Table Of ContentStudies in Systems, Decision and Control 221
Zhenhua Wang
Yi Shen
Model-Based
Fault
Diagnosis
Methods for State-Space Systems
Studies in Systems, Decision and Control
Volume 221
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Zhenhua Wang Yi Shen
Model-Based Fault Diagnosis
Methods for State-Space Systems
Zhenhua Wang Yi Shen
School of Astronautics School of Astronautics
Harbin Institute of Technology Harbin Institute of Technology
Harbin, Heilongjiang, China Harbin, Heilongjiang, China
National Natural Science Foundation of China
Natural Science Foundation of Heilongjiang Province
This work was supported by National Natural Science Foundation of China (61773145,
61973098) and the key research and development of Heilongjiang Province of China
(GZ20210199).
ISSN 2198-4182 ISSN 2198-4190 (electronic)
Studies in Systems, Decision and Control
ISBN 978-981-19-6705-4 ISBN 978-981-19-6706-1 (eBook)
https://doi.org/10.1007/978-981-19-6706-1
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To Cunxi and Muzhi
Preface
Fault diagnosis techniques provide an effective way of improving the safety and
reliability of technical processes. Due to the increasing demand for higher safety and
reliability of modern engineering systems, fault diagnosis techniques have received
considerable attention both in the academic community and in industry. Since the
beginning of the 1970s, numerous fault diagnosis methods have been proposed in
the literature. Nowadays, model-based fault diagnosis is one of the most important
research areas in control theory and applications.
Although many books and research monographs on fault diagnosis have been
published in the past decades, very few of the existing books study model-based
fault diagnosis methods in a unified framework and in a comprehensive manner. This
motivates us to write a book to comprehensively introduce model-based diagnosis
methods in the state-space framework.
This book involves three main tasks of fault diagnosis, fault detection, fault isola-
tion, and fault estimation, and this book covers three mainstream model-based fault
diagnosis methods: observer-based methods, Kalman filter-based methods, and parity
space approaches. The outline of this book is as follows.
Chapter 1 introduces some basic concepts related to model-based fault diagnosis
and gives an overview of model-based fault diagnosis methods.
Chapter 2 introduces the modelling of monitored systems, which provides a model
basis for the subsequent chapters.
Chapters 3–9 cover observer-based fault diagnosis methods, which are the focus of
this book. The observer-based residual generation methods are studied in Chaps. 3–
5. Chapter 6 presents two residual evaluation methods for observer-based fault detec-
tion. The fault isolation strategies based on structured residual generation and direc-
tional residual generation are introduced in Chaps. 7 and 8. Two observer-based fault
estimation methods are discussed in Chap. 9.
Chapter 10 covers the Kalman filter-based fault diagnosis methods. Similar to
the observer-based methods, Chap. 10 also involves residual generation, residual
evaluation, fault isolation, and fault estimation.
vii
viii Preface
Chapter 11 introduces fault detection and isolation using the parity space
approach, which is an important fault diagnosis technique paralleled to the observer-
based methods.
This book gives basic concepts, fundamental principles, and detailed procedures
for the presented fault diagnosis techniques. The intended audience includes engi-
neering students, academic researchers, and professional engineers. This book can
be used as a textbook for a graduate course in fault diagnosis. In writing this book,
we aim to use simple and efficient methods to make the design procedures intuitive
and easy to follow. Moreover, most methods are illustrated by a simple numerical
example with detailed procedures in order to help newcomers assimilate and use the
methods.
This book originates from several editions of lecture notes that were used as
teaching material for the graduate course “Fault Diagnosis Techniques for Control
Systems” in the Department of Control Science and Engineering at Harbin Institute
of Technology. We would like to thank the graduate students who selected this course
for providing us the opportunities to practice and improve the lectures.
We would like to express our sincere gratitude to Prof. Jie Chen and Prof. Steven
X. Ding for their excellent research monographs, which inspired us to write this
book. We are indebted to Prof. Ding, who read the whole manuscript and gave us
valuable suggestions.
We would like to thank Prof. Peng Shi and Prof. Cheng-chew Lim of the University
of Adelaide, Prof. Qinghua Zhang of Inria, Prof. Tarek Raïssi and Dr. Thach Nogoc
Dinh of Conservatoire national des arts et métiers, and other colleagues for their
helpful discussions and valuable support.
We are very grateful to our families for their understanding and constant support.
Finally, we would like to acknowledge the financial support from National
Natural Science Foundation of China (Grant No. 61973098,61773145) and the key
research and development program of Heilongjiang Province of China (Grant No.
GZ20210199).
Harbin, China Zhenhua Wang
July 2022 Yi Shen
Contents
1 Introduction .................................................. 1
1.1 Basic Concepts in Fault Diagnosis .......................... 1
1.2 Model-Based Fault Diagnosis Methods ...................... 2
1.2.1 Observer-Based Methods .......................... 3
1.2.2 Parity Space Approaches ........................... 5
1.2.3 Parameter Estimation Methods ...................... 6
1.3 Outline of the Book ....................................... 6
References .................................................... 8
2 Modelling for Fault Diagnosis .................................. 13
2.1 Modelling of Nominal Systems ............................. 13
2.2 Modelling of Faults ....................................... 17
2.3 Description of Uncertainties ............................... 19
2.4 Conclusion .............................................. 21
References .................................................... 21
3 Observer-Based Residual Generation ........................... 23
3.1 Residual Generation Based on Analytical Redundancy ......... 23
3.2 Observer-Based Residual Generation for Continuous-Time
Systems ................................................. 24
3.3 Observer-Based Residual Generation for Discrete-Time
Systems ................................................. 30
3.4 Conclusion .............................................. 33
References .................................................... 34
4 Robust Residual Generation Based on Unknown Input
Observer ..................................................... 35
4.1 UIO-Based Residual Generation for Continuous-Time
Systems ................................................. 35
4.2 UIO-Based Residual Generation for Discrete-Time Systems .... 41
4.3 Conclusion .............................................. 43
References .................................................... 44
ix
x Contents
5 Optimal Robust Residual Generation ........................... 47
5.1 Optimal Robust Residual Generation for Continuous-Time
Systems ................................................. 47
5.2 Optimal Robust Residual Generation for Discrete-Time
Systems ................................................. 55
5.3 Conclusion .............................................. 60
References .................................................... 60
6 Residual Evaluation Based on Threshold Computation ........... 61
6.1 Residual Evaluation Based on Peak-to-Peak Analysis .......... 61
6.1.1 Residual Evaluation for Continuous-Time Systems .... 61
6.1.2 Residual Evaluation for Discrete-Time Systems ....... 66
6.2 Residual Evaluation Based on Interval Analysis .............. 71
6.2.1 Residual Evaluation for Continuous-Time Systems .... 72
6.2.2 Residual Evaluation for Discrete-Time Systems ....... 77
6.3 Conclusion .............................................. 81
References .................................................... 82
7 Fault Isolation Based on Structured Residual Generation ......... 85
7.1 Sensor Fault Isolation Based on Dedicated Observer
Scheme ................................................. 85
7.2 Sensor Fault Isolation Based on Simplified Observer
Scheme ................................................. 92
7.3 Sensor Fault Isolation Based on Generalized Observer
Scheme ................................................. 100
7.4 Actuator Fault Isolation Based on Structured Residual
Generation .............................................. 105
7.5 Conclusion .............................................. 112
References .................................................... 113
8 Fault Isolation Based on Directional Residual Generation ......... 115
8.1 Observer-Based Directional Residual Generator .............. 115
8.2 Directional Residual Generator Design for Systems
with Fully Measurable States .............................. 117
8.3 Directional Residual Generator Design for General LTI
Systems ................................................. 120
8.4 FDI Based on Directional Residual Generation ............... 130
8.5 Conclusion .............................................. 134
References .................................................... 134
9 Observer-Based Fault Estimation ............................... 137
9.1 Adaptive Observer-Based Fault Estimation ................... 137
9.2 Fault Estimation Based on Augmented State Observer ......... 143
9.3 Conclusion .............................................. 155
References .................................................... 156
