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Model-Based Fault Diagnosis Techniques Design Schemes, Algorithms and Tools.pdf
Model-Based Fault Diagnosis Techniques
Series Editors' Foreword
Preface
Contents
Notation
Part I: Introduction, Basic Concepts and Preliminaries
Chapter 1: Introduction
1.1 Basic Concepts of Fault Diagnosis Technique
1.2 Historical Development and Some Relevant Issues
1.3 Notes and References
Chapter 2: Basic Ideas, Major Issues and Tools in the Observer-Based FDI Framework
2.1 On the Observer-Based Residual Generator Framework
2.2 Unknown Input Decoupling and Fault Isolation Issues
2.3 Robustness Issues in the Observer-Based FDI Framework
2.4 On the Parity Space FDI Framework
2.5 Residual Evaluation and Threshold Computation
2.6 FDI System Synthesis and Design
2.7 Notes and References
Chapter 3: Modelling of Technical Systems
3.1 Description of Nominal System Behavior
3.2 Coprime Factorization Technique
3.3 Representations of Systems with Disturbances
3.4 Representations of System Models with Model Uncertainties
3.5 Modelling of Faults
3.6 Modelling of Faults in Closed-Loop Feedback Control Systems
3.7 Case Study and Application Examples
3.7.1 Speed Control of a DC Motor
Model of DC Motor
Models of DC Motor Control System
Modelling of Faults
3.7.2 Inverted Pendulum Control System
Nonlinear System Model
Disturbances
Linear Model
Discrete-Time Model
LCF of the Nominal Model
Model Uncertainty
Modelling of Faults
Closed-Loop Model
3.7.3 Three-Tank System
Nonlinear Model
Linear Model
Model Uncertainty
Modelling of Faults
Closed-Loop Model
3.7.4 Vehicle Lateral Dynamic System
Nominal Model
Disturbances
Model Uncertainties
Modelling of Faults
3.7.5 Continuous Stirred Tank Heater
System Dynamics and Nonlinear Model
Linear Model
Model Uncertainties and Unknown Inputs
Modelling of Faults
3.8 Notes and References
Chapter 4: Fault Detectability, Isolability and Identifiability
4.1 Fault Detectability
4.2 Excitations and Detection of Multiplicative Faults
4.3 Fault Isolability
4.3.1 Concept of System Fault Isolability
4.3.2 Fault Isolability Conditions
4.4 Fault Identifiability
4.5 Notes and References
Part II: Residual Generation
Chapter 5: Basic Residual Generation Methods
5.1 Analytical Redundancy
5.2 Residuals and Parameterization of Residual Generators
5.3 Issues Related to Residual Generator Design and Implementation
5.4 Fault Detection Filter
5.5 Diagnostic Observer Scheme
5.5.1 Construction of Diagnostic Observer-Based Residual Generators
5.5.2 Characterization of Solutions
5.5.3 A Numerical Approach
5.5.4 An Algebraic Approach
5.6 Parity Space Approach
5.6.1 Construction of Parity Relation Based Residual Generators
5.6.2 Characterization of Parity Space
5.6.3 Examples
5.7 Interconnections, Comparison and Some Remarks
5.7.1 Parity Space Approach and Diagnostic Observer
5.7.2 Diagnostic Observer and Residual Generator of General Form
5.7.3 Applications of the Interconnections and Some Remarks
5.7.4 Examples
5.8 Notes and References
Chapter 6: Perfect Unknown Input Decoupling
6.1 Problem Formulation
6.2 Existence Conditions of PUIDP
6.2.1 A General Existence Condition
6.2.2 A Check Condition via Rosenbrock System Matrix
6.2.3 An Algebraic Check Condition
6.3 A Frequency Domain Approach
6.4 UIFDF Design
6.4.1 The Eigenstructure Assignment Approach
6.4.2 Geometric Approach
6.5 UIDO Design
6.5.1 An Algebraic Approach
6.5.2 Unknown Input Observer Approach
6.5.3 A Matrix Pencil Approach to the UIDO Design
6.5.4 A Numerical Approach to the UIDO Design
6.6 Unknown Input Parity Space Approach
6.7 An Alternative Scheme-Null Matrix Approach
6.8 Discussion
6.9 Minimum Order Residual Generator
6.9.1 Minimum Order Residual Generator Design by Geometric Approach
6.9.2 An Alternative Solution
6.10 Notes and References
Chapter 7: Residual Generation with Enhanced Robustness Against Unknown Inputs
7.1 Mathematical and Control Theoretical Preliminaries
7.1.1 Signal Norms
L2 ( l2 ) Norm
Peak Norm
2 (Euclidean) Norm
infty Norm
7.1.2 System Norms
Hinfty Norm
Peak-to-Peak Gain
Generalized H2 Norm
H2 Norm
Matrix Norm Induced by the 2 Norm for Vectors
Frobenius-Norm
infty Norm
7.1.3 Computation of H2 and Hinfty Norms
7.1.4 Singular Value Decomposition (SVD)
7.1.5 Co-Inner-Outer Factorization
7.1.6 Model Matching Problem
7.1.7 Essentials of the LMI Technique
7.2 Kalman Filter Based Residual Generation
Recursive Computation for Optimal State Estimation
Recursive Computation for Kalman Filter Gain
7.3 Robustness, Fault Sensitivity and Performance Indices
7.3.1 Robustness and Sensitivity
7.3.2 Performance Indices: Robustness vs. Sensitivity
7.3.3 Relations Between the Performance Indices
7.4 Optimal Selection of Parity Matrices and Vectors
7.4.1 Sf,+/Rd as Performance Index
7.4.2 Sf,-/Rd as Performance Index
7.4.3 JS-R as Performance Index
7.4.4 Optimization Performance and System Order
7.4.5 Summary and Some Remarks
7.5 Hinfty Optimal Fault Identification Scheme
7.6 H2/H2 Design of Residual Generators
7.7 Relationship Between H2/H2 Design and Optimal Selection of Parity Vectors
7.8 LMI Aided Design of FDF
7.8.1 H2 to H2 Trade-off Design of FDF
7.8.2 On the H- Index
7.8.3 H2 to H- Trade-off Design of FDF
7.8.4 Hinfty to H- Trade-off Design of FDF
7.8.5 Hinfty to H- Trade-off Design of FDF in a Finite Frequency Range
7.8.6 An Alternative Hinfty to H- Trade-off Design of FDF
7.8.7 A Brief Summary and Discussion
7.9 The Unified Solution
7.9.1 Hi/Hinfty Index and Problem Formulation
7.9.2 Hi/Hinfty Optimal Design of FDF: The Standard Form
7.9.3 Discrete-Time Version of the Unified Solution
7.9.4 A Generalized Interpretation
7.10 The General Form of the Unified Solution
7.10.1 Extended CIOF
7.10.2 Generalization of the Unified Solution
7.11 Notes and References
Chapter 8: Residual Generation with Enhanced Robustness Against Model Uncertainties
8.1 Preliminaries
8.1.1 LMI Aided Computation for System Bounds
8.1.2 Stability of Stochastically Uncertain Systems
8.2 Transforming Model Uncertainties into Unknown Inputs
8.3 Reference Model Based Strategies
8.3.1 The Basic Idea
8.3.2 A Reference Model Based Solution for Systems with Norm-Bounded Uncertainties
8.4 Residual Generation for Systems with Polytopic Uncertainties
8.4.1 The Reference Model Scheme Based Scheme
8.4.2 H- to Hinfty Design Formulation
8.5 Residual Generation for Stochastically Uncertain Systems
8.5.1 System Dynamics and Statistical Properties
8.5.2 Basic Idea and Problem Formulation
8.5.3 An LMI Solution
8.5.4 An Alternative Approach
8.6 Notes and References
Part III: Residual Evaluation and Threshold Computation
Chapter 9: Norm-Based Residual Evaluation and Threshold Computation
9.1 Preliminaries
9.2 Basic Concepts
9.3 Some Standard Evaluation Functions
Peak Value
RMS Value
9.4 Basic Ideas of Threshold Setting and Problem Formulation
9.4.1 Dynamics of the Residual Generator
9.4.2 Definitions of Thresholds and Problem Formulation
9.5 Computation of Jth,RMS,2
9.5.1 Computation of Jth,RMS,2 for the Systems with the Norm-Bounded Uncertainty
9.5.2 Computation of Jth,RMS,2 for the Systems with the Polytopic Uncertainty
9.6 Computation of Jth,peak,peak
9.6.1 Computation of Jth,peak,peak for the Systems with the Norm-Bounded Uncertainty
9.6.2 Computation of Jth,peak,peak for the Systems with the Polytopic Uncertainty
9.7 Computation of Jth,peak,2
9.7.1 Computation of Jth,peak,2 for the Systems with the Norm-Bounded Uncertainty
9.7.2 Computation of Jth,peak,2 for the Systems with the Polytopic Uncertainty
9.8 Threshold Generator
9.9 Notes and References
Chapter 10: Statistical Methods Based Residual Evaluation and Threshold Setting
10.1 Introduction
10.2 Elementary Statistical Methods
10.2.1 Basic Hypothesis Test
10.2.2 Likelihood Ratio and Generalized Likelihood Ratio
Detection when theta1 (>0) Is Known and theta0=0
Detection when theta1 Is Unknown and theta0=0
10.2.3 Vector-Valued GLR
10.2.4 Detection of Change in Variance
Testing with the chi2 Statistic Given by Lapin
Testing Using GLR Given by Basseville and Nikiforov
10.2.5 Aspects of On-Line Realization
On-Line Implementation with a Fixed Sample Size N
On-Line Implementation in a Recursive Manner
Setting a Counter
10.3 Criteria for Threshold Computation
10.3.1 The Neyman-Pearson Criterion
10.3.2 Maximum a Posteriori Probability (MAP) Criterion
10.3.3 Bayes' Criterion
10.3.4 Some Remarks
10.4 Application of GLR Testing Methods
10.4.1 Kalman Filter Based Fault Detection
10.4.2 Parity Space Based Fault Detection
10.5 Notes and References
Chapter 11: Integration of Norm-Based and Statistical Methods
11.1 Residual Evaluation in Stochastic Systems with Deterministic Disturbances
11.1.1 Residual Generation
11.1.2 Problem Formulation
11.1.3 GLR Solutions
11.1.4 An Example
11.2 Residual Evaluation Scheme for Stochastically Uncertain Systems
11.2.1 Problem Formulation
11.2.2 Solution and Design Algorithms
11.3 Probabilistic Robustness Technique Aided Threshold Computation
11.3.1 Problem Formulation
11.3.2 Outline of the Basic Idea
11.3.3 LMIs Used for the Solutions
11.3.4 Problem Solutions in the Probabilistic Framework
11.3.5 An Application Example
The Sample Size N
11.3.6 Concluding Remarks
11.4 Notes and References
Part IV: Fault Detection, Isolation and Identification Schemes
Chapter 12: Integrated Design of Fault Detection Systems
12.1 FAR and FDR
12.2 Maximization of Fault Detectability by a Given FAR
12.2.1 Problem Formulation
Problem of Maximizing SDF Under a Given FAR (PMax-SDF)
12.2.2 Essential Form of the Solution
12.2.3 A General Solution
12.2.4 Interconnections and Comparison
Relationship to the PUIDP
Relationship to H2/H2 Optimal Design Scheme
Relationship to Hinfty/Hinfty and H-/Hinfty Optimal Schemes
12.2.5 Examples
12.3 Minimizing False Alarm Number by a Given FDR
12.3.1 Problem Formulation
Problem of Minimizing SDFA Under a Given FDR (PMin-SDFA)
12.3.2 Essential Form of the Solution
12.3.3 The State Space Form
12.3.4 The Extended Form
12.3.5 Interpretation of the Solutions and Discussion
12.3.6 An Example
12.4 On the Application to Stochastic Systems
12.4.1 Application to Maximizing FDR by a Given FAR
12.4.2 Application to Minimizing FAR by a Given FDR
12.4.3 Equivalence Between the Kalman Filter Scheme and the Unified Solution
12.5 Notes and References
Chapter 13: Fault Isolation Schemes
13.1 Essentials
13.1.1 Existence Conditions for a Perfect Fault Isolation
13.1.2 PFIs and Unknown Input Decoupling
13.1.3 PFIs with Unknown Input Decoupling (PFIUID)
13.2 Fault Isolation Filter Design
13.2.1 A Design Approach Based on the Duality to Decoupling Control
13.2.2 The Geometric Approach
13.2.3 A Generalized Design Approach
13.3 An Algebraic Approach to Fault Isolation
13.4 Fault Isolation Using a Bank of Residual Generators
13.4.1 The Dedicated Observer Scheme (DOS)
13.4.2 The Generalized Observer Scheme (GOS)
13.5 Notes and References
Chapter 14: Fault Identification Schemes
14.1 Fault Identification Filter Schemes and Perfect Fault Identification
14.1.1 Fault Detection Filters and Existence Conditions
14.1.2 FIF Design with Measurement Derivatives
14.2 On the Optimal FIF Design
14.2.1 Problem Formulation and Solution Study
14.2.2 Study on the Role of the Weighting Matrix
14.3 Approaches to the Design of FIF
14.3.1 A General Fault Identification Scheme
14.3.2 An Alternative Scheme
14.3.3 Identification of the Size of a Fault
14.3.4 Fault Identification in a Finite Frequency Range
14.4 Fault Identification Using an Augmented Observer
14.5 An Algebraic Fault Identification Scheme
14.6 Adaptive Observer-Based Fault Identification
14.6.1 Problem Formulation
14.6.2 The Adaptive Observer Scheme
Observer
Auxiliary Filter
Fault Estimator
14.7 Notes and References
Chapter 15: Fault Diagnosis in Feedback Control Systems and Fault-Tolerant Architecture
15.1 Plant and Control Loop Models, Controller and Observer Parameterizations
15.1.1 Plant and Control Loop Models
15.1.2 Parameterization of Stabilizing Controllers, Observers, and an Alternative Formulation of Controller Design
15.1.3 Observer and Residual Generator Based Realizations of Youla Parameterization
15.1.4 Residual Generation Based Formulation of Controller Design Problem
15.2 Residual Extraction in the Standard Feedback Control Loop and a Fault Detection Scheme
15.2.1 Signals at the Access Points in the Control Loop
15.2.2 A Fault Detection Scheme Based on Extraction of Residual Signals
15.3 2-DOF Control Structures and Residual Access
15.3.1 The Standard 2-DOF Control Structures
15.3.2 An Alternative 2-DOF Control Structure with Residual Access
15.4 On Residual Access in the IMC and Residual Generator Based Control Structures
15.4.1 An Extended IMC Structure with an Integrated Residual Access
15.4.2 A Residual Generator Based Feedback Control Loop
15.5 Notes and References
References
Index
Advances in Industrial Control
For further volumes:
www.springer.com/series/1412
Steven X. Ding
Model-Based
Fault Diagnosis
Techniques
Design Schemes, Algorithms and Tools
Second Edition
Prof. Dr. Steven X. Ding
Inst. Automatisierungstechnik und Komplexe
Systeme (AKS)
Universität Duisburg-Essen
Duisburg, Germany
ISSN 1430-9491
Advances in Industrial Control
ISBN 978-1-4471-4798-5
DOI 10.1007/978-1-4471-4799-2
Springer London Heidelberg New York Dordrecht
ISSN 2193-1577 (electronic)
ISBN 978-1-4471-4799-2 (eBook)
Library of Congress Control Number: 2012955658
© Springer-Verlag London 2008, 2013
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
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does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
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Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
To My Parents and Eve Limin
Series Editors’ Foreword
The series Advances in Industrial Control aims to report and encourage technol-
ogy transfer in control engineering. The rapid development of control technology
has an impact on all areas of the control discipline. New theory, new controllers,
actuators, sensors, new industrial processes, computer methods, new applications,
new philosophies. . . , new challenges. Much of this development work resides in
industrial reports, feasibility study papers and the reports of advanced collaborative
projects. The series offers an opportunity for researchers to present an extended ex-
position of such new work in all aspects of industrial control for wider and rapid
dissemination.
When assessing the performance of a control system, it is easy to overlook the
fundamental question of whether the actual system configuration and set up has all
the features and hardware that will enable the process to be controlled per se. If the
system can be represented by a reasonable linear model, then the characteristics of
a process that create limitations to achieving various control performance require-
ments can be identified and listed. Such information can be used to produce guide-
lines that give a valuable insight as to what a system can or cannot achieve in terms
of performance. In control systems analysis textbooks, these important properties
are often given under terms such as “input–output controllability” and “dynamic
resilience”.
It is interesting to see similar questions arising in the study of fault detection
and isolation (FDI) systems. At a fundamental level, the first question is not one
of the performance of the fault detection and analysis system, but of whether the
underlying process has the structure and properties to allow faults to be detected,
isolated and identified. As with the analysis of the control case, if the system can
be represented by a linear model then definitions and conditions can be given as to
whether the system is generically fault detectable, fault isolatable and fault identifi-
able. Fault detectability is about whether a system fault would cause changes in the
system outputs independently of the type and size of the fault, fault isolatability is
a matter of whether the changes in the system output caused by different faults are
distinguishable (from for example, system output changes caused by the presence
of a disturbance) and finally fault identifiability is about whether the mapping from
vii
viii
Series Editors’ Foreword
the system output to the fault is unique since if this is so then the fault is identifiable.
With the fundamental conditions verified, the engineer can proceed to designing the
FDI system. All these issues, along with design techniques based on models with
demonstrative case study applications can be found in this comprehensive second
edition of Professor Steven Ding’s book Model-Based Fault Diagnosis Technique:
Design Schemes, Algorithms and Tools that has now entered the Advances in Indus-
trial Control series of monographs.
The key practical issues that complicate the design of a FDI system come from
two sources. Firstly from the process: Many process plants and installations are
often subject to unknown disturbances and it is important to be able to distinguish
these upsets from genuine faults. Similarly process noise, emanating from the mech-
anisms within the process and from the measurements sensors themselves, is usually
present in real systems so it is important that process measurement noise does not
trigger false alarms. The second set of issues arises from FDI design itself where
model uncertainty is present. This may exhibit itself as simply imperfect process-
operational knowledge with the result that the FDI system is either too sensitive or
too insensitive. Alternatively, model uncertainty (model inaccuracy) may well exist
and the designer will be advised to use a robust FDI scheme. Professor Ding pro-
vides solutions, analysis and discussion of many of these technical FDI issues in his
book.
A very valuable feature of the book presentation is the use of five thematic case
study examples used to illuminate the substantial matters of theory, algorithms and
implementation. The case study systems are:
• speed control of a dc motor;
• an inverted pendulum control system;
• a three-tank system;
• a vehicle lateral dynamical system; and
• a continuous stirred tank heater system.
Further, a useful aspect of these case study systems is that four of them are linked
to laboratory-scale experimental rigs, thus presenting the academic and engineering
reader with the potential to obtain direct applications experience of the FDI tech-
niques described.
The first edition of this book was a successful enterprise and since its publication
in 2008 the model-based FDI field has grown in depth and insight. Professor Ding
has taken the opportunity to update the book by adding more recent research findings
and including a new case study example from the industrial process area. The new
edition is a very welcome addition to the Advances in Industrial Control series.
Industrial Control Centre,
Glasgow, Scotland, UK
M.J. Grimble
M.A. Johnson
Preface
Model-based fault diagnosis is a vital field in the research and engineering domains.
In the past years since the publication of this book, new diagnostic methods and suc-
cessful applications have been reported. During this time, I have also received many
mails with constructive remarks and valuable comments on this book, and enjoyed
interesting and helpful discussions with students and colleagues during classes, at
conferences and workshops. All these motivated me to work on a new edition.
The second edition retains the original structure of the book. Recent results on the
robust residual generation issues and case studies have been added. Chapter 14 has
been extended to include additional fault identification schemes. In a new chapter,
fault diagnosis in feedback control systems and fault-tolerant control architectures
are addressed. Thanks to the received remarks and comments, numerous revisions
have been made.
A part of this book serves as a textbook for a Master course on Fault Diagno-
sis and Fault Tolerant Systems, which is offered in the Department of Electrical
Engineering and Information Technology at the University of Duisburg-Essen. It is
recommended to include Chaps. 1–3, 5, 7 (partly), 9, 10, 12–15 (partly) in this edi-
tion for such a Master course. It is worth mentioning that this book is so structured
that it can also be used as a self-study book for engineers in the application fields of
automatic control.
I would like to thank my Ph.D. students and co-worker for their valuable con-
tributions to the case study. They are Tim Könings (inverted pendulum), Hao Luo
(three-tank system and CSTH), Jedsada Saijai and Ali Abdo (vehicle lateral dy-
namic system), Ping Liu (DC motor) and Jonas Esch (CSTH).
Finally, I would like to express my gratitude to Oliver Jackson from Springer-
Verlag and the Series Editor for their valuable support.
Duisburg, Germany
Steven X. Ding
ix
Contents
Part I
Introduction, Basic Concepts and Preliminaries
1
2
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Introduction .
. . .
1.1 Basic Concepts of Fault Diagnosis Technique . . .
. . . . . . . . .
1.2 Historical Development and Some Relevant Issues . . . . . . . . .
1.3 Notes and References
. . . . . .
. . . . . . . . . . .
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. . . . .
. .
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. . . . .
Basic Ideas, Major Issues and Tools in the Observer-Based FDI
Framework .
. . . . . . .
2.1 On the Observer-Based Residual Generator Framework . . . . . .
2.2 Unknown Input Decoupling and Fault Isolation Issues . . . . . . .
2.3 Robustness Issues in the Observer-Based FDI Framework . . . . .
2.4 On the Parity Space FDI Framework . . . . . . . . . . . . . . . .
2.5 Residual Evaluation and Threshold Computation .
. . . . . . . . .
2.6 FDI System Synthesis and Design . . . . . . . . . . . . . . . . . .
. . .
2.7 Notes and References
. . . . . . . . . .
. . .
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3 Modelling of Technical Systems .
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. . . . . . .
. . .
3.1 Description of Nominal System Behavior . . . . . . . . .
. . . . .
3.2 Coprime Factorization Technique . . . . . . . . . . . . . . . . . .
. . . . . . . . .
3.3 Representations of Systems with Disturbances . .
3.4 Representations of System Models with Model Uncertainties
. . .
3.5 Modelling of Faults
. . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Modelling of Faults in Closed-Loop Feedback Control Systems . .
. . . . . . . . . . . . . . .
3.7 Case Study and Application Examples
3.7.1 Speed Control of a DC Motor . . . . . . . . . . . . . . . .
3.7.2
Inverted Pendulum Control System . . . . . . . . . . . . .
3.7.3 Three-Tank System . . . . . . . . . . . . . . . . . . . . .
3.7.4 Vehicle Lateral Dynamic System . . . . . . . . . . . . . .
3.7.5 Continuous Stirred Tank Heater . . . . . . . . . . . . . . .
. . . . . .
3.8 Notes and References
. . . . .
. . . . .
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3
4
8
10
13
13
14
15
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xi
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