 
Development of the h-s graph approach for process FDI 
0.14 
0.12 
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(a) 
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Node number 
(b) 
Fig. 6.5.1 Fault signatures for fault 23 for different fault magnitudes: (a) error; (b) normalized error. 
with one normalized h and s fault signature for different magnitudes of the fault 
symptom. This feature will also minimize the number of fault signatures in the reference 
fault database. 
The normalized h and s reference fault signatures are averaged for the different fault 
magnitudes and are illustrated in Fig. 6.5.2. As discussed, the shift in the h-s graph may 
appear to be similar for some fault conditions. Fig. 6.5.2 demonstrates that the derived h 
and s signatures are uncorrelated with regard to fault direction and magnitude, 
6.5.2 The area error method 
The second method is based on the area defined by the shift between the reference and 
the fault graphs. Since there is no area between any single reference and fault node 
(straight line), two consecutive nodes are used. To visualize this concept, Fig. 6.5.3 
illustrates the area of the error for different nodes. 
The first node is used as an example. The figure shows that area 1 is defined by the 
first and second nodes of the reference (a) and fault (b) graphs. To define the area, the 
nodes of the reference and fault graphs are connected with straight lines and are the 
equivalent of the Euclidean distance given by 
.(O^MO-MOf-kOHaof (6.5.3) 
with ha, h0, sa, sb the h and s at the i-th reference and fault nodes respectively. By 
connecting the reference and fault graphs, each area is therefore defined between four 
nodes. 
However, for some faults the reference and fault graphs cross lines between nodes 
(area 3). In this case, an intermediate point iiKJ+i) is defined between the nodes and the 
area can be viewed as a summation of two triangular areas. 
96 
Development of the h-s graph approach for process FDI 
\ L .1 iu^ Tf 
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— Fin 
12 3 4 5 6 7 
Node number 
(a) 
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(C) 
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?- ^. 
-?s.. 
^^M 
4 5 6 7 
Node number 
! 
0.8 
0.6 
V, 
1 02 
.a 
§ -02 • o 
-0.S 
-08 
12 3 4 5 
Node number 
(b) 
2 3 4 5 
Mode number 
(d) 
juluiiL j. iih 
1 m« ran U . HH ran 
3 4 & 
Node number 
(e) (0 
hllri 
12 3 4 5' 
Node number 
(g) 
# 
Node number 
00 
Fig. 6.5.2 The normalized error signatures for Ihe PBMR for normal power operation. 
97 
Development of the h-s graph approach for process FD1 
—• reference system: a 
-O faul! condition: b 
node a/b connection 
!i+s+ 
Fig. 6,5.3 Classifying the areas between the reference and fault h-s graphs. 
In contrast to the error method where h and s are calculated separately, the area of the 
error encapsulates the shift in both h and s. Therefore, it is necessary to define the fault 
directions independently for h and s at each node. This concept is visualized in the 
bottom right corner of Fig. 6.5.3 (solid circle: reference node; unfilled circle; fault node). 
The figure shows that the sign is different for h and 5 in opposite fault directions. 
Accordingly, the same areas are used for h and 5 in combination with the appropriate 
fault directions. The area error signature s^aO) is calculated for each node with (6.5.4) 
sarea(0; 
rMai)[r,c.(i)J.(i + l)h] + r„a (i + l)[r„. (? + l) -L (i)J dir(fauh) a and b do not cross 
r,rta(i)[r^(i)l(i,„„)] ,dir (fault) a and b cross 
(6.5.4) 
with 1 the perpendicular distance from rarea to node i and dir(fault) the fault direction. 
Following (6.5.4), the h and j signatures are normalized using (6.5.2). To illustrate this 
notation, fault 11 is used as an example and is shown in Fig. 6.5.4. 
Ln Fig. 6.5.4 (a), the areas are firstly calculated for each node whereafter the fault 
directions (b) are determined for h and s. The h and s signatures are derived in (c) by 
multiplying (a) and (b) for each node. Lastly, the signatures are normalized in (d) to 
obtain signatures that are independent of the fault magnitude. The normalized h and s 
area error fault signatures are averaged (similar to the first method) for the different fault 
magnitudes and are illustrated in Fig. 6.5.5. The figure shows that the area error method 
also produces uncorrelated fault signatures for all the faults. 
98 
Development of the h-s graph approach for process FDJ 
25 
X 
1 re 
< 
? 
10 ? 
s lull, 1 
1 3 i 5 S V 8 
Node number 
(a) Calculate area 
1 2 3 4 5 6 1 6 
Node number 
(b) Determine fault directions 
c 10 
s 
.20 
s 
1 in in 
U 111 " |U 1 
1 ' 
2 3 4 S ? 
Node number 
S 02 
^ o 
I*. 
?OLfl 
??? 
HI 
1 1 in in 
-
U 111 u |U 1 . 
1 2 3 4 5 6 7 S 
NodO njmOer 
(c) Derive h and 5 by means of (a) and (b) (d) Normalize h and s signatures 
Fig. 6.5.4 Deriving h and s fault signatures with the area error method for fault 11, 
To increase the effectiveness of the proposed method during fault isolation, the derived 
signatures must be different in the sense that the correlation4 between any two signatures 
are low. This characteristic reduces the probability that the correct fault signature is 
classified as another. Based on this criterion, the 25 single fault signatures are compared 
and a correlation coefficient (defined by Eq. 6.6.10) is calculated. In total, the correlation 
coefficients are calculated for 300 cases. The average correlations for the error and area 
error methods are 24.86 % and 19.95 % respectively. The low correlation averages show 
that the two methods can be applied to isolate the correct fault signature and reject the 
remaining signatures. 
6.6 Fault detection and isolation with the h-s graph approach 
In this section, the procedure of fault detection and isolation is discussed based on the 
h-s graph approach. Firstly, some general assumptions are made regarding the properties 
of measurement and process noise. Also, the single fault extraction procedure is 
presented together with the construction of the h-s graph at different power levels. 
4The correlation is explained in more detail during the fault isolation phase. In terms of fault signature 
generation, the term merely describes how similar any two objects are. The mathematical formulation for 
the correlation coefficient is presented in (6.6.10). 
99 
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(ro' 
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Development of the h-s graph approach for process FDI 
6.6.1 Noise properties 
In real plant conditions, the measurements are normally corrupted with random noise 
originating from the process, sensors and actuators. If the influence of the noise is known 
or can be approximated, it follows that the error r(t) is the sum of the fault condition r^t) 
and the noise rN(t) given by [6] 
r(t)=rf(t)+rN(t) (6.6.1) 
Firstly, some assumptions are formulated regarding the measurement noise vector rN(t): 
• The vector is random and normally distributed (central limit theorem). 
• The mean of the vector is zero: E{rN(t)} = 0. 
• Whiteness of the vector: <J>W(T) = E{rN(t)rN(t- T)T} = 0. 
• The vector is uncorrelated: ®w(0) = E{rN(t)rN(t)T} = I. 
In the thesis, the noise vector rN(t) is modelled with a normally distributed (zero mean) 
random number generator which is not correlated in time. 
6.6.2 Fault detection 
In this section, fault detection of the error window average is discussed. To detect a fault 
condition, the time varying mean of the error is tested for a nonzero value against a given 
threshold. The reason a threshold value is considered and not zero is because the mean of 
the errors are generally corrupted with noise and modelling errors, even if no fault is 
present. The latter is implemented as a statistical hypothesis test and is given by 
Ho: ur < uf no fault -. 
Hi: H, > uf fault K°'° ' 
with Uf the threshold value. 
To test for a fault condition, the hypothesis test is implemented as a %2 test and is 
mainly based on the central %2 distribution [6]. This technique is not computational 
complex and is employed since the error vector is normally distributed and the test is a 
choice between only two hypotheses. Consider the error vector in (6.6.1) is given by 
r(t) = [ri(t),r2(t),...,rn(t)]T (6.6.3) 
101 
Development of the h-s graph approach for process FDI 
with n the number of measurements. For the PBMR MPS, separate error vectors will 
consist of h and s respectively. The window average of the vector series is computed as 
1 m f(t
;m) = —-Xr(t-i) (6.6.4) 
i~rm i=0 
with m the time window. Because the error vector is assumed to be normally distributed, 
the multivariate normal density function for the window average is 
m = (, J. |,2exp[-l/2r>:'r] (6.6.5) 
The covariance matrix y/ of the window average is obtained by 
1 1 m 
Vi =-77^(0)+—-rI(m + l-t)[Vir(t) + ^(t)] (6.6.6) 
m + 1 (m + 1) i=i 
The test for fault detection is performed as 
H.:f(t)W»(t)<^ 
H,:f»y:'r(t)^ > 
with rT (t)\|/j1r(t) the test statistic and %2a the threshold. The thresholds are chosen as 
Jx°f(r)dr = l-a (6.6.8) 
with a the false alarm rate. The false alarm rate, also called the test size, is defined as the 
probability that Hi is chosen whilst Ho occurs. To minimize the number of false alarms, 
the variable is chosen empirically for the specific application. The hypothesis tests are 
performed for both h and s and a fault condition is detected if either of the two tests fire. 
6.6.3 Fault isolation 
Following the detection of a fault condition, the next important task is fault isolation. To 
identify the specific location, cause or component responsible for the malfunction, the h-s 
graph procedure is now applied. Firstly, (6.5.1) to (6.5.4) are used to construct the fault 
signatures describing the actual operating conditions: h error, h area error, s error and s 
area error. With the reference fault database developed in section 6.5, the four signatures 
are compared to the single faults in the database in order to correctly classify the 
corresponding fault condition. This task is achieved by applying shape analysis and 
classification. 
102 
Development of the h-s graph approach for process FDI 
To perform the task of fault recognition, a statistical classifier is used to match the fault 
condition to the corresponding reference fault signature sref'm the database. Three tests 
are used: (1) the root mean squared error (RMSE), (2) the correlation coefficient (CQ and 
(3) the r-square statistic (RSQ). 
a.) The RMSE is also known as the standard error of the regression and is given by 
^SE = J1S(»(0-»-(0)2 (6-6.9) 
A value closer to zero will indicate the best match to a reference fault signature. 
b.) The CC computes the correlation coefficient between the actual and the reference 
fault signatures and is calculated by 
ISwfrP)-»)(»?* (O-'M (6.6.10) 
"^?•^(•-(Hf) 
An important property of (6.6.10) is that the CC < 1. A value closer to one indicates 
the best recognition. 
c.) The RSQ is the ratio of the sum of squares of the regression and the sum of the 
squares, given by 
ASP-.! SlXPfrtP-'fP))' (6.6.11) 
EX0(-P)-»)' 
where w(i) are the weights. Similar to the CC, RSQ takes a value between 0 and 1, 
with a value closer to 1 indicating the best match. 
To increase the integrity of the recognition algorithm, all three statistics are combined to 
match the actual fault signature to the correct reference signature. The fault isolation 
index, FII, is defined and is computed by 
FII = ^RMSE2 + (1 - CC)2 + (1 - RSQ)2 (6.6.12) 
with isolation equal to the reference signature with a minimum FII, ideally zero. To 
correctly identify a fault condition in the PBMR MPS, all four fault signatures must 
correspond to a minimum FII for the same reference fault condition. 
It must be noted that the fault signature that corresponds to a minimum FII, is the 
best possible fit to a reference fault, although not necessarily the correct fault condition. 
To reduce the probability of misclassification, the reference fault database must therefore 
be designed to include the most probable system faults. As discussed, single faults may 
103 
Development of the h-s graph approach for process FDI 
occur simultaneously (multiple faults) and combinations thereof will increase the amount 
of reference fault signatures significantly. To restrict the fault database to single faults 
only, a single fault extraction procedure is devised to classify unknown signatures with a 
high FII to possible combinations of single faults. The extraction procedure is discussed 
next. 
6.6.4 Single fault extraction method 
During a multiple fault occurrence (unknown signature), the challenge is to identify the 
single faults comprising the multiple fault condition. A method of single fault extraction 
is proposed and is based on a systematic subtraction procedure of single reference fault 
signatures. The procedure is illustrated in Fig. 6.6.1. 
Firstly, the multiple fault signature (obtained with 6.5.1) is normalized with the k-th 
node after which the first reference signature m is subtracted. The remaining single fault 
signature is normalized and compared to all the signatures in the reference fault database, 
based on the FII. This procedure is repeated until all the reference fault signatures are 
subtracted. After the multiple fault signature is normalized with all the k-th nodes, the 
first single fault is classified as the reference fault m corresponding to the minimum FII. 
Lastly, the second single fault is identified as the reference fault signature m used during 
the subtraction procedure of the first fault. 
(\\- s(i) i = 1,2,.. >n norm VV 
s(k) k = l,2,...,n 
m = / 
k* n 
i ' 
Sx(0 = Snom,(i)-Sref(m)(i) "1 = 1,2,...,/ 1 
s c 
jcnonn \ 
n- s»(i) max,"
=1 ??0) 
1 ' 
FIIS (k,m,i)-,JRMSE2+(l CC)2 +(l RSQ)2 j —1,2,...,/ 
m = / 
k = n 
' 
Sl(i) = S
ref(a)0)
 a = S
ref(m)
atmin(F//
S, (
k>mJ)) 
s2 (0 = s
ret(b) (0 b = sref(m) subtracted at s, 
Fig. 6.6.1 Flow diagram of the single fault extraction method. 
104 
Development of the h-s graph approach for process FDI 
To demonstrate the implementation of the method, faults 26 to 32 are used to extract the 
contributing single faults. The fault database is therefore restricted to only single 
reference faults, i.e. faults 1 to 25. Also, no measurement noise is added in this example. 
This is done in section 6.7 when the h-s graph approach is applied to monitor the PBMR 
MPS for faults. 
Table 6.6.1 summarizes the minimum FII values for h and s together with the 
average recognition and rejection averages. The FII for recognition is calculated as the 
average of the minimum h and s values for both faults. Similarly, the FII for rejection is 
computed as the average of the remaining h and s values. The table shows that both the 
single faults are correctly identified for all the multiple fault conditions. The minimum 
FII is less than 0.06, which implies that all the single faults were closely matched to their 
corresponding reference fault signatures. The effectiveness of the method will however 
be examined when unknown signatures are introduced in the PBMR MPS in noisy 
conditions. 
To illustrate the single fault extraction method, faults 30 and 31 listed in Table 6.6.1 
are used as an example. Fig. 6.6.2 illustrates the single extracted h and s error signatures 
together with their resultant multiple fault signatures. This figure and figures 6.5.2 (b), (d) 
and (f) show that the single extracted signatures are highly correlated. Accordingly, low 
FII values are observed. The results indicate that in the PBMR MPS, the single fault 
signatures superimpose in multiple fault conditions. Note that this observation is only 
based on the examined fault conditions and the subtraction procedure of the devised 
method. 
6.6.5 The h-s graph and reference fault signatures at different power 
levels 
In sections 6.4 to 6.6.4, all the fault simulations corresponded with the system operating 
at full power, i.e. 100 % MCR and 100 % MCRI. This is usually not the case during real 
plant conditions seeing that the operating point constantly changes due to varying load 
demands. To accommodate the varying plant conditions, the h-s graph approach must 
therefore be applicable at different power levels during normal power operation (mode 
5b). 
FII 
number Fault 1(h) Fault 10) Fault 2(h) Fault 2(5) Ave. 
recognition 
Ave. 
rejection 
26 0.003399 0.067509 0.03341 0.02756 0.03297 2.5991 
27 0.008757 0.004962 0.01327 0.00648 0.00836 2.5299 
28 0.006173 0.002938 0.03239 0.13774 0.04481 2.6643 
29 0.010277 0.018514 0.01199 0.00926 0.01251 2.4993 
30 0.012502 0.002728 0.01165 0.16455 0.04786 2.4857 
31 0.006268 0.003875 0.03213 0.16967 0.05298 2.8574 
32 0.000622 0.003287 0.01923 0.18314 0.05156 2.5419 
Table 6.6.1 Classification results with the FII for multiple faults 26 to 32 at 100 % MCR. 
105 
Development of the h-s graph approach for process FD1 
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3 4 5 
Node number 
(a) (b) 
Fig. 6.6.2 The extracted h and s error signatures for the two single faults comprising faults: (a) 30; (b) 31. 
As discussed in sections 6.3 and 6.5, the most important advantages of using the h-s 
graph for process FDI are: 
• The reference plant model remains constant over the operating range. 
• Each of the fault conditions is characterized with only one reference fault signature 
for different fault magnitudes. 
To further reduce the fault database, the reference fault signatures must also remain 
constant, i.e. one signature for different power levels. Based on this assumption, the 
reference fault signatures are captured whilst the operating point is set to 90 %, 80%,..., 
40 % MCR. As an example, the reference fault signatures are computed for faults 11 and 
19 and illustrated in Fig. 6.6.3. The fault signatures are presented for the minimum and 
maximum fault magnitudes and power levels during normal power operation. 
The figure indicates that the two fault signatures stay relatively constant over the 
operating range. Similarly, each of the remaining single fault conditions in the PBMR 
MPS showed comparable results with little variation. It is therefore concluded that each 
fault signature is highly correlated during operating point changes and fault magnitude 
variations, and that the fault signatures are uncorrelated with regard to each other. 
Accordingly, the fault database is minimized with only one5 reference fault signature for 
each single fault condition. 
To construct the actual fault signatures during normal power operation of the plant, 
the reference model must be shifted to different operating points on the h-s graph. To 
achieve this goal, a reference value or point must be known for both h and s. This value 
will be used as starting point to reconstruct the reference model at the operating point of 
interest. 
One signature per fault condition comprises one fault signature for h and s, and is derived with each 
signature method. This amount to four signatures per fault condition and can for simplicity be stored as a 
vector (signatures are sequenced) signature. 
106 
Development of the h-s graph approach for process FD1 
3 4 5 6 7 
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UiJtlVlOOS MCR 
3**M0V 100* MCR 
? AJMF4 JQ^^Kfl 
3 4 5 6 7 
Node number 
3 4 5 6 7 
Mode number 
(c) (d) 
Fig. 6.6.3 The normalized signatures for a l % and 10 % change at 40 % and 100 % MCR: (a) fault i 1 
error; (b) fault 19 error; (c) fault 11 area error; (d) fault 19 area error. 
The reference point is selected as the point with the lowest cycle temperature and 
pressure, the LPC inlet (point 1). Since the h-s graph only shifts in the horizontal plane 
during normal power operation, the reference value for h is chosen as a constant, i.e. zero. 
The next step is to calculate ,s at the reference point for different operating points. To 
obtain the reference values, the plant is ramped from 100 % to 40 % MCR during normal 
power operation, and back to full power. The reference values are calculated as the 
average 5 at each power level. 
Following this, shape features are extracted from the reference h-s graph to define 
each of the eight nodes. The two features that are selected are: the length / between the 
reference point and each node and the angle 6 between / and zero h. This parametric 
representation is illustrated in Fig. 6.6.4 (a) and the reconstruction of the reference h-s 
graph at a different operating point is shown in Fig. 6.6.4 (b). Starting at the reference 
point (zero h and j at the new operating point), each node is placed at (/n,#n)> with n the 
node number. Based on the proposed reconstruction method, the reference h-s graph at 
100 % MCR is shifted to the new operating point, and therefore, only one reference 
model is needed to characterize the system6. 
With regard to one reference model, the improvement in model prediction by means of 
transformation (T-P to h-s) is proven for the PBMR MPS and is documented in Appendix B 
107 
Development of the h-s graph approach for process FDI 
A 
h Reference node 1 ai ww opem-tag. poini 
jr*-
K; 
: ' ????-4^* ^ 
? 
(a) (b) 
Fig. 6.6.4 The reference h-s graph: (a) shape features; (b) reconstruction. 
Although the method is easily applied in theory, real-life application provides more 
complex challenges. This is due to the fact that some system characteristics change as a 
result of normal plant variations and alterations of the process. In order to increase the 
effectiveness of the h-s graph approach, the reference model must therefore accommodate 
these variations and is discussed in the following section. 
6.7 Process variations and the reference h-s graph 
In large scale engineering plants, it is common phenomena that plant characteristics 
change during the course of operation. This directly affects the performance of the fault 
diagnosis system and increases the variation (error) between the reference model and the 
actual system. For this reason, it is important to adjust the reference model (i.e. the shape) 
to the actual operating conditions to minimize the variation. 
Also, faster load changes are achieved in the PBMR by using the GBPC valve in 
addition to the ICS during normal power operation. Although fast and accurate set point 
tracking is realized, this method of power control reduces the cycle efficiency and 
changes the shape of the reference h-s graph. The h-s graph is illustrated in Fig. 6.7.1 for 
GBPC valve operation and indicates that the graph shifts simultaneously in the vertical 
and horizontal directions. Since valve operation is performed during noimal power 
operation of the plant, the additional shift must also be incorporated in the reference 
model. In the thesis, the following process variations are considered for the PBMR MPS: 
(1) Plant efficiencies tend to be slightly lower at reduced power levels. 
(2) Performance characteristics of the components change due to normal wear and system 
maintenance (new or replacement parts). 
(3) GBPC valve operation in addition to the ICS. 
108 
Development of the h-s graph approach for process FD1 
Fig. 6.7.1 The h-s graph for GBPC valve operation at different power levels. 
Firstly, the reference h-s graph is adjusted to include valve operation and reduced plant 
efficiencies at different operating points. As a proposed solution, an n-dimensional 
variation surface (VS) is defined as the variation between the shape features for the actual 
operating conditions and the reference model. In this case, the n-dimensional surface 
encompasses the magnitude of the variation, the normalized percentage of the GBPC 
valve opening and the power level for each node. 
To create the VS, the shape features (/n,<?n) of the h-s graph are extracted during 
GBPC valve operation. A GBPC valve transient is realized by opening the GBPC valve 
in 1 % increments whilst ramping the plant from 100 % MCR down to 40 % MCR. This 
however, amounts to an unmanageable number of operating points. To simplify the 
problem, the extracted features are reduced to 21 operating points by using an 
n-dimensional cubic spline interpolation algorithm {'interprf [66]). By applying an 
n-dimensional factor, additional parameters that can vary the operating point may be 
defined in the future, e.g. the CWT. The operating points are: 100 %, 90 %,..., 40 % 
MCR with the GBPC valve closed, 50 % and 100 % open. The variation in each of the 
shape features is therefore characterized by an enclosed region and is defined by the 21 
operating points. 
By defining the enclosed surfaces and applying the interpolation algorithm, the 
variation of the shape features can therefore be estimated at any operating point. To 
visualize the four-dimensionai surface (fourth dimension is the node numbers), three 
dimensions are varied whilst the fourth is kept constant. The VS for each of the shape 
features is illustrated in Fig. 6.7.2. In Fig. 6.7.2 (a) to (d), the GBPC valve opening is 
constant for each node whereas the GBPC valve opening is varied in (e) and (f). The 
figure shows that larger variations occur at reduced power levels and is the result of lower 
plant efficiencies. Also, the figure illustrates that the magnitude of variation for / is very 
small. This is an indication that the reference model needs minimal adjustment to 
minimize the variation. 
To test the performance of the reference h-s graph with the VS, three random 
operating points are selected for the PBMR MPS. The three test cases are (manifold 
pressure/normalized GBPC valve opening): (1) 6856 kPa (76 %)/0.285; (2) 5569 kPa 
(62 %) /0.589; and (3) 4641 kPa (51.5 %)/0.862. The normalized h and s are calculated 
with both Flownex and the reference h-s graph, and are summarized in Table 6.7.1. 
109 
Development of the h-s graph approach for process FDI 
100 
Power level 60 40 8 5 4 3 2' 
Node number 
1 6 s 4 3 2 , 
Node number 
-1 L 
100 
80 
60 Power level 
40 
(a) (b) 
Power level 40 s 7 6 5 4 3 2 1 
Node number 
7 6 6 4 3 2"i 
Node number 
(c) (d) 
Power level 
0.4 <>?« 
Valve open 
Power level 
Valve open 
(e) (f) 
Fig. 6.7.2 Variation surface for valve operation: (all nodes) GBPC 1 %open (a) /; (b) 9; 
(all nodes) GBPC 25 % open (c) /; (d) 9; 
(node 2 only) GBPC 0-100 % open (e) /; (0 8. 
110 
Development of the h-s graph approach for process FD1 
Node ? Test < :ase 1 Testi :ase2 Test i case 3 Flownex h-s graph Flownex h-s graph Flownex h-s graph 
h\ 0.0224 0.0224 0.0210 0.0214 0.0204 0.0205 
hi 0,1127 0.1128 0.1104 0.1106 0.1079 0.1083 
h3 0.0231 0.0232 0.0218 0.0220 0.0211 0.0216 
M 0.1124 0.1125 0.1083 0.1084 0.1013 0.1019 
hS 0.5254 0.5254 0.5333 0.5337 0.5516 0.5505 
he 0.9402 0.9402 0.9429 0.9428 0.9482 0.9476 
hi 0.5329 0.5330 0.5406 0.5410 0.5590 0.5580 
hi 0.1422 0.1424 0.1377 0.1378 0.1303 0.1311 
s\ 0.3496 0.3472 0.3864 0.3883 0.4121 0.4141 
s2 0.3667 0.3643 0.4039 0.4057 0.4299 0.4319 
s3 0.2337 0.2313 0.2719 0.2739 0.3004 0.3023 
s4 0.2463 0.2438 0.2851 0.2869 0.3143 0.3150 
$5 0.6226 0.6200 0.6713 0.6734 0.7210 0.7232 
s6 0.8470 0.8445 0.8917 0.8936 0.9320 0.9317 
s7 0.8566 0.8540 0.9002 0.9020 0.9385 0.9393 
sS 0.5207 0.5183 0.5539 0.5557 0.5714 0.5728 
% Diff 0.297467 0.247773 0.147321 
Table 6.7.1 Results for the h and 5 calculations. 
Table 6.7.1 shows that the percentage difference between Flownex and the estimated h-s 
graph values is less than 0.3 %. The high correlation between the values demonstrates 
that the h-s graph is a simple but effective way to estimate the values for the reference 
model at different operating points. In addition, process variations are characterized by 
interpolating the VS with a reduced number of reference points 
To incorporate process variation number (2) in the PBMR MPS, the VS is 
implemented online in real-time during normal power operation of the plant. The two 
surfaces are adjusted at regular time intervals to minimize the variation between the 
reference model and the plant, subject to the type of variation (e.g. valve operation) and a 
healthy system. In addition, the VS will also be adjusted after maintenance or repair to 
describe any altered system characteristics. It is important to note that the time interval of 
adjustment is dependent on the amount and magnitude of variation, and is only 
determined after the system is online. In general, the reference model is not altered if the 
magnitude of variation stays within an acceptable tolerance. 
As discussed in section 6.6.5, the reference fault signatures stay constant over the 
operating range for different magnitudes of the fault. However, to utilize the minimized 
fault database with only single reference fault signatures, each signature must be highly 
correlated during process variations (GBPC valve operation). To consider valve operation 
in the PBMR MPS, the GBPC valve is opened 50 % and 100 % respectively during each 
of the 25 single fault conditions and the h-s graph together with the VS is used to estimate 
the reference model for the specific operating point. Next, the four signatures are 
calculated for the fault conditions and compared to the reference fault database. As an 
example, consider the fault signatures of single faults 11 and 23 illustrated in Fig. 6.7.3. 
Ill 
Development of the h-s graph approach for process FDI 
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Fig. 6.7.3 The normalized signatures at 100 % MCR for GBPC valve operation: (a) fault 11 error; 
(b) fault 23 error; (c) fault 11 area error; (d) fault 23 area error. 
The figure shows that the correlation between each of the single fault signatures is very 
high during valve operation. Similarly, each of the remaining single fault signatures in the 
PBMR MPS showed comparable results if the VS corresponds to the minimal variation at 
the specific operating point. The single reference fault signatures will therefore be 
sufficient to characterize fault conditions in the PBMR MPS during valve operation. 
In conclusion, some important observations regarding the VS are summarized as 
follows: 
• By integrating vertical shift into the h-s graph by means of the VS, various normal 
process variations can be correctly characterized. 
• The single reference fault signatures stay relatively constant for process variations if 
the reference mode! incorporates the VS. 
• The VS is implemented in real-time to minimize variation between the actual plant 
and the reference model, i.e. to minimize modelling errors. 
112 
Development of the h-s graph approach for process FDI 
6.8 Application of the h-s graph approach in the PBMR MPS 
In this section, the proposed process fault diagnosis approach is validated with an 
application in the PBMR MPS. It is important to note that all the results presented are 
based on the complex simulation model of the actual plant. Also, to emulate actual plant 
conditions, random noise is added to all the measurements (discussed in section 6.6.1). 
The following transient variations are considered: 
• Faults are induced during steady state for normal power operation. 
• Faults are induced during load following for normal power operation. 
To verify that the faults are identified at an early stage, the fault magnitude must be very 
small at the time of detection. For application in the PBMR MPS, a fault magnitude of 
1 % is deemed to be sufficient. The following fault magnitudes are considered: 
• Abrupt fault with 1 % bias. 
• Drift fault corresponding to a 2 % change in an hour. 
One problem that arises during online application is to select the correct fault isolation 
algorithm, i.e. for a single or multiple fault condition. As discussed in section 6.6, the 
known single fault reference signatures will show a low FII, whereas unknown faults will 
show high values. To determine the tolerance of the FII for known signatures, the faults 
are randomly induced during steady state operation of the plant. 
6.8.1 Fault conditions during steady state operation of the plant 
Firstly, the plant is operated at full power in steady state with all the valves fully closed. 
Since no valve operation is performed, the reference h-s graph can be used without the 
VS. Random noise with a = 1 is added to the plant measurements and a sampling window 
of 10 seconds (i.e. 10 samples) is selected. 
To simulate the fault conditions during normal power operation, the 32 fault 
conditions are randomly induced for 10 seconds with a bias value of 1 % (abrupt fault). 
After each fault condition, the plant is returned to the original steady state conditions 
before the next fault is induced. The reason the faults are randomly induced in succession 
is to combine 32 fault simulations into one. To determine the FII tolerance for the known 
signatures in the PBMR MPS, the correct algorithm is selected in this example and 
depends on the vector fault condition (single or multiple). The vector of randomly 
induced faults is: 
[21,25,9,6,20,5,19,12,7,29,31,10,22,3,14,13,28,1,27,18,15,32,17,23,26,30,4,8,2,16,24,11] 
Figure 6.8.1 shows the isolated faults for each of the simulated fault conditions, and 
Table 6.8.1 summarizes the results of the isolation algorithm and the FII. 
113 
Development of the h-s graph approach for process FDI 
% 15 
E 
1000 
Time [s] 
(a) 
& 15 
£ 
1000 
Time [s] 
(b) 
Fig. 6.8.1 The isolated faults during steady state operation of the PBMR at 100 % MCR: (a) single fault 1; 
(b) single fault 2. 
Fault 
vector 
Isolated 
fault 
FII 
Fault 1 (error) Fault l(area) Fault 2(error) Ave. recognition Ave. rejection 
21 21 0.340212 0.061578 0 0.200895 6.134653 
25 25 0.330755 0.067270 0 0.199013 5.534043 
9 9 0.027219 0.037339 0 0.032279 7.242336 
6 6 0.078239 0.011379 0 0.044809 5.485466 
20 20 0.044314 0.015763 0 0.030038 8.504902 
5 5 0.072332 0.017033 0 0.044683 6.528084 
19 19 0.031160 0.020857 0 0.026008 8.171386 
12 12 0.162649 0.025451 0 0.094050 6.586299 
7 7 0.055919 0.010281 0 0.033110 4.777097 
29 29 0.011763 0 0.015805 0.013784 2.502175 
31 31 0.111671 0 0.012473 0.062072 2.867006 
10 10 0.027143 0.063293 0 0.045218 4.991760 
22 22 0.314045 0.046812 0 0.180428 8.798796 
3 3 0.102076 0.130887 0 0.116482 4.840005 
14 14 0.141838 0.040288 0 0.091063 6.440418 
13 13 0.019705 0.005849 0 0.012777 7.218782 
28 28 0.087813 0 0.008665 0.048239 2.655320 
1 1 0.117890 0.093892 0 0.105891 5.726515 
27 27 0.027957 0 0.010244 0.019110 2.532352 
18 18 0.045612 0.054659 0 0.050135 6.524358 
15 15 0.349312 0.031016 0 0.190164 4.896510 
32 32 0.228303 0 0.007329 0.117816 2.537446 
17 17 0.045351 0.053808 0 0.049579 5.847439 
23 23 0.056249 0.026494 0 0.041371 6.469139 
26 26 0.030836 0 0.036241 0.033539 2.596791 
30 30 0.101663 0 0.009977 0.055820 2.480615 
4 4 0.323812 0.056115 0 0.189963 5.129935 
8 8 0.036454 0.035389 0 0.035921 5.903668 
2 2 0.107486 0.141373 0 0.124430 6.710999 
16 16 0.085756 0.014903 0 0.050329 5.442663 
24 24 0.079989 0.045644 0 0.062817 8.584188 
11 11 0.061249 0.038322 0 0.049785 5.205250 
Table 6.8.1 Summary of isolated faults during steady state by means of a sample window. 
114 
Development of the h-s graph approach for process FDI 
The table shows that each of the randomly induced faults is correctly isolated. Also, the 
results indicate that the FII is low for multiple fault conditions if the single fault 
extraction method is employed. Therefore, by selecting the proper isolation algorithm, 
each of the faults can be correctly identified. 
Table 6.8.1 shows that the average FII for all the single signatures is less than 0.45. 
Accordingly, a FII tolerance of 0.5 is chosen for the known single signatures in the 
PBMR MPS. Once this limit is exceeded, the single fault extraction algorithm determines 
if the unknown signature is caused by a multiple fault condition. 
Next, the isolation ability of the h-s graph approach is verified in the presence of 
process and measurement noise. During each of the single fault conditions, random noise 
is added to the measurement channels with an increase in variance. For this test case, the 
sample window average is not computed and approximately 3000 samples are generated 
for the single fault conditions. Table 6.8.2 summarizes the average (all the samples) and 
maximum (any single sample) isolation percentages for the 25 single faults consisting of 
different noise and fault magnitudes. The isolation percentage is determined by 
isolation percentage = 
V n total J 
xl00 (6.8.1) 
with n the number of total and correct isolations determined by the lowest FII. 
The table shows that all the single faults are correctly isolated in the noise free 
measurements. However, the results indicate that the number of correct isolations 
gradually decreases with an increase in noise magnitude and that the isolation percentage 
increases if the fault magnitude increases. Therefore, the conclusion drawn from the 
observations is that random noise affects the isolation ability of the h-s graph approach at 
the beginning of some fault conditions. Nonetheless, the maximum isolation percentages 
indicate that the method is able to correctly isolate all of the single faults in some cases 
for larger noise magnitudes. 
In addition, Table 6.8.2 indicates that the isolation percentage slightly increases if 
the error and area error methods are not used in combination for the average calculations. 
In contrast, the results listed in Table 6.8.1 show that if a sample window is used, the FII 
is lower for the area error method and increases the average isolation percentage. 
Therefore, the second conclusion drawn is that random noise affects the isolation ability 
of the signature generation methods if the measurements are not averaged over a 
sampling window. 
Both methods Error method 
1% shange 5% shange 1 % change 5 % change 
Var (a) A(%) M (%) A (%) M (%) A (%) M (%) A (%) M (%) 
0 100 100 100 100 100 100 100 100 
1 99 100 100 100 100 100 100 100 
2 97 100 100 100 99 100 100 100 
3 96 100 98 100 98 100 100 100 
4 96 100 97 100 97 100 99 100 
Table 6.8.2 Average (A) and maximum (M) isolation percentage for 3000 samples (single faults). 
115 
Development of the h-s graph approach for process FDI 
The second test validates the ability of the single fault extraction procedure to isolate the 
contributing single faults in noisy conditions. The previous example is adapted to 
generate 3000 samples comprising random noise. Table 6.8.3 summarizes the average FII 
of both single faults and the average rejection of the remaining reference fault signatures. 
The table shows that the averages of the FII are very low, which indicates that the 
contributing single faults can be correctly isolated. Also, the table shows that an increase 
in the noise magnitude slightly increases the FII. Therefore, it is concluded that the 
isolation ability of the single fault extraction procedure decreases if the noise magnitude 
increases. 
Next, the h-s graph approach is applied during load following in the PBMR MPS. 
6.8.2 Fault conditions during load following of the plant 
As discussed in Chapter 3, the plant will be mostly operated to accurately follow varying 
load demands. Since the expected time of normal power operation is more than 325 days 
per year [47], fault diagnosis is essential to prolong the lifespan of the plant. A typical 
load following transient of the plant is shown in Fig. 6.8.2 (a). During the transient, the 
following plant characteristics are relevant: 
• Helium is injected and removed from the MPS at a rate of 7.5 kg/s by means of the 
ICS. 
• The outlet temperature of the reactor is controlled at 900 °C with the control rods. 
• The bypass valves are 0-100 % open. 
Starting at point 1, the plant is operated at full power in steady state with all the bypass 
valves closed. At point 2, the GBPC valve is opened to 45 % and 100 % respectively. 
Following this, the GBPC valve is fully closed and helium is extracted and injected from 
point 4 onwards. At point 12, the GBPC valve is opened to 90 % and then closed for the 
remaining time of the transient. 
Figure 6.8.2 (b) shows the normalized mean error between the Flownex calculations 
and the h-s reference graph with the VS. The figure shows that the highest errors occur 
during valve operation with the valves 90 % to 100 % open. Although the error 
magnitude is acceptable for the investigation, it can be minimized by incorporating more 
FII (error method)  
Fault 26 Fault 27 Fault 28 Fault 29 Fault 30 Fault 31 Fault 32 
Var(o) I R I R I R I R I R I R I R 
0 0.032 2.599 0.008 2.529 0.044 2.664 0.012 2.499 0.047 2.485 0.052 2.857 0.079 2.541 
1 0.033 2.593 0.011 2.531 0.045 2.663 0.013 2.500 0.056 2.476 0.052 2.862 0.117 2.538 
2 0.033 2.598 0.019 2.535 0.048 2.657 0.014 2.491 0.056 2.482 0.062 2.831 0.117 2.533 
3 0.036 2.599 0.023 2.526 0.051 2.663 0.015 2.492 0.082 2.496 0.063 2.875 0.129 2.545 
4 0.036 2.587 0.026 2.528 0.053 2.675 0.015 2.484 0.084 2.487 0.064 2.852 0.136 2.543 
Table 6.8.3 The isolation (I) and rejection (R) averages of the FIITor multiple faults 26 to 32. 
116 
Development of the h-s graph approach for process FDI 
1000 1500 2000 2500 3000 3500 4000 
Time (s) 
(a) 
500 1000 1500 2000 2500 3000 
Time (s) 
(b) 
Fig. 6.8.2 Load following transient during normal power operation of the PBMR MPS: (a) power level; 
(b) normalized error between Flownex and the reference h-s graph comprising the VS. 
reference points in the VS. The errors at large valve openings are expected and supported 
by the larger variations observed in Fig. 6.7.2 (e) and (f). 
To emulate fault conditions in the system, each of the single faults are induced at 
t - 1000 seconds and multiple faults at 1000 and 1700 seconds respectively. In both 
single and multiple fault simulations, the fault magnitude increases to a maximum of 2 % 
at 4000 seconds (drift fault). Therefore, regarding multiple faults, the magnitude of each 
fault is different at the end of the transient. Similar to the steady state simulations, 
random noise with a = 1 is added to the plant measurements and a sampling window of 
10 seconds is selected. The missed alarm rate is chosen as a = 0.01 and the hypothesis 
thresholds for fault detection are selected as 2.5 and 0.1 for h and s respectively. The 
results of the 32 fault simulations are summarized in Table 6.8.4. The notation in the 
table is as follows: 'Time' denotes the time of fault detection; 'Magnitude' represents the 
fault magnitude at the time of detection and the 'average Fir is calculated for the 
remaining part of the transient. 
An example of fault isolation is illustrated in figures 6.8.3 and 6.8.4 for fault 18. 
Figure 6.8.3 (a) shows that the single fault is detected after approximately 140 sample 
windows, i.e. 1400 seconds. Figure 6.8.3 (b) depicts the average FII after fault detection 
which shows that the results correlate well with the values listed in Table 6.8.1. 
50 100 150 200 250 300 350 400 
Sample window 
50 100 150 200 250 300 350 400 
Sample window 
(a) (b) 
Fig. 6.8.3 Single fault detection during load following: (a) isolated fault; (b) FII after detection. 
117 
Development of the h-s graph approach for process FDI 
Fault Sample window Magnitude ? (%) change Fault 1 Fault 2 Ave. 
(ave.) (ave.) rejection 
1 140 0.26 0.12779 0 4.6266 
2 160 0.4 0.15017 0 5.4256 
3 150 0.33 0.14058 0 5.7899 
4 140 0.26 0.22926 0 4.4365 
5 140 0.26 0.05392 0 3.4567 
6 150 0.33 0.05408 0 4.2355 
7 170 0.46 0.03996 0 3.4664 
8 150 0.33 0.04335 0 4.6687 
9 160 0.4 0.03895 0 4.4777 
10 140 0.26 0.05457 0 6.1346 
11 150 0.33 0.06008 0 5.5466 
12 150 0.33 0.11350 0 4.4566 
13 170 0.46 0.01542 0 5.7688 
14 160 0.4 0.10990 0 6.3456 
15 140 0.26 0.29287 0 5.5467 
16 160 0.4 0.06074 0 4.9587 
17 160 0.4 0.05983 0 5.4366 
18 140 0.26 0.06051 0 3.5393 
19 150 0.33 0.03138 0 3.6577 
20 150 0.33 0.03625 0 4.6767 
21 170 0.46 0.24245 0 5.6626 
22 170 0.46 0.21775 0 4.4367 
23 160 0.4 0.04993 0 3.4777 
24 150 0.33 0.07581 0 5.3425 
25 150 0.33 0.30053 0 6.2554 
26 150|200 0.33|0.26 0.04047 0.02959 2.4799 
27 150|220 0.33|0.43 0.02306 0.01686 2.4628 
28 150|210 0.33|0.35 0.05821 0.04256 2.5975 
29 150|210 0.33|0.35 0.01663 0.01212 2.3649 
30 150|200 0.33|0.26 0.06736 0.04921 2.3587 
31 150|210 0.33|0.35 0.07491 0.05476 2.7452 
32 150|220 0.33|0.43 0.14219 0.10395 2.4743 
Table 6.8.4 Summary of isolated faults (fl|f2) during load following. 
The fault signatures are illustrated in Fig. 6.8.4 for normal variations of the process. The 
variations include: injection at 2100 seconds, steady state operation at 2500 seconds, 
extraction at 3000 seconds and valve operation at 3650 seconds. The results indicate that 
the h and s signatures are highly correlated and stay approximately constant. As a result, 
one reference signature will be sufficient for isolation during normal variations of the 
process. Therefore, the conclusion drawn from the observations is that each of the single 
reference fault signatures is valid during steady state operation and normal transient 
variations of the process. 
As discussed, the classification of unknown signatures (multiple fault conditions) is 
more complex. To demonstrate the single fault extraction procedure, fault 29 is used as 
an example and is illustrated in Fig. 6.8.5. Note that the single fault isolation algorithm is 
used in Fig. 6.8.5 (a). Figure 6.8.5 (a) shows that the first fault is detected after 1500 
seconds. 
118 
Development of the h-s graph approach for process FDI 
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Fig. 6,8.4 The normalized signatures for fault 18 during load following: (a) error; (b) area error. 
The figure indicates that the FII is steady for the known single fault until the second fault 
is induced at 1700 seconds. As a result, the FII increases owing to the fact that the second 
fault starts to mask the first (unknown signature). Since the magnitude of the second fault 
increases faster, it is visible that the second fault becomes more dominating after 2600 
seconds. Consequently, the second fault masks the first fault completely (i.e. the FIIw'iW 
decrease below 0.5 again) and the multiple fault is classified as the second single fault. 
To reduce fault masking, the single fault extraction procedure is used once the FU 
surpasses the single fault limit. Figure 6.8.5 (b) shows that the threshold is exceeded at 
2100 seconds, and consequently, the FII is calculated for the probable extracted single 
faults. The figure indicates that the FII decreases and stays relatively steady for the 
known single signatures after isolation, which suggests that the algorithm is less sensitive 
to the magnitude of the fault. As a result, the probability of fault masking is minimized 
during multiple fault conditions. 
Overall, the results indicate that all the examined faults can be correctly isolated with 
the h-s graph approach during normal power operation of the PBMR MPS. 
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single fault extraction procedure, 
119 
Development of the h-s graph approach for process FDI 
6.9 Summary and conclusions 
This chapter focussed on the development and implementation of the h-s graph approach 
for process fault diagnosis in the PBMR MPS. 
Section 6.2 firstly introduced enthalpy and entropy after which section 6.3 illustrated 
the general construction of the h-s graph. In the thesis, a simplified version of the h-s 
graph is used and comprises eight nodes. 
Section 6.4 showed the effects of the reference faults on h and s and illustrated the 
shift on the h-s graph. Following this, two methods are devised in section 6.5 for 
generating reference fault signatures. 
In section 6.6, the hypothesis for fault detection is discussed and the statistical 
classifier, the FII is devised for recognition. In the final part of this section, the single 
fault extraction procedure is developed to isolate the contributing single faults in a 
multiple fault condition. 
In section 6.7, an n-dimensional VS is defined to incorporate process variations in 
the reference h-s graph. Lastly, the proposed fault diagnosis approach is applied in 
section 6.8 to the PBMR MPS. 
Some of the important conclusions reached in this chapter are: 
• The examined faults can be characterized by a distinctive shift in the enthalpy and 
entropy and are visualized on an h-s graph. The Brayton cycle can be described by 
the h-s graph, in which any point on the graph represents the thermodynamic state of 
the process. 
• In the PBMR MPS, primary power control is achieved by using the inventory control 
system. This type of power control allows the shape of the h-s graph to remain 
constant over the power range during normal operation. 
• To isolate a fault condition, the error and area error methods are devised. These 
methods are applied to create normalized reference fault signatures that stay 
relatively constant. This statement holds during normal power operation for the 
following transients: 
- Changes in the fault magnitude. 
- Changes in the operating point. 
- Variations of the normal process, i.e. injection, extraction and valve operation. 
Accordingly, only one reference signature (for each method) is necessary to correctly 
isolate the fault during normal power operation of the plant. 
• Random noise affects the isolation ability of the h-s graph approach if the magnitude 
of the noise increases; however, a larger fault magnitude improves the isolation 
percentage. As a result, the effects of noise can be averaged by using a sampling 
window which improves the isolation percentage. 
120 
Development of the h-s graph approach for process FDI 
• In order to match the fault signatures to the corresponding reference fault signatures, 
a statistical classifier is formulated and termed the FIL 
• To incorporate variations of the normal process into the reference h-s graph, 
n-dimensional interpolation is used together with the VS. The n-dimensions can be 
expanded to include additional variables that alter the shape of the reference model 
during normal power operation. 
• The single fault extraction procedure is devised to isolate the contributing single 
faults from unknown, multiple fault symptoms. 
The following chapter presents the validation of the proposed approach for process fault 
diagnosis with an application in the PBMM prototype plant. 
121 
CHAPTER 7 
Validation of the h-s graph approach for process FDI 
Chapter 6 described the development and implementation of the h-s graph approach for 
process FDI in a thermodynamic system. This chapter focuses on the validation of the 
h-s graph approach and demonstrates the feasibility of the method with an application in 
the prototype PBMM plant. 
7.1 Introduction 
The main objective of this chapter is to validate the h-s graph approach for process fault 
diagnosis with an application in the Pebble Bed Micro Model (PBMM). The PBMM is a 
prototype gas turbine power plant and is based on the first configuration of the PBMR. 
The PBMM, which consists of a closed-loop three-shaft system, was developed to gain 
understanding into the dynamic behaviour of the PBMR design and to evaluate control 
methodologies for transition sequences like start up and load rejection. Although the 
PBMM is not an exact scaled version of the PBMR plant, it has the same topology and 
main components. 
In section 7.2, the differences between the three-shaft and single shaft PBMR models 
are described and compared with the topology of the PBMM plant. Also, a general layout 
of the plant is illustrated which emphasizes some of the modelling difficulties discussed 
in the next section. 
Section 7.3 discusses the development of a Flownex simulation model of the PBMM 
plant. A comparison between the simulation and plant data revealed that unmodelled heat 
paths from the complex metallic support structure of the turbo machinery caused 
discrepancies between the Flownex model and the plant measurements. Accordingly, the 
simulation model was adjusted and the modelling error minimized. 
In order to validate the h-s graph approach, real plant data (contains process and 
measurement noise) from two test runs are used. Section 7.4 describes the two sets of 
data; dataset one encapsulates a turbo failure and the second is logged during a thrust load 
test. The heater temperature transient is taken as an emulated fault condition in the second 
dataset. 
122 
Validation of the h-s graph approach for process FDI 
In section 7.5, the single faults that are considered for the validation process are modelled 
in Flownex and compared with the PBMM data. Additionally, four extra fault conditions 
are modelled to extend the reference fault database to six single faults. 
Section 7.6 describes the procedure of process FDI with the h-s graph approach. 
Firstly, the distribution of the measured noise is established which is a prerequisite for the 
hypothesis test used for fault detection. Next, the emulated faults are detected without 
delay and correctly isolated using the FII. 
In section 7.7, the improvement in model performance is demonstrated by 
transforming the measurements. This goal is accomplished by using the T-P and h-s 
models derived at full power to predict the reference values at reduced power. 
Some concluding remarks are summarized in section 7.8. 
7.2 Differences between the PBMR models and the PBMM 
The original design of the PBMR is based on a three-shaft, closed-loop intercooled 
recuperative Brayton cycle. The most noticeable difference between the two models is the 
number of turbines and shafts. Whilst the three-shaft model has two free running shafts 
and one shaft running at 50 Hz, the single shaft model has one interconnected shaft 
running at 50 Hz. 
In the MPS, the three shafts are each connected to a separate turbine, the HPT, LPT 
and the PT. Therefore, to monitor the turbines individually and not as a single unit, two 
additional nodes are required on the h-s graph. Figure 7.2.1 illustrates the layout of the 
HPB - High Pressure Compressor Bypass Valve 
HPBC - High Pressure Compressor Bypass Control Valve 
LPB - Low Pressure Compressor Bypass Valve 
LPBC - Low Pressure Compressor Bypass Control Valve 
GBP - Gas Cycle Bypass Valve 
HCV - High Pressure Coolant Velve 
LCV • Low Pressure Coolant Valva 
RBP - Recuperator Bypass Valve 
SIV • Start-up Blower System Inline Valve 
SBSV - Start-up Blower System isolation Valve 
SBPC - Start-up Blower System Bypass Control Valva 
SBP - Start-up Blower System Bypass Valve 
HICS - Helium Inventory Control System 
Fig. 7.2.1 Schematic showing the three-shaft MPS of the first PBMR configuration [46]. 
123 
Validation of the h-s graph approach for process FD1 
Fig. 7.2.2 Gas flow path through the three-shaft MPS [46], 
three-shaft PBMR model and Fig. 7,2.2 depicts the gas flow path through the MPS. The 
theoretical h-s graph with the additional nodes is shown in Fig. 7.2.3. 
To verify the operation of the three-shaft configuration, the prototype PBMM plant 
was constructed at the North-West University. A schematic layout of the PBMM MPS is 
shown in Fig. 7.2.4. Although the overall performance characteristics of the prototype 
plant closely resemble that of the PBMR plant, some of the differences are as follows: 
• The pebble bed nuclear reactor is emulated by a 420 kW high temperature resistive 
heater. The heater has like the pebble bed a large thermal capacity and is rated for a 
maximum outlet temperature of 700 °C. 
Entropy 
Fig. 7.2.3 The theoretical h-s graph for the three-shaft PBMR model. 
124 
Validation of the h-s graph approach for process FD1 
<Csoiing yy] ? ? poling ;.| 
Fig. 7.2.4 Simplified schematic showing the PBMM three-shaft MPS. 
• The working fluid of the PBMM is nitrogen instead of helium. The main reason for 
this is the use of turbochargers that are used in internal combustion engines with ab 
as the working fluid. Nitrogen has basically the same thermo-physical properties as 
air but contains no oxygen (flammable and corrosive). 
• The external load in the PBMM is emulated by a compressor (ELC) and a power 
dissipation loop which consists of an external load cooler. 
• The compressors are single stage centrifugal compressors rather than the multi-stage 
axial flow turbo machines. The performance characteristics of centrifugal and axial 
flow machines are essentially the same within the system with reference to pressure 
ratio and isentropic efficiency versus non-dimensional mass flow. 
Similar to the PBMR, the primary method of power control is achieved by injecting or 
extracting nitrogen inventory from the cycle. This process is slow and faster load changes 
are accommodated by using the bypass valves. The solid model of the PBMM is shown 
in figure 7.2.5 which demonstrates the basic layout of the plant. 
125 
Validation of the h-s graph approach for process FDI 
Fig. 7.2.5 Solid model of the PBMM [67]. 
7.3 Modelling the PBMM plant in Flownex 
The steady state operating point of the PBMM plant is dependent on various controlled 
variables, making each operating point different. The variables are the heater outlet 
temperature, the suction pressure of the LPC, the valve position in the external power 
dissipation loop, position of the compressor bypass valves and the cooling water flow rate 
through each cooler. The cooling water temperature is not a controlled variable as it 
varies with ambient conditions and has to be measured. 
Two steady state conditions were tested against the PBMM data to validate the 
Flownex model. The schematic diagram of the Flownex model is shown In Fig. 7.3.1 and 
the plant configuration and equipment details are described in the PBMR micro model 
data pack [68]. During the two simulations, the LPC suction pressure is changed from 95 
kPa to 115 kPa. The heater outlet temperature and other controlled variables are kept 
constant and are summarized in Table 7.3.1. 
Parameter Value 
Heater outlet temperature (°C) 600 
Suction pressure of LPC (kPa absolute) 95, 115 
Cooling water flow rate through coolers (kg/s) 2.5 
Cooling water temperature (°C) 13 
Cooling water pressure (kPa) 350 
Nitrogen purity (%) 10
ELC valve opening Open 
Compressor bypass valves Closed 
Table 7.3.1 PBMtvt steady state conditions. 
126 
Validation of the h-s graph approach for process FD1 
Fig. 7.3.1 Schematic diagram showing the PBMM Flownex model. 
Table 7.3.2 lists the results of the measured PBMM data and the Flownex model 
calculations for the two steady state conditions. The values presented are for the 
measured nodes depicted in Fig. 7.2.4. The results show that there are considerable 
differences between the mode! and the PBMM data [67], 
The temperature of the HP gas leaving the HPC is increased by more than 40 °C as a 
result of gas passing through the pressure vessel which houses the heater and the turbo 
machinery (Fig. 7.2.5). The increased temperature is believed to come from the heater 
and the metallic support structure of the turbo machinery. 
Temperature Pressure Temperature Pressure 
Component (°C) (kPa) -95 (°C) (kPa)--115 
PBMM FLNX PBMM FLNX PBMM FLNX PBMM FLNX 
LPC inlet 21.5 15.0 94.1 93.4 24.7 15.2 114.1 113.1 
1C inlet 80.7 78.8 147.9 160.7 84.2 79.1 179.2 194.7 
HPC inlet L7.4 14.6 148.4 160.2 20.9 14.9 179.4 194.1 
RX inlet (HP) 126.7 79.9 255.0 280.1 129.5 80.2 306.6 339.0 
Heater ialet 399.2 399.2 254.2 278.5 349.8 394.5 305.8 337.3 
HPT inlet 586.0 600.0 252,0 278.1 604.4 600.0 302.7 336.8 
LPT inlet 511.8 540.1 171.3 187.5 510.4 540.1 205.9 227.1 
PT inlet 433.0 480.5 111.8 123.1 436.9 480.4 132.7 148.9 
RX inlet (LP) 400.2 447.7 91.4 95.7 402.0 447.5 112.0 115.8 
PC inlet 164.3 130.9 96.6 95.0 172.3 135.9 116.7 115.0 
Difference (%) 1.6; 8 1.93 8.53 
Table 7.3.2 Steady state values for the two operating points. 
127 
Validation of the h-s graph approach for process FBI 
Also, the HPC pressure is higher in the simulations than observed in the data. Given that 
the LPC suction pressure is set, this could be due to either leakage in the cycle or an over-
estimation of the compressor performance in the simulations. If the HP manifold pressure 
is set in the simulations, the effect of the compressor performance would be less 
noticeable. 
The results for the 95 kPa operating point of the PBMM are presented on the h-s 
graph in Fig. 7.3.2 (a). The figure confirms the discrepancies between the Flownex model 
and the data and shows that the increase in entropy across the turbines is larger than 
expected. To compensate for the temperature differences, the heat loss from the turbines, 
heater and the pressure vessel to the ambient are calculated from the PBMM data. 
Following this, additional heat transfer paths are incorporated in the Flownex simulation 
model and the heat transfer coefficients adjusted until satisfactory results are achieved. 
The heat transfer paths are modelled from measured data seeing as the heat losses 
occur from undefined, complex geometries [67]. Table 7.3.3 summarizes the results of 
the Flownex simulation with the additional heat transfer paths. The results Indicate that 
the correlation between the Flownex model and the PBMM data is acceptable with an 
absolute difference of less than 0.6 %. The results are illustrated on an h-s graph and are 
shown in Fig. 7.3.2 (b). The figure illustrates that the correlation between the improved 
Flownex model and the PBMM plant data is good. The model is now used to simulate the 
appropriate operating points in the PBMM data. 
7.4 The PBMM data used for fault emulation 
This section describes the PBMM plant data used to emulate the fault conditions. Thus 
far, several successful steady state and transient runs have been completed on the PBMM 
plant. Due to the high costs of components and the unsafe operating conditions that may 
occur from directly inducing faults in the system, only experimental data from previous 
test runs is used for the emulation of faults. 
[2 14 16 l.S 2 2.2 2.4 
Entropy [kJ/(kg.K)] 
1.4 1.6 1.8 2 22 Z.4 
Entropy (kJ/(kg.K)] 
(a) (b) 
Fig. 7.3.2 The practical h-s graphs for the PBMM steady state simulation at 95 kPa: (a) heat losses; 
(b) additional heat transfer paths modelled. 
128 
Validation of the h-s graph approach for process FDI 
Temperature Pressure Temperature Pressure 
Component (°C) (kPa). -95 (°C) (kPa)- 115 
PBMM FLNX PBMM FLNX PBMM FLNX PBMM FLNX 
LPC inlet 21.5 21.6 94.1 94.0 24.7 24.6 114.1 114.0 
1C inlet 80.7 80.8 147.9 L48.1 84.2 83.3 179.2 178.9 
H.PC inlet 17.4 17.5 148.4 148.0 20.9 21.0 179.4 178.5 
RX inlet (HP) 126.7 126.S 255.0 254.8 129.5 129.4 306.6 306.5 
Heater inlet 399.2 399.4 254.2 254.0 349.8 349.5 305.8 305.9 
HPT inlet 586.0 586.0 252.0 250.3 604.4 604.0 302.7 302.0 
LPT inlet 511.8 515.5 171.3 168.2 510.4 514.2 205.9 201.1 
PT inlet 433.0 436.4 11). 8 109.7 436.9 439.5 132.7 130.5 
RX inlet {LP) 400.2 398.8 91.4 90.2 402.0 400.4 112.0 110.9 
PC inlet 164.3 164.5 96.6 96.7 172.3 172.9 116.7 116.9 
Difference (%) 0.2<: 1 0.54 0.1 2 0.51 
Table 7.3.3 Results for the two operating points (additional heat transfer paths modelled). 
Firstly, thrust tests are conducted on the PBMM to determine the thrust load on the turbo 
units (comprising the turbo/compressor and the turbine). These tests were conducted 
because of a bearing failure on the HP turbo that resulted in complete failure of the unit 
after only 60 hours of operation. As discussed, the turbochargers used are 'off-the-shelve' 
single stage centrifugal machines, generally used in an open cycle configuration on earth 
moving equipment. In this open cycle configuration, the differential pressure across the 
turbo unit is almost zero (inlet and outlet to atmospheric pressures), whilst it varies 
considerably in the closed cycle of the PBMM. 
Two sets of data are used to emulate fault conditions in the PBMM. The first is data 
logged during the failure of the turbo unit and the second is data from a thrust test 
afterwards. During the thrust test, the heater outlet temperature and LPC suction pressure 
are increased from bootstrap conditions7 to 650 °C and 115 kPa respectively which give 
the variation in thrust. These variations result in changing pressure ratios across the turbo 
units and are normally not favourable, since the cycle efficiency is a function of the 
overall pressure ratio of the system. During normal operation of the MPS, these changing 
pressure ratios can therefore be interpreted as possible component or process anomalies. 
The differential pressure across the turbo unit is given by (7.4.1) 
Ap = ( rin.iurb'mc P out,turbine )-( 
cout .compressor Pin, compressor 
) (7.4.,) 
With the net positive thrust direction from the turbine to the compressor, the thrust force 
on the turbo unit is calculated as 
'During bootstrap conditions in the PBMM, the Brayton cycle becomes self-sustainable at 
approximately T0 = 580 °C and P0 = 95 kPa. 
129 
Validation of the h-s graph approach for process FD1 
T - -&/ .P,(^
2)-A,(^-^)-M^-<2) 
+ Pl (dV ~ rf/ ) + Po (du ~ d* ) ~ Po., (d2,2 ) 
(7.4.2) 
with subscripts c and t denoting the compressor and turbine; pt the lubrication chamber 
pressure, ds the shaft diameter, ds the shaft diameter at the c or t side, d2 the c or t outlet 
diameter and di the c ox t inlet diameter. The differential pressures, thrust forces, pressure 
ratios, pressures, temperatures and vibration levels are illustrated for the turbo units in 
figures 7.4.1 and 7.4.2 respectively. 
In dataset 1. samples 1 to 1510 is used with the failure of the HP turbo unit at 
approximately sample 1500. In dataset 2, samples 4030 to 5530 are used for the 
validation. In both datasets, nitrogen is injected or extracted and therefore comprises 
normal transient variations of the process. 
In the First dataset, injection commences from samples 410 to 442, 459 to 499, 524 
to 564 and 1131 to 1288, with intervals of approximately 40 samples. In the second 
dataset, extraction starts from samples 5100 to 5533. Now that the datasets and transient 
conditions are explained, the emulated fault conditions are described. In dataset 1, the 
1000 1500 2Q00 2500 3000 3500 
Sample Number 
(a) 
"0 500 1O00 1500 2000 2500 3O0O 3500 
Sample Number 
EOO 1000 1500 200O 2500 3000 3500 
SampSe Number 
(b) 
500 1000 1500 2000 2500 3000 3500 
Sample Number 
(c) (d) 
Fig. 7.4.1 Turbo machinery parameters for bearing failure: (a) pressure ratio; (b) pressures/temperatures; 
(c) vibration level; (d) differential pressure/thrust. 
130 
Validation of the h~s graph approach for process FDI 
1000 2000 3000 4000 500Q 6000 7000 8000 
Sample Number 
(a) 
- LPTU 
- HPTU 
1000 2000 3O00 4000 5000 6000 7000 8000 
Sample Number 
(C) 
1000 2000 3000 4000 5000 6000 7000 8000 
Sample Number 
(b) 
1000 2000 3000 4000 5000 6000 7000 8000 
Sample Number 
(d) 
Fig. 7.4.2 Turbo machinery parameters for thrust test: (a) pressure ratio; (b) pressures/temperatures; 
(c) vibration level; (d) differential pressure/thrust. 
pressure ratios of the turbos vary briefly during injection and settles for normal steady 
state operation. However, the HP compressor pressure ratio shows an increase during 
injection with a significant increase in thrust force when compared to the LP turbo unit. 
Also, the differential pressure of the LP turbo unit stays approximately constant, whilst 
the increase across the HP turbo unit is about 8 kPa. Conversely, Fig. 7.4.1 (c) shows that 
the vibration levels stay within normal operational limits. This makes analysis of the 
vibration level (magnitude) less effective to detect the pressure ratio fault in the specific 
component. A frequency analysis of the vibration level can however be more sensitive to 
the specific fault condition. The emulated fault condition is modelled as a single fault by 
means of an increase in the HP turbo pressure ratio starting from 0 % at sample 410 to a 
maximum of 2 % at sample L000. The heater outlet temperature is kept constant at 
650 °C during the transient. 
As discussed, dataset 2 comprises only a section of the total thrust test. The dataset 
shows a decrease in the pressure ratios of the turbo units whilst the temperatures stay 
approximately constant. Figure 7.4.2 (b) shows that the HPT inlet temperature decreases 
following the steady state conditions. Therefore, the second emulated fault is modelled as 
a decrease in HPT inlet temperature which signifies a probable heater malfunction. It 
must be noted that during normal operating conditions, the heat source outlet temperature 
I3l 
Validation of the h-s graph approach for process FD1 
is controlled and a decrease will be rectified accordingly. For the validation of the h-s 
graph approach, a decrease in temperature is simply used to emulate a change in normal 
operating conditions. 
Similar to the first dataset, Fig. 7.4.2 (c) shows that the vibration levels are within 
operational limits during the transient. The emulated fault starts at sample 5080 and 
increases to 2 % at sample 5130. Since the extraction of nitrogen starts at sample 5100, 
the fault occurs during a transient variation and steady state operation of the process. 
After a 2 % change in the fault magnitude, the fault stays constant. 
7.5 Simulation of the emulated faults in Flownex 
The Flownex model described in section 7.3 is now applied to validate the steady state 
conditions prior to the emulated faults. This is done to validate the integrity of the model 
to simulate the correct fault signatures. Table 7.5.1 lists the plant parameters for the two 
steady state conditions during normal power operation of the MPS. The PBMM data are 
averaged for the periods of interest to minimize the effects of measurement noise. These 
parameters are used to simulate the corresponding operating points in Flownex. The 
results of the Flownex simulations are summarized in Table 7.5.2 and are illustrated on 
the h-s graph in Fig. 7.5.1. The table shows a good comparison between the PBMM data 
and the Flownex results, with a maximum difference of 0.11 %. The model can therefore 
be used to simulate the emulated fault conditions. 
It is important to note that the operating point of the PBMM is dependent on two 
additional variables. Therefore, the reference model must incorporate the VS with 
n-dimensional interpolation. Since the valve openings and the cooling water flow rate is 
fixed for the periods of interest, the reference models are simply calculated for the actual 
operating conditions. To create the reference fault signatures, the model at 100 % MCR 
(115 kPa) is used. 
In order to validate the effectiveness of the h-s graph approach, a reference fault 
database is created with additional fault signatures. The motivation for additional 
reference signatures is to demonstrate the ability of the method to reject the incorrect 
signatures. A total of six fault conditions comprising the two emulated and four 
additional faults are modelled in Flownex. The fault magnitudes are listed in Table 7.5.3 
and the results of the Flownex simulations are summarized in Table 7.5.4. 
Parameter Dataset 1 Dataset 2 
Heater outlet temperature (°C) 
Suction pressure of LPC (kPa absolute) 
Cooling water flow rate through coolers (kg/s) 
Cooling water temperature (°C) 
Cooling water pressure (kPa) 
Nitrogen purity (%) 
Compressor bypass valves  
Table 7.5.1 Parameters for the two steady state simulations. 
650 650 
101 105 
PC = 2.5 PC = 2.02 
IC = 2.5 1C= 1.68 
-19 -16 
350 350 
100 100 
Closed Closed 
132 
Validation of the h-s graph approach for process FDI 
Dataset 1 Dataset 2 
Component Temperature (°C) Pressure (kPa) Temperature (°C) Pressure (kPa) 
PBMM FLNX PBMM FLNX PBMM FLNX PBMM FLNX 
LPC inlet 24.45 24.54 101.02 101.0 22.07 21.98 105.05 105.0 
IC inlet 93.07 93.08 167.7 167.93 91.29 92.35 178.94 178.46 
HPC inlet 21.20 21.23 167.9 167.4 18.63 18.68 178.37 177.89 
RX inlet (HP) 138.48 138.57 303.35 303.19 136.62 136.44 325.5 325.28 
Heater inlet 371.3 371.44 302.88 302.07 368.5 368.28 324.05 324.1 
HPT inlet 649.97 650.0 301.53 301.78 650.07 650.0 322.92 323.79 
LPT inlet 548.97 554.02 196.8 197.5 550.6 550.48 213.01 212.99 
PT inlet 462.14 458.13 130.09 131.24 472.8 473.21 137.95 138.76 
RX inlet (LP) 428.75 428.15 101.88 102.94 427.06 427.23 106.73 107.78 
PC inlet 185.14 185.18 102.13 102.14 187.4 187.79 107.01 107.04 
Difference (%) 0.03 0.11 0.05 0.08 
Table 7.5.2 Steady state results for the two PBMM datasets, 
In order to create reference fault signatures, the error and area error methods are used. 
The normalized signatures of the six faults are shown in Fig. 7.5.2. The figure shows that 
the correlation between the different signatures is low, which indicates that the reference 
fault database of the PBMM is unique. 
1.4 1.6 1.8 2 2 2 2.4 2( 
Entropy [kJ/(kg.K)] 
(a) 
1.2 14 1.6 1.8 2 2.2 2.4 2.6 
Entropy [kJ/(kg.K)] 
(b) 
Fig. 7.5.1 The h-s graphs for the steady state PBMM datasets; (a) dataset 1; (b) dataset 2. 
Fault Direction Normal Limit (2 %) 
1. HPC pressure ratio Increase 1.0 1.1 (scaling factor) 
2. Heater outlet temperature Decrease 650 °C 635 °C 
3. LPC pressure ratio Decrease 1.0 0.9 (scaling factor) 
4. HPT pressure ratio Increase 1.0 l.l (scaling factor) 
5. Intercooler heat transfer area Decrease 36.5 m2 30 m2 
6. Recuperator heat transfer area Decrease 257.3 m2 250 m2 
Table 7.5.3 PBMM emulated fault conditions modelled in Flownex. 
133 
Validation of the h-s graph approach for process FDI 
Fault 1 Fault 2 Fault 3 Fault 4 Fault 5 Fault 6 
Node T P T P T P T P T P T P 
(°Q (kPa) (°C) (kPa) (°C) (kPa) (°C) (kPa) CO (kPa) CO (kPa) 
1. 24.6 101.0 21.8 105.0 24.5 101.0 24.5 101.0 24.6 101.0 24.6 101.0 
2. 92.9 167.7 88.0 172.5 94.5 171.3 92.2 166.7 92.8 167.5 93.1 167.9 
3. 21.2 167.2 18.4 171.9 21.3 170.8 21.2 166.2 22.5 167.0 21.2 167.4 
4. 138.6 302.3 135.5 308.9 138.3 310.6 140.5 312.7 139.1 301.4 138.6 303.2 
5. 371.7 301.2 364.1 307.7 369.1 309.4 369.3 311.7 372.1 300.3 370.0 302.1 
6, 650.0 300.9 635.0 307.4 650.0 309.1 650.0 311.4 650.0 300.0 650.0 301.8 
7. 548.9 198.7 536.7 203.6 549.3 203.5 544.4 197.8 549.0 198.2 549.0 199.2 
8. 472.9 131.2 463.0 135.4 472.1 133.0 469.2 130.9 473.1 131.1 472.8 131.4 
9. 428.4 103.5 420.2 107.5 426.3 103.7 425.4 103.5 428.7 103.5 428.2 103.5 
10. 185.1 102.8 184.8 106.9 185.8 102.9 184.5 102.8 185.0 102.8 186.7 102.8 
Table 7.5.4 Flownex results for the six emulated fault conditions. 
For each of the six faults, four reference fault signatures are created. As a result, the 
reference fault database comprises 24 single fault signatures. The database is now used 
together with the single fault FDI algorithm to classify any of the modelled fault 
conditions in the PBMM data. 
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Fig. 7.5.2 Normalized fault signatures for the 6 PBMM faults: (a) h error; (b) s error; (c) h area error; 
(d) s area error. 
134 
Validation of the h-s graph approach for process FDI 
7.6 Fault detection in the PBMM 
The PBMM plant is similar to the PBMR subjected to random process and measurement 
noise as seen in figures 7.4.1 and 7.4.2. One of the reasons the measurement data is 
corrupted with noise is because no signal conditioning (sensor FDI) is implemented in the 
PBMM due to time and budget constraints. In the previous chapter, random noise with a 
normal distribution and zero mean is added to the Flownex data to emulate a normally 
distributed error vector for the fault detection algorithm. In a real application like the 
PBMM, these properties cannot be assumed and must be determined. Firstly, an analysis 
of the temperature and pressure measurements is done to determine the magnitude and 
the statistical properties of the noise, i.e. the distribution, ja and c2. The noise component 
of the PBMM measurements is determined by taking the residuals (average of the data 
minus the data) of the variables during the fault free steady state simulations. 
To determine the distribution of the random noise component, a normal probability 
plot is used with a linear line joining the first and third quartiles of the data. This is done 
to evaluate the linearity of the data. The normal probability plots are shown in Fig. 7.6.1 
for a temperature and pressure measurement of the PBMM. Both plots are linear, which 
means that the data can be approximated by a normal distribution (other distributions will 
introduce curvature in the plot). Table 7.6.1 lists the estimated statistical properties of the 
measurement noise for the PBMM data. The results show that the mean of the residuals 
are zero and the variance in temperature and pressure are very small. 
The single fault FDI algorithm is now applied to classify the emulated faults in the 
data. The enthalpy and entropy residual vectors for the PBMM are given by 
r*(0 = [ri;(t),r,J(t),...,rJJo(t)]T and rs (t) = [rJ (t),r/(t),...,r;°(t)]T (7.6.1) 
The missed alarm rate is selected as a = 0.01, the FII limit for known reference signatures 
is chosen as 0.5, the sample time window comprises 10 samples, and the hypothesis 
thresholds for h and 5 are selected as 2.5 and 0.1 respectively. 
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Fig. 7.6.1 Normal probability plots for measurements in the PBMM: (a) temperature; (b) pressure. 
135 
Validation of the h-s graph approach for process FDI 
Statistic Temperature (°C) Pressure (kPa) 
Mean (p) 0 0 
Variance (ff2) 0.1988 0.1445 
Max. deviation 2.9423 2.5729 
Distribution Normal Normal 
Table 7.6.1 Statistical properties of the PBMM measurement noise. 
As discussed, the emulated faults start at approximately sample 410 in dataset 1 and at 
sample 1080 in dataset 2. In dataset 1, the Hi/, and Hi, fault detection tests fired at the 
next sampling interval (sample 420). In dataset 2, Hi/, fired at the next sampling interval 
(sample 1090) and H\s fired at sample 1270. Table 7.6.2 summarizes the results of the 
fault detection in the two datasets. The table shows that during the steady state runs prior 
to the fault conditions, no false alarms are triggered. Also, after the introduction of the 
faults, no missed alarms are observed. The thresholds selected for the hypothesis tests are 
therefore sufficient to the limit the false alarm rate during normal noisy conditions and 
trigger the h-s graph method for fault isolation after fault detection. The fault isolation 
procedure is summarized as follows: firstly, the four fault signatures are created for each 
sample window and compared to the six reference fault signatures by calculating the F1I. 
The FH is calculated for the error and area error methods and is determined for h and s. 
The results of the FII for the error and area error methods are shown in Fig. 7.6.2 and the 
average FII for each method is summarized in Table 7.6.3. In dataset 1 and 2, 109 and 41 
sample windows are calculated respectively after fault detection. 
Figure 7.6.2 (a) shows that the fault in dataset 1 is correctly isolated {FII decreases 
below unknown reference signature limit) after approximately 15 sample windows (570 
samples). This is expected since the pressure ratio first showed a decrease (unknown 
signature) before increasing after 600 samples. Following sample window 72 (1140 
samples), the pressure ratio decreases again before increasing to a maximum. The FII 
responded correctly by increasing beyond the unknown reference signature limit. In 
Fig. 7.6.2 (b), the fault in dataset 1 is correctly isolated with the area error method after 
only a few sample windows. Although the average FII is lower, the area error method 
responded slowly to the unknown signature at sample window 72 for the decrease in 
pressure ratio. The slow response of the FII can be attributed to the fact that the fault 
magnitude of the unknown signature is smaller than 1%. 
Figure 7.6.2 (c) and (d) indicate that the fault in dataset 2 is correctly isolated with 
the error and area error methods. The figures show that the FII is below the known 
reference signature limit commencing at the first sample window after detection. 
Action Dataset 1 Dataset 2 Steady state (samples) Fault (samples) Steady state (samples) Fault (samples) 
False alarms 
Fault detection 
Missed alarms 
0 
0 420 
0 
0 
0 1090 
0 
Table 7.6.2 Alarms during fault detection for the PBMM datasets. 
136 
Validation of the h-s graph approach for process FDI 
40 60 80 
Sample number 
-10 60 80 
Sample number 
(a) (b) 
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Sample number 
(C) (d) 
Fig. 7.6.2 FII for the emulated faults in the PBMM after fault detection: (a) dataset I, error; (b) dataset 1, 
area error; (c) dataset 2, error; (d) dataset 2, area error. 
Table 7.6.3 shows that on average, the FII is 0.218 for the isolated fault signatures and 
2.925 for the rejection of the incorrect signatures. The results presented therefore indicate 
that the proposed h-s graph approach can be successfully applied to isolate known faults 
during normal plant operation. Similarly, as demonstrated for the PBMR, the reference 
fault database can be expanded to include all the probable system faults. This will 
minimize the probability of incorrect isolation. 
7.7 The T-P and h-s models applied to the PBMM 
In this section, data from the PBMM is used to show that the transformation of 
measurements can improve model performance in a practical application. Firstly, the 
Average FII Dataset 1 Dataset 2 Error Area Error Area 
Recognition 
Rejection 
0.3791 0.1536 
3.1625 3.6434 
0.2201 0.1211 
2.6291 2.2635 
Table 7.6.3 Average FII for the PBMM fault conditions after fault detection. 
137 
Validation of the h-s graph approach for process FDI 
reference T-P and h-s graphs (without VS) are derived for the 100 % MCR (115 kPa) 
steady state data. Following this, the models are used to reconstruct the reference graphs 
for 40 % MCR (95 kPa). The plant data from the PBMM operating at 40 % MCR is used 
as reference instead of Flownex. The T-P and h-s graphs are illustrated in Fig. 7.7.1 for 
the two operating points and Table 7.7.1 summarizes the calculated values for 40 % MCR 
(turbines are monitored as one unit, i.e. only 8 nodes). 
The table shows that the percentage difference for P is not as large as observed in the 
PBMR at reduced power (Appendix B). This is due to the fact that the pressure difference 
between full and reduced power is in the order of several MPa for the PBMR, whilst only 
a few kPa in the PBMM. The results listed indicate that the transformation of the 
measurements improves the error between the actual data and the model estimates by 
0.25 % and 8.45 %. The modelling error of the reference h-s model is therefore sufficient 
to correctly estimate the values at different operating points (provided the temperatures 
and pressure ratios stay constant). 
7.8 Summary and conclusions 
This chapter focussed on the validation of the h-s graph approach by applying the method 
to real plant data from the prototype PBMM plant. 
Firstly, section 7.2 describes the differences between the PBMR and the PBMM 
topologies. The PBMM, which is a scaled version of the three-shaft PBMR configuration, 
requires ten monitoring nodes to supervise all the main components in the MPS. 
Section 7.3 discussed the development of a PBMM simulation model in Flownex. 
The results of the first Flownex model revealed a number of differences between the 
plant measurements and the model and it was concluded that the extra heat was gained 
from the heater and the metallic support structures in the pressure vessel. Additional 
constraints were imposed on the Flownex model and the final model showed satisfactory 
results. 
In section 7.4, the noisy plant data is used to emulate two fault conditions. The main 
1.6 1.8 2 2.2 
Entropy [kJ/(kg.K)] 
150 200 250 
Pressure (kPa) 
(a) (b) 
Fig. 7.7.1 Practical graphs of the Brayton cycle for full and reduced power (measured): (a) h-s; (b) T-P. 
138 
Validation of the h-s graph approach for process FDI 
Node 7 F 
i h 5 
Data M Data M Data M Data M 
I. 21.5 24.7 94.1 94.1 294.66 297.86 1.439 1.439 
2. 80.7 84.2 147.9 158.9 353.86 357.36 1.489 1.491 
3. 17.4 20.9 148.4 159.1 290.56 294.06 1.293 1.296 
4. 126.7 129.5 255 286.3 399.86 402.66 1.452 1.455 
5. 399.2 349.8 254.2 285.5 672.36 622.96 1.888 1.892 
6. 586 604.4 252 282.4 859.16 877.56 2.234 2.237 
7. 400.2 402 91.4 91.7 673.36 675.16 2.267 2.264 
8. 164.3 172.3 96.6 96.4 437.46 445.46 1.834 1.836 
Diff 0.45 8.56 0.20 0.09 
Table 7.7.1 Results for the reference models (PBMM operating at 40 % MCR). 
reason faults are not directly induced in the system is because of possible system damage 
and unsafe operating conditions. 
To validate the selected fault conditions, the faults are simulated in Flownex and 
compared with the emulated data in section 7.5. The results confirmed that Flownex can 
accurately model the thermodynamic system. 
Section 7.6 described the fault detection and isolation procedure with the h-s graph 
approach. By applying the proposed method, the emulated fault conditions are quickly 
detected and correctly isolated. 
Lastly, section 7.7 presented a comparison between the T-P and h-s reference models 
at reduced power levels. The results indicated that even though the operating range of the 
PBIVIM plant is much smaller compared to the PBMR, the transformation of 
measurements improves model performance considerably. 
The following are some of the important conclusions reached in this chapter: 
• The h-s graph approach is only dependent on the thermodynamic cycle being 
represented on an h-s graph. The type of and number of components do not affect the 
effectiveness of the method (PBMM comprises ten nodes with an electrical heater as 
heat source). 
• The h-s graph approach can be implemented in a real nonlinear dynamic system 
comprising noisy measurements. 
• The implementation of the h-s graph approach is not dependent on a linear 
transformation, state space representation or transfer function describing the complex 
nonlinear system. Furthermore, given the many unknown factors in the PBMM, this 
will undoubtedly be a complex task. 
• Since the h-s graph comprises a closed cycle, the effects of fault propagation are 
incorporated in the reference fault signatures. 
139 
CHAPTER 8 
Conclusions and recommendations 
This chapter summarizes the conclusions drawn in the thesis and documents the original 
contributions of the study. Recommendations and suggestions for future research are also 
presented. 
8.1 Introduction 
As discussed in Chapter 1, the main concern of the thesis is to develop a novel approach 
to fault diagnosis in a nonlinear dynamic HTGR NPP. 
Chapter 2 surveyed advanced techniques for sensor and process fault diagnosis. 
Redundant and non-redundant techniques for sensor fault diagnosis were evaluated 
together with process history-and model-based methods for process fault diagnosis. 
Chapter 3 discussed the general topology of the PBMR MPS. From this chapter 
onwards, the PBMR was used as the reference HTGR NPP. In the second part of Chapter 
3, the probable fault symptoms of the PBMR MPS were derived. 
The sensor fault diagnosis methodology was developed in Chapter 4. The integrated 
reasoning architecture was presented and the sensor validation and fusion module, 
SENSE was proposed. 
Application of traditional process FDI techniques was the topic of Chapter 5. 
Process supervision with limit value checking was presented and linear mathematical 
modelling of a power turbine was demonstrated. Based on the criterion for an advanced 
fault diagnosis technique, their limitations did not favour them for implementation in the 
PBMR. 
The h-s graph approach for process fault diagnosis was derived in Chapter 6. The 
method uses the h-s graph as a reference model to describe the health of the system. 
Based on residuals between the graph and plant observations, fault signatures are 
generated for fault pattern recognition. For the case of multiple fault symptoms, a single 
signature subtraction procedure was proposed. 
The validation of the h-s graph approach for process fault diagnosis was presented in 
Chapter 7 by means of an application to real plant data from the prototype PBMM. 
The following sections summarize the conclusions drawn from this study. 
140 
Conclusions and recommendations 
8.2 Conclusions 
The conclusions presented are grouped according to the following thesis objectives: 
/. Determine the most relevant mechanisms for component degradation in an HTGR 
MPS and formulate suitable fault classes. 
2. Develop a novel integrated architecture for sensor fault diagnosis in an HTGR MPS. 
3. Develop a novel approach for process fault diagnosis in an HTGR MPS. 
4. Validate the proposed process fault diagnosis approach through an application in 
the PBMM. 
8.2.1 Component degradation and suitable fault classes 
During the lifespan of any engineering system, faults are unavoidable factors that degrade 
system performance. Firstly, a sensitivity analysis was conducted to determine the 
parameters that influence the performance of the MPS. Direct relations between these 
parameters and known fault symptoms (caused by the degradation mechanisms) were 
then derived. 
Concerning the parameters that result in degraded component behaviour, it is 
concluded that three universal types of parameter changes result in MPS 
underperformance. The parameters are grouped into three fault classes and comprise the 
resistance in fluid flow, leakages between components and efficiency changes in 
components. 
In addition, it was observed from the sensitivity analyses that for some faults, a small 
parameter change reflected only as a marginal change in system performance. Therefore, 
the conclusion was drawn that incipient behaviour of these faults would be very difficult 
to detect and supported the motivation for the development of an advanced process fault 
diagnosis approach. 
8.2.2 Sensor fault diagnosis 
One of the main concerns is the detection of common mode failure (drift in the same 
direction at the same rate) among a set of redundant measurements. Although this 
phenomenon is extremely uncommon with only a few occurrences over several decades 
[16], the sensor fault diagnosis system must provide for these situations. Techniques 
based on consistency checks will surely fail in this case. To provide for common mode 
failure of one group of redundant measurements, the PCA technique is adopted into the 
sensor fault diagnosis methodology. The challenge however is to determine which sensor 
configuration will deliver a valid estimate for the faulty variables. The following are 
concluded about the proposed integrated architecture: 
141 
Conclusions and recommendations 
• The intelligent search algorithm provides the PCA model with the most likely 
healthy (m-1 sensors) sensor configurations. However, if more than one input is 
corrupted in a configuration, it cannot produce a valid estimate. 
• The PCA technique can model most of the nonlinear process behaviour if the process 
dynamics are relatively slow, as for an HTGR NPP. This was verified experimentally 
on PBMR and PBMM data. The obvious question now is, "Why don't we use the 
same PCA model for process fault diagnosis?" The reason is: PCA fault isolation is 
based on one faulty variable in a group of correlated signals (faults occur 
independently in each sensor), whilst in the process, faults are reflected in many 
variables simultaneously, therefore, isolation would be impossible. 
• Since the sensor residuals are calculated for each sensor independently, multiple 
simultaneous failures can be detected. Therefore, this integrated architecture will be 
capable of detecting common mode failure among a group of redundant sensors. 
• The proposed approach produces a better fused estimate for the sensed variable than 
any single sensor. 
• One of the motivations for the proposed integrated architecture is that it can be 
implemented independent of the mathematical structure of the process. 
• The results obtained and documented in the thesis show that the objective regarding 
detection of instrument drift was realized. The data utilized in the first case study 
was representative of a real process, which served as validation for the proposed 
approach. 
8.2.3 Process fault diagnosis 
In Chapter 1, the desirable qualities for an advanced process fault diagnosis approach are 
listed. With these objectives in mind, this thesis demonstrated the h-s graph approach for 
process fault detection and isolation in an HTGR NPP. The following conclusions were 
drawn regarding this graphical model-based approach (based on normal power 
operation): 
• The overall health of the system can be quantified with a minimal amount of 
measured variables. 
• The mathematical structure of the process is not a requirement for the development 
of the reference plant model. 
• Faults in the system can be characterized by distinctive deviations in the shape of the 
h-s graph. 
142 
Conclusions and recommendations 
• Since the temperature and pressure ratios remain relatively constant over the 
operating region, the process can be described with only one reference h-s graph (no 
GBPC operation). This, however, is not the case for the temperature and pressure 
graph. 
• Normalized static fault signatures can be extracted from the h-s graph with the error 
and area error methods that are representative of a dynamic fault condition. 
• The normalized h-s fault signatures stay relatively constant with negligible variation 
for: changes in the fault magnitude, changes in the operating point and transient 
variations (injection, extraction and valve operation) of the normal process. 
Therefore, a fault condition can be characterized at any operating point with only one 
reference fault signature. 
• The results obtained showed that the proposed single fault extraction method can 
successfully isolate the contributing single faults by sequentially subtracting 
reference fault signatures. 
• During multiple fault symptoms, the contributing single faults appear to superimpose 
on each other. 
• Normal plant ageing is incorporated into the graph with an n-dimensional variation 
surface. It is concluded from the obtained results that the error surface needs minimal 
training data to make a meaningful interpolation. The variation surface is trained for 
new conditions (typically after plant inspection or maintenance) when the conditions 
are deemed normal. 
• If an accurate simulation model of the process is not available, the reference 
h-s graph can be developed with real data from the process. This will inherently 
reduce the modelling error between the model and the process. 
The desirable qualities listed in objective 2 of this thesis are realized to a certain degree 
with the h-s graph approach for process fault diagnosis. The following are concluded 
about the qualities listed: 
• Fault propagation is inherently accommodated in the reference fault signatures since 
the cycle is closed. Faults take approximately 5 seconds to propagate throughout the 
system. 
• Noise magnitude influences the isolation ability of the approach. However, the 
approach performed well on the PBMM data which comprised process and 
measurement noise. 
• Modelling errors between the simulation model and the plant Influence the isolation 
ability of the approach to some extent. This conclusion is based on the results 
143 
Conclusions and recommendations 
obtained from the verification procedure in Chapter 7 (modelling uncertainties 
between the plant data and the Flownex model were discussed). 
• Model development and re-training are rather simplistic. Model development 
requires only steady state data for one operating point subject to no valve operation. 
Furthermore, the model is re-trained by adding the new operating point to the 
variation surface. 
• The simulations showed that a small change in the fault magnitude (i.e. 1 %) 
produced signatures that are highly correlated. Therefore, the fault symptoms can be 
characterized by single reference signatures. 
• This thesis demonstrated that the h-s graph approach can be applied during transient 
variations of the normal process. 
• Isolation of multiple fault symptoms was achieved by devising a single fault 
extraction procedure. It is demonstrated in this study that the contributing single 
faults can be isolated. 
8.2.4 Validation of the process fault diagnosis approach 
This objective was achieved by application of the proposed h-s graph approach to real 
noisy plant data from the PBMTVI. The validation was realized experimentally by 
emulated fault symptoms in two datasets. The following conclusions were drawn 
regarding the validation process in the PBMM: 
• The approach is not dependent on the number of nodes (components) represented on 
the h-s graph. It was demonstrated that a reference model and fault signatures could 
be developed for a thermodynamic system with additional components (PBMM plant 
comprises three turbines). 
• The tasks of process fault detection and isolation were achieved without deriving a 
mathematical model of the plant. 
144 
Conclusions and recommendations 
8.3 Original contributions 
The original scientific contributions of the thesis in order of significance are as follows: 
• The application of the h-s graph to visualize heat and work transfer in a closed-or 
open cycle thermodynamic system is not new. However, applying the h-s graph in a 
new way for the tasks of fault detection and isolation in an HTGR NPP is an original 
idea. Power control by means of an inventory control system facilitates a graphical 
h-s reference model that remains invariant over the power range (proved). 
Consequently, the devised error and area error methods provide static reference h-s 
fault signatures that remain invariant to operating point changes, transient variations 
of the normal process and changes in the fault magnitude. 
• Techniques like the non-temporal parity space algorithm, principle component 
analysis, data fusion with confidence estimation and statistical analyses are not new. 
The contribution of the thesis lies in the integration of these ideas to form a new 
comprehensive methodology to sensor fault diagnosis. Individually, these techniques 
were proven to be unsuccessful for fault diagnosis in some situations. By combining 
their strengths in an integrated architecture, an advanced sensor fault diagnosis 
approach is realized that enables reliable and accurate estimates of the sensed 
variables. 
8.4 Recommendations for future research 
Although there are still many factors to consider before real life implementation, the 
study forms a basis for a new approach to process fault diagnosis in an HTGR NPP. The 
following areas warrant further research: 
• The h-s graph approach needs to undergo a full Monte Carlo analysis to fully 
comprehend the influence of noise and modelling uncertainty on the detection and 
isolation abilities of the graph. Both these factors were investigated to some extent, 
but not simulated for every possible operating point change or fault magnitude 
variation. 
• In the thesis, the constant reference fault signatures for different variations of the 
normal process were experimentally verified. A formal analytical prove for the 
universal applicability of the method over the entire operating range needs to be 
done. This will prove that the reference fault signatures are static provided that the 
correct reference model is utilized at the operating point. 
• The devised error and area error fault signature generation methods need to be 
compared. Although both methods provided uncorrelated fault signatures for the 
given fault conditions, the possibility of combining these signatures to improve fault 
isolation needs to be investigated. 
145 
Conclusions and recommendations 
• The investigated fault symptoms need to be extended to cover a wider range of 
system malfunctions. The critical faults discussed in Chapter 3 could be 
accommodated into the reference fault database. 
• Given the previous recommendation, the method needs to be extended for 
supervision during mode and state transitions of the plant. In addition, the fault 
diagnosis system would be a valuable asset during plant start-up. 
• In the thesis, the h-s graph approach uses reference plant data to determine the 
correct position of the reference model. A more intelligent method must be devised 
to position the reference graph in the h-s plane for different operating point 
variations. 
• The applicability of the proposed approach needs to be investigated for other 
thermodynamic systems comprising open-or closed cycles. 
146 
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[64] A. Bejan, "Heat transfer". John Wiley & Sons, Inc., New York, 1993. 
[65] A. Bejan, "Entropy generation minimization". CRC Press, Florida, 1996. 
[66] Matlab, "User guide", R14 version 7, 2004. 
[67] O. Widlund, G. Geffraye, J. Van Ravenswaay, N. Tauveron, W. Van Niekerk, 
"Comparison of the thermal-fluid analysis codes Cathare and Flownex with 
experimental data from the Pebble Bed Micro Model", 4th International conference 
on heat transfer, Fluid mechanics and thermodynamics, Cairo, Egypt, 2005. 
[68] J. T. Labuschagne, "PBMR micro model data pack", North-West University, no. 
PBMM-0066 rev. 2, Potchefstroom, South Africa, 2003. 
[69] E. Kreysig, "Advanced engineering mathematics", 7th edition, John Wiley & Sons, 
Canada, 1993. 
152 
Appendices 
A. Normal distribution and the central limit theorem 
Consider a set of independent random variables that have the same distribution function 
xi, X2,..., xn. Since their distributions are identical, they have the same mean n and 
variance a2. Let j/„ = xi+X2+ ...+x„. The central limit theorem states that the variable 
zn = y-^ (A.1.1) 
is asymptotically normal with mean 0 and variance 1. This is the distribution function 
F„(x) of zn that satisfies [69] 
It is important to note that the distribution type of the x variables is not important. 
Although the theorem states the equality only for n in the limit, the standard normal 
distribution is a good approximation even if the observations are limited in size [6]. 
Therefore, if the distribution of the x variables is known, the approximation error can 
be computed for any number of observations. 
153 
Appendices 
B. The temperature-pressure versus enthalpy-entropy graphs 
As discussed in Chapter 6, the shape of the h-s graph remains approximately constant 
over the operating range for power control with the ICS. For control options comprising 
the control valves, the reference model needs minimal adjustment by means of the VS. 
This is one of the primary motivations for the transformation from temperature-pressure 
(T-P) to h-s. For different power levels, the h-s graph shifts to the correct absolute 
pressure, but maintains the constant shape. In contrast, the shape of the T-P graph 
changes in the P-plane due to constant pressure ratios at different power levels. 
Figure B.l.l (a) and (b) shows the shift direction and shape of the theoretical h-s and 
T-P graphs for full and reduced power levels. Figure B.l.l (c) and (d) shows the graphs 
for the practical cycle of the PBMR (specific entropy is referenced to To = 0 °C and 
PQ = 10 MPa). The graphs show that the transformation to h-s results in a constant graph 
over the power range. For this reason, one graph can be used as reference model. 
Decrease in pressure Decrease in pressure 
\A^.. 
(a) (b) 
5000 
4500 
4000 
3500 
§ 3000 
g 2500 
f 2000 uu 
1500 
1000 
500 
3 4 5 6 7 
Entropy [kJ/(kg.K) 
4000 6000 
Pressure (kPa) 
(c) (d) 
Fig. B.l.l Theoretical and practical graphs of the Brayton cycle for full and reduced power: (a) h-s; 
(b) T-P; (c) PBMR h-s; (d) PBMR T-P 
154 
Appendices 
B.l The h-s graph shape at different power levels 
To show that the transformation from T-P to h-s improves model performance1, an 
analytical prove for the constant shape of the h-s graph at different power levels is 
provided subject to power control with the ICS and no valve operation. 
Let x and y be different operating points with [s\hl] and [s2,h2] any two successive 
points on the h-s graph. Let [PX,TX] and [P2,!2] be the corresponding temperatures and 
pressures at these points on the graph. Since the mapping from T to h is calculated by 
(6.2.3) and given that the temperatures stay constant over the operating range, it follows 
that the enthalpy is also constant. 
Given that the pressure ratios stay constant at different operating points, the pressure 
ratios for any two successive points are given by (B.l. 1) 
= c„ = c„ (BAA) 
with cpx = cp the pressure ratios. From (6.2.5) it follows that 
At operating point x: Asx - cp In 
At operating point y: Asy = cp In 
fjl^ 
, T1 
y 
\ y J 
-R\a 
R\n 
f p2\ 
v P1 
f p2\ 
y 
, Pl , \ y J 
(B.l.2) 
(B.l.3) 
Under normal operating conditions, the shape will be a constant only if As* = Asy and 
A/k = Ahy. Therefore (B.l.2) and (B.l.3) must be equal and can be written as 
-Rln 
:.c J1 , 
\ y J 
U*(ln«)-ln(Cf)) = 0 
.cp\a. 
( rplrp\ \ 
* y 
rp\rp1 
\ * y J 
+ i?(ln«)-ln(c;)) = 0 
:.c,ln(l) + /?(0) = 0 (B.1.4) 
Equation (B.1.4) shows that As* = Asy. Since the enthalpy is constant over the operating 
range, it follows that Ahx = Ahy. This proves that the transformation from T-P to h-s 
results in a constant shape between successive points for different operating points. 
'Model performance in this context signifies the error between the calculated Flownex and predicted 
(derived by the reference model) values. The minimal error corresponds to the better performance. 
155 
Appendices 
B.2 The T-P and h-s models applied to the PBMR 
Following the validation of the constant shape of the h-s graph at different power levels, 
the 100 % MCR operating point is used to compare model performance. As described in 
section 6.6.5, the first node (LPC inlet) is used as reference for each operating point. To 
evaluate model performance, the same set of features is extracted from the PBMR T-P 
graph at 100 % MCR. By using the extracted features and the reconstruction procedure 
discussed in section 6.6.5, the reference graphs are reconstructed at different operating 
points. 
To demonstrate the improvement in model performance between the two devised 
reference models, six operating points are chosen. At each of the operating points, the 
Flownex model is used to calculate the values for T, P, h and s. By reconstructing the 
reference models at the different operating points, the values for T, P, h and s are derived 
analytically. Tables B.2.1 and B.2.2 summarize the results for T-P and h-s at the six 
operating points. The T, P, h and s are normalized with the following reference values: 
900 °C, 9000 kPa, 5000 kJ/kg and 10 kJ/(kg.K) respectively. The notation in the tables is 
as follows: FL is the value calculated with Flownex, RM is the value derived by the 
reference model (T-P or h-s) and Diffis the absolute difference between the Flownex and 
reference models in percentage (%). 
Since node one is used as reference point for the reconstruction of the graphs, it can 
be seen from Tables B.2.1 and B.2.2 that the errors between Flownex and the reference 
models are very small for this node. Conversely, Table B.2.1 shows that the percentage 
error between Flownex and the reference T-P model is large over the entire power range. 
This is expected as Fig. B. 1.1 (d) showed a large difference between the 100 % MCR and 
40 % MCR graphs in thep-plane. The transformation to h-s improves model performance 
by more than 32 % for reduced power and Table B.2.2 shows that the error between the 
models is less than 0.25 % for all power levels. 
Node- 90% MCR 80% MCR 70% MCR 60% MCR 50% MCR 40% MCR FL RM FL RM FL RM FL RM FL RM FL RM 
Tl 0.0255 0.0254 0.0252 0.0254 0.0250 0.0254 0.0252 0.0254 0.0253 0.0254 0.0253 0.0254 
72 0.1214 0.1211 0.1212 0.1211 0.1211 0.1211 0.1214 0.1211 0.1216 0.1211 0.1219 0.1211 
73 0.0244 0.0243 0.0241 0.0243 0.0239 0.0243 0.0236 0.0243 0.0234 0.0243 0.0240 0.0243 
74 0.1185 0.1181 0.1186 0.1181 0.1188 0.1181 0.1189 0.1181 0.1189 0.1181 0.1189 0.1181 
75 0.5554 0.5545 0.5548 0.5545 0.5551 0.5545 0.5551 0.5545 0.5555 0.5545 0.5555 0.5545 
T6 0.9996 0.9995 0.9994 0.9995 0.9994 0.9995 0.9995 0.9995 0.9997 0.9995 0.9998 0.9995 
77 0.5672 0.5672 0.5665 0.5672 0.5661 0.5672 0.5661 0.5672 0.5661 0.5672 0.5662 0.5672 
73 0.1549 0.1554 0.1548 0.1554 0.1542 0.1554 0.1542 0.1554 0.1542 0.1554 0.1544 0.1554 
PI 0.2892 0.2892 0.2547 0.2547 0.2222 0.2222 0.1899 0.1899 0.1576 0.1576 0.1253 0.1253 
PI 0.5058 0.5313 0.4457 0.4969 0.3890 0.4643 0.3321 0.4321 0.2754 0.3997 0.2193 0.3675 
P3 0.5027 0.5279 0.4430 0.4934 0.3866 0.4609 0.3301 0.4286 0.2737 0.3963 0.2179 0.3640 
PA 0.8923 0.9634 0.7870 0.9290 0.6872 0.8964 0.5875 0.8642 0.4877 0.8318 0.3880 0.7996 
P5 0.8841 0.9544 0.7798 0.9199 0.6809 0.8874 0.5821 0.8551 0.4833 0.8228 0.3844 0.7905 
P6 0.8496 0.9160 0.7491 0.8816 0.6539 0.8490 0.5587 0.8168 0.4636 0.7844 0.3685 0.7521 
PI 0.2953 0.2959 0.2602 0.2615 0.2271 0.2289 0.1942 0.1967 0.1612 0.1643 0.1282 0.1321 
P8 0.2911 0.2913 0.2564 0.2568 0.2237 0.2243 0.1912 0.1920 0.1586 0.1597 0.1262 0.1274 
Diff 3.64 7:93 12.67 18.28 25.00 33.16 
Table B.2.1 Temperature and pressure results for the Flownex and reference models. 
156 
Appendices 
Node 90 % MCR 80 % MCR 70 % MCR 60 % MCR 50 % MCR 40 % MCR FL RM FI. RM FI. RM FL RM FI. RM FL RM 
h\ 0.0256 0.0258 0.0251 0.0258 0.0247 0.0258 0.0247 0.0258 0.0246 0.0258 0.0244 0.0258 
hi 0.1165 0.1166 0.1160 0.1166 0.U55 0.1166 0.1154 0.1166 0.1153 0.1166 0.1153 0.1166 
hi 0.0259 0.0262 0.0253 0.0262 0.0248 0.0262 0.0241 0.0262 0.0235 0.0262 0.0238 0.0262 
hA 0.1162 0.1165 0.1156 0.1165 0.U52 0.1165 0.1147 0.1165 0.1142 0.1165 0.1144 0.1165 
h5 0.5240 0.5238 0.5229 0.5238 0.5227 0.5238 0.5222 0.5238 0.5221 0.5238 0.5218 0.5238 
h(> 0.9388 0.9391 0.9381 0.9391 0.9377 0.9391 0.9372 0.9391 0.9370 0.9391 0.9366 0.9391 
hi 0.5319 0.5321 0.5311 0.5321 0.53O6 0.5321 0.5304 0.5321 0.5303 0.5321 0.5302 0.5321 
h% 0.1465 0.1472 0.1462 0.1472 0.1455 0.1472 0.1452 0.1472 0.1447 0.1472 0.1451 0.1472 
s\ 0.3216 0.3216 0.3474 0.3474 0.3754 0.3754 0.4084 0.4084 0.4474 0.4474 0.4950 0.4950 
s2 0.3383 0.3381 0.3643 0.3639 0.3925 0.3919 0.4257 0.4249 0.4648 0.4639 0.5126 0.5115 
s3 0.2049 0.2049 0.2307 0.2307 0.2587 0.2587 0.2911 0.2917 0.3296 0.3307 0.3779 0.3783 
s4 0.2169 0.2165 0.2430 0.2423 0.2714 0.2704 0.3041 0.3033 0.3427 0.3423 0.3903 0.3899 
s5 0.5879 0.5875 0.6136 0.6133 0.6420 0.6414 0.6745 0.6744 0.7134 0.7133 0.7610 0.7609 
56 0.8127 0.8128 0.8388 0.8386 0.8670 0.8666 0.8997 0.8996 0.9386 0.9386 0.9863 0.9862 
si 0.8227 0.8230 0.8486 0.8488 0.8767 0.8768 0.9092 0.9098 0.9479 0.9488 0.9955 0.9964 
58 0.4925 0.4932 0.5187 0.5190 0.5464 0.5471 0.5789 0.5800 0.6177 0.6190 0.6656 0.6666 
Diff 0.03 0.09 0.13 0.20 0.24 0. 21 
Table B.2,2 Enthalpy and entropy results for the Flownex and reference models. 
The errors observed in h and s are due to a small change in cycle efficiency at reduced 
power levels. For the purpose of fault detection and fault signature generation, the errors 
are acceptable. To demonstrate the improvement in model performance, the manifold 
leakage to turbine inlet fault is used as an example and illustrated in Fig B.2,1. The 
normalized error fault signatures are created for T, P, h and s at 40 % and 100 % MCR 
respectively. Although the statement regarding constant signatures for h and s is 
discussed in section 6.6.5, this figure illustrates the signatures for rand P. 
The T and h signatures showed similar results as calculated in Tables B.2.1 and 
B.2.2. As expected, the P signatures did not show any similarities for the different power 
levels (large P errors observed in Table B.2.1). The figure shows that the transformed 5 
signatures are highly correlated at different power levels and can therefore be 
characterized with one fault signature. The transformation to h-s is thus important since 
the faults will be characterized with different T-P signatures at different operating points. 
C8 
D.6 
0.4 
0,2 
0 
?0.2 
-0.4 
-0.6 
-0. 
p^ T«t«n&!JCH 
1 PX TOO* MCfll 
1. 1 .1 -u 1 
3 4 5 6 
Node number 
S 0.2 
-0.6 
-o.e 
-1 
flat lOC* hCR 
* it :<£rt. MCfl 
xa!4C% MW 
1 -1 rl rfll ll 
3 4 s 6 
Node number 
(a) (b) 
Fig. B.2.! Normalized error signatures for fault 15: (a) T-P; (b) h-s, 
157