كتاب Model-Based Fault Diagnosis Techniques
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 كتاب Model-Based Fault Diagnosis Techniques

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Model-Based Fault Diagnosis Techniques
Design Schemes, Algorithms and Tools
Second Edition
Steven X. Ding  

كتاب Model-Based Fault Diagnosis Techniques  M_b_f_10
و المحتوى كما يلي :


Contents
Part I Introduction, Basic Concepts and Preliminaries
1 Introduction 3
1.1 Basic Concepts of Fault Diagnosis Technique 4
1.2 Historical Development and Some Relevant Issues . 8
1.3 Notes and References 10
2 Basic Ideas, Major Issues and Tools in the Observer-Based FDI
Framework 13
2.1 On the Observer-Based Residual Generator Framework 13
2.2 Unknown Input Decoupling and Fault Isolation Issues . 14
2.3 Robustness Issues in the Observer-Based FDI Framework . 15
2.4 On the Parity Space FDI Framework 16
2.5 Residual Evaluation and Threshold Computation 17
2.6 FDI System Synthesis and Design 18
2.7 Notes and References 18
3 Modelling of Technical Systems . 21
3.1 Description of Nominal System Behavior 22
3.2 Coprime Factorization Technique 23
3.3 Representations of Systems with Disturbances . 25
3.4 Representations of System Models with Model Uncertainties . 25
3.5 Modelling of Faults . 27
3.6 Modelling of Faults in Closed-Loop Feedback Control Systems 29
3.7 Case Study and Application Examples . 31
3.7.1 Speed Control of a DC Motor 31
3.7.2 Inverted Pendulum Control System . 34
3.7.3 Three-Tank System . 38
3.7.4 Vehicle Lateral Dynamic System 41
3.7.5 Continuous Stirred Tank Heater . 46
3.8 Notes and References 49
xixii Contents
4 Fault Detectability, Isolability and Identifiability . 51
4.1 Fault Detectability 51
4.2 Excitations and Detection of Multiplicative Faults . 56
4.3 Fault Isolability . 57
4.3.1 Concept of System Fault Isolability . 57
4.3.2 Fault Isolability Conditions . 58
4.4 Fault Identifiability 65
4.5 Notes and References 67
Part II Residual Generation
5 Basic Residual Generation Methods 71
5.1 Analytical Redundancy . 72
5.2 Residuals and Parameterization of Residual Generators 75
5.3 Issues Related to Residual Generator Design and Implementation . 78
5.4 Fault Detection Filter 79
5.5 Diagnostic Observer Scheme 81
5.5.1 Construction of Diagnostic Observer-Based Residual
Generators 81
5.5.2 Characterization of Solutions 82
5.5.3 A Numerical Approach . 91
5.5.4 An Algebraic Approach . 96
5.6 Parity Space Approach 98
5.6.1 Construction of Parity Relation Based Residual Generators 98
5.6.2 Characterization of Parity Space 101
5.6.3 Examples . 102
5.7 Interconnections, Comparison and Some Remarks . 103
5.7.1 Parity Space Approach and Diagnostic Observer 104
5.7.2 Diagnostic Observer and Residual Generator of General
Form . 108
5.7.3 Applications of the Interconnections and Some Remarks 111
5.7.4 Examples . 113
5.8 Notes and References 115
6 Perfect Unknown Input Decoupling . 117
6.1 Problem Formulation 117
6.2 Existence Conditions of PUIDP . 119
6.2.1 A General Existence Condition . 119
6.2.2 A Check Condition via Rosenbrock System Matrix . 120
6.2.3 An Algebraic Check Condition . 122
6.3 A Frequency Domain Approach . 126
6.4 UIFDF Design 128
6.4.1 The Eigenstructure Assignment Approach . 129
6.4.2 Geometric Approach . 133
6.5 UIDO Design 141
6.5.1 An Algebraic Approach . 141
6.5.2 Unknown Input Observer Approach . 142Contents xiii
6.5.3 A Matrix Pencil Approach to the UIDO Design 146
6.5.4 A Numerical Approach to the UIDO Design 150
6.6 Unknown Input Parity Space Approach . 152
6.7 An Alternative Scheme—Null Matrix Approach 153
6.8 Discussion 154
6.9 Minimum Order Residual Generator 154
6.9.1 Minimum Order Residual Generator Design by Geometric
Approach . 155
6.9.2 An Alternative Solution . 157
6.10 Notes and References 160
7 Residual Generation with Enhanced Robustness Against Unknown
Inputs . 163
7.1 Mathematical and Control Theoretical Preliminaries 164
7.1.1 Signal Norms 165
7.1.2 System Norms 167
7.1.3 Computation of H2 and H? Norms 169
7.1.4 Singular Value Decomposition (SVD) 171
7.1.5 Co-Inner–Outer Factorization 171
7.1.6 Model Matching Problem 174
7.1.7 Essentials of the LMI Technique 175
7.2 Kalman Filter Based Residual Generation 177
7.3 Robustness, Fault Sensitivity and Performance Indices . 180
7.3.1 Robustness and Sensitivity . 181
7.3.2 Performance Indices: Robustness vs. Sensitivity 182
7.3.3 Relations Between the Performance Indices 182
7.4 Optimal Selection of Parity Matrices and Vectors 184
7.4.1 Sf,+/Rd as Performance Index . 184
7.4.2 Sf,?/Rd as Performance Index . 188
7.4.3 JS?R as Performance Index . 190
7.4.4 Optimization Performance and System Order 192
7.4.5 Summary and Some Remarks 193
7.5 H? Optimal Fault Identification Scheme 196
7.6 H2/H2 Design of Residual Generators . 198
7.7 Relationship Between H2/H2 Design and Optimal Selection
of Parity Vectors . 201
7.8 LMI Aided Design of FDF . 208
7.8.1 H2 to H2 Trade-off Design of FDF . 208
7.8.2 On the H? Index 213
7.8.3 H2 to H? Trade-off Design of FDF . 221
7.8.4 H? to H? Trade-off Design of FDF 223
7.8.5 H? to H? Trade-off Design of FDF in a Finite Frequency
Range 225
7.8.6 An Alternative H? to H? Trade-off Design of FDF 226
7.8.7 A Brief Summary and Discussion 229xiv Contents
7.9 The Unified Solution . 230
7.9.1 Hi/H? Index and Problem Formulation 230
7.9.2 Hi/H? Optimal Design of FDF: The Standard Form . 231
7.9.3 Discrete-Time Version of the Unified Solution . 234
7.9.4 A Generalized Interpretation 235
7.10 The General Form of the Unified Solution . 238
7.10.1 Extended CIOF . 239
7.10.2 Generalization of the Unified Solution . 241
7.11 Notes and References 244
8 Residual Generation with Enhanced Robustness Against Model
Uncertainties . 249
8.1 Preliminaries . 250
8.1.1 LMI Aided Computation for System Bounds 250
8.1.2 Stability of Stochastically Uncertain Systems 251
8.2 Transforming Model Uncertainties into Unknown Inputs 252
8.3 Reference Model Based Strategies . 254
8.3.1 The Basic Idea 254
8.3.2 A Reference Model Based Solution for Systems
with Norm-Bounded Uncertainties . 254
8.4 Residual Generation for Systems with Polytopic Uncertainties . 261
8.4.1 The Reference Model Scheme Based Scheme . 262
8.4.2 H? to H? Design Formulation . 266
8.5 Residual Generation for Stochastically Uncertain Systems . 267
8.5.1 System Dynamics and Statistical Properties . 268
8.5.2 Basic Idea and Problem Formulation 269
8.5.3 An LMI Solution . 270
8.5.4 An Alternative Approach 277
8.6 Notes and References 280
Part III Residual Evaluation and Threshold Computation
9 Norm-Based Residual Evaluation and Threshold Computation . 285
9.1 Preliminaries . 286
9.2 Basic Concepts 288
9.3 Some Standard Evaluation Functions 289
9.4 Basic Ideas of Threshold Setting and Problem Formulation 291
9.4.1 Dynamics of the Residual Generator 292
9.4.2 Definitions of Thresholds and Problem Formulation 293
9.5 Computation of Jth,RMS,2 296
9.5.1 Computation of Jth,RMS,2 for the Systems
with the Norm-Bounded Uncertainty 296
9.5.2 Computation of Jth,RMS,2 for the Systems
with the Polytopic Uncertainty . 300
9.6 Computation of Jth,peak,peak . 302
9.6.1 Computation of Jth,peak,peak for the Systems
with the Norm-Bounded Uncertainty 302Contents xv
9.6.2 Computation of Jth,peak,peak for the Systems
with the Polytopic Uncertainty . 305
9.7 Computation of Jth,peak,2 306
9.7.1 Computation of Jth,peak,2 for the Systems
with the Norm-Bounded Uncertainty 306
9.7.2 Computation of Jth,peak,2 for the Systems
with the Polytopic Uncertainty . 309
9.8 Threshold Generator . 310
9.9 Notes and References 312
10 Statistical Methods Based Residual Evaluation and Threshold
Setting . 315
10.1 Introduction . 315
10.2 Elementary Statistical Methods . 315
10.2.1 Basic Hypothesis Test 315
10.2.2 Likelihood Ratio and Generalized Likelihood Ratio 318
10.2.3 Vector-Valued GLR . 320
10.2.4 Detection of Change in Variance 322
10.2.5 Aspects of On-Line Realization . 323
10.3 Criteria for Threshold Computation . 325
10.3.1 The Neyman–Pearson Criterion . 325
10.3.2 Maximum a Posteriori Probability (MAP) Criterion 326
10.3.3 Bayes’ Criterion . 327
10.3.4 Some Remarks 328
10.4 Application of GLR Testing Methods 328
10.4.1 Kalman Filter Based Fault Detection 329
10.4.2 Parity Space Based Fault Detection . 335
10.5 Notes and References 337
11 Integration of Norm-Based and Statistical Methods 339
11.1 Residual Evaluation in Stochastic Systems with Deterministic
Disturbances . 339
11.1.1 Residual Generation . 340
11.1.2 Problem Formulation 341
11.1.3 GLR Solutions 342
11.1.4 An Example . 345
11.2 Residual Evaluation Scheme for Stochastically Uncertain Systems 346
11.2.1 Problem Formulation 347
11.2.2 Solution and Design Algorithms 348
11.3 Probabilistic Robustness Technique Aided Threshold Computation 357
11.3.1 Problem Formulation 357
11.3.2 Outline of the Basic Idea 359
11.3.3 LMIs Used for the Solutions . 360
11.3.4 Problem Solutions in the Probabilistic Framework . 361
11.3.5 An Application Example 363
11.3.6 Concluding Remarks 365
11.4 Notes and References 366xvi Contents
Part IV Fault Detection, Isolation and Identification Schemes
12 Integrated Design of Fault Detection Systems . 369
12.1 FAR and FDR 370
12.2 Maximization of Fault Detectability by a Given FAR 373
12.2.1 Problem Formulation 373
12.2.2 Essential Form of the Solution . 374
12.2.3 A General Solution . 376
12.2.4 Interconnections and Comparison 379
12.2.5 Examples . 383
12.3 Minimizing False Alarm Number by a Given FDR . 386
12.3.1 Problem Formulation 387
12.3.2 Essential Form of the Solution . 388
12.3.3 The State Space Form 390
12.3.4 The Extended Form . 392
12.3.5 Interpretation of the Solutions and Discussion . 393
12.3.6 An Example . 397
12.4 On the Application to Stochastic Systems 398
12.4.1 Application to Maximizing FDR by a Given FAR . 399
12.4.2 Application to Minimizing FAR by a Given FDR 400
12.4.3 Equivalence Between the Kalman Filter Scheme
and the Unified Solution . 400
12.5 Notes and References 402
13 Fault Isolation Schemes . 405
13.1 Essentials 406
13.1.1 Existence Conditions for a Perfect Fault Isolation . 406
13.1.2 PFIs and Unknown Input Decoupling 408
13.1.3 PFIs with Unknown Input Decoupling (PFIUID) 411
13.2 Fault Isolation Filter Design . 412
13.2.1 A Design Approach Based on the Duality to Decoupling
Control 413
13.2.2 The Geometric Approach 416
13.2.3 A Generalized Design Approach 418
13.3 An Algebraic Approach to Fault Isolation 427
13.4 Fault Isolation Using a Bank of Residual Generators 431
13.4.1 The Dedicated Observer Scheme (DOS) 432
13.4.2 The Generalized Observer Scheme (GOS) . 436
13.5 Notes and References 439
14 Fault Identification Schemes . 441
14.1 Fault Identification Filter Schemes and Perfect Fault Identification . 442
14.1.1 Fault Detection Filters and Existence Conditions 442
14.1.2 FIF Design with Measurement Derivatives . 446
14.2 On the Optimal FIF Design . 449
14.2.1 Problem Formulation and Solution Study 449
14.2.2 Study on the Role of the Weighting Matrix . 451Contents xvii
14.3 Approaches to the Design of FIF 456
14.3.1 A General Fault Identification Scheme . 457
14.3.2 An Alternative Scheme . 457
14.3.3 Identification of the Size of a Fault . 458
14.3.4 Fault Identification in a Finite Frequency Range 460
14.4 Fault Identification Using an Augmented Observer . 461
14.5 An Algebraic Fault Identification Scheme 463
14.6 Adaptive Observer-Based Fault Identification 464
14.6.1 Problem Formulation 464
14.6.2 The Adaptive Observer Scheme . 465
14.7 Notes and References 468
15 Fault Diagnosis in Feedback Control Systems and Fault-Tolerant
Architecture 471
15.1 Plant and Control Loop Models, Controller and Observer
Parameterizations 472
15.1.1 Plant and Control Loop Models . 472
15.1.2 Parameterization of Stabilizing Controllers, Observers,
and an Alternative Formulation of Controller Design 473
15.1.3 Observer and Residual Generator Based Realizations
of Youla Parameterization 475
15.1.4 Residual Generation Based Formulation of Controller
Design Problem . 476
15.2 Residual Extraction in the Standard Feedback Control Loop
and a Fault Detection Scheme 478
15.2.1 Signals at the Access Points in the Control Loop 478
15.2.2 A Fault Detection Scheme Based on Extraction of Residual
Signals 479
15.3 2-DOF Control Structures and Residual Access . 481
15.3.1 The Standard 2-DOF Control Structures 481
15.3.2 An Alternative 2-DOF Control Structure with Residual
Access 483
15.4 On Residual Access in the IMC and Residual Generator Based
Control Structures 485
15.4.1 An Extended IMC Structure with an Integrated Residual
Access 485
15.4.2 A Residual Generator Based Feedback Control Loop 487
15.5 Notes and References 488
References . 491
Index .
Index
A
Adaptive threshold, 310
Analytical redundancy, 6, 72
output observer based generation, 74
parity relation based generation, 107
B
Bezout identity, 24
Bounded Real Lemma, 170, 175
C
Case study
CSTH, 46, 78, 80, 94, 122, 125, 152, 213,
264, 301
DC motor, 31, 114, 298, 311
inverted pendulum, 34, 95, 97, 103, 120,
139, 156, 234, 261, 425, 427, 459
three-tank system, 38, 55, 65, 67, 336, 345
vehicle lateral dynamic system, 41, 146,
180, 229, 277, 363, 438, 444
Co-inner–outer factorization (CIOF), 171
extended CIOF, 239
Coprime factorization
left coprime factorization (LCF), 23
right coprime factorization (RCF), 23
D
Design form of residual generators, 79
Diagnostic observer (DO), 81
E
Excitation subspace, 56
Extended IMC (EIMC), 485
F
False alarm rate (FAR)
in the norm-based framework, 372
in the statistical framework, 359, 371
Fault detectability
definition, 52, 56
existence conditions, 52
Fault detectability in the norm-based
framework, 372
Fault detectability indices, 414
Fault detection, 4
Fault detection filter (FDF), 79
Fault detection rate (FDR)
in the norm-based framework, 373
in the statistical framework, 371
Fault identifiability
definition, 66
Fault identification, 4
Fault identification filter (FIF), 443
Fault isolability
check conditions, 58
definition, 57
Fault isolability matrix, 414
Fault isolation, 4
Fault transfer matrix, 54
FD (fault detection), 4
FDI (fault detection and isolation), 4
FDIA (fault detection, isolation and analysis),
4
G
Generalized internal model control (GIMC),
479
Generalized likelihood ratio (GLR), 319
Generalized optimal fault identification
problem (GOFIP), 451
GKYP-Lemma, 176
H
Hardware redundancy, 4
S.X. Ding, Model-Based Fault Diagnosis Techniques, Advances in Industrial Control,
DOI 10.1007/978-1-4471-4799-2, © Springer-Verlag London 2013
499500 Index
I
Implementation form of residual generators, 79
Inner–outer factorization (IOF), 171
K
Kalman filter scheme, 178, 329
L
Least square estimate, 463
Likelihood ratio (LR), 318
Luenberger equations, 81
a numerical solution, 93
characterization of the solution, 89
Luenberger type output observer, 81
M
Maximum likelihood estimate, 319
Mean square stability, 251, 252
Minimum order of residual generators, 86
Missed detection rate (MDR)
in the statistical framework, 371
Model matching problem (MMP), 174
Model uncertainties
additive perturbation, 25
multiplicative perturbation, 25
norm bounded type, 26
polytopic type, 26
stochastically uncertain type, 26
Modelling of faults, 27
actuator faults, 28
additive faults, 28
faults in feedback control systems, 30
multiplicative faults, 28
process or component faults, 28
sensor faults, 28
N
Norm of vectors
2 (Euclidean) norm, 167
? norm, 167
Norm-based residual evaluation
limit monitoring, 288
trend analysis, 288
Norms of matrices
Frobenius-norm, 169
? norm, 169
spectral norm, 169
O
Optimal design of residual generators
H
?/H? design, 393
H2/H2 design, 198
H2 optimization problem, 208
H2 to H? design, 221
H2 to H2 design, 212
Hi/H? design, see also the unified
solution, 231
H? optimal fault identification, 196
H? to H? design, 223
H? to H? design – an alternative solution,
226
H? to H? design in a finite frequency
range, 225
Optimal fault identification
H? optimal fault identification problem
(H? OFIP), 449
Oscillation detection and conditional
monitoring, 313
Output observer, 74
P
Parameter identification methods, 8
Parameterization of all observers, 474
Parameterization of residual generators, 77
Parity space approach
characterization of residual generator, 102
construction of residual generator, 100
minimum order of residual generator, 101
Perfect fault identification (PFI)
existence condition, 443
solutions, 443
Perfect fault isolation (PFIs)
definition, 407
existence conditions, 407
fault isolation filter, 413
Perfect unknown input decoupling problem
(PUIDP), 118
Performance indices
H
? index, 214
Hi/H? index, 231
index with inequalities, 182
JS?R index, 182
JS/R index, 182
Sf,+ index, 181
Sf,? index, 181
PI-observer, 462
Plausibility test, 5
Post-filter, 77
R
Residual evaluation, 7
Residual evaluation functions
average value, 290
peak value, 289
RMS value, 291
Residual generation, 6
Residual generator, 6Index 501
Residual generator bank
dedicated observer scheme (DOS), 432
generalized observer scheme (GOS), 436
Residual signal
observer-based, 75
parity relation based, 100
S
Sensor fault identification, 424, 444
Sensor fault isolation, 432, 444
Set of detectable faults (SDF), 372
Set of disturbances that cause false alarms
(SDFA), 371
Signal norms
L2 (l2) norm, 165
L? (l?) norm, 166
peak norm, 166
root mean square (RMS), 165, 291
Signal processing based fault diagnosis, 4
Simultaneous state and disturbance estimator,
469
Soft- or virtual sensor, 74
Software redundancy, 6, 72
SVD, 171
System norm
generalized H2 norm, 168
H2 norm, 169
H? norm, 168
induced norm, 167
peak-to-peak gain, 168
T
Tchebycheff inequality, 352
The unified solution
a generalized interpretation, 236
discrete-time version, 234
general form, 242, 378
standard form, 232, 376
Thresholds
Jth,peak,2, 294
Jth,peak,peak, 294
Jth,RMS,2, 295
U
Unified solution of parity matrix, 191
Unknown input decoupling
an algebraic check condition, 122
check condition via Rosenbrock system
matrix, 121
frequency domain approach, 126
minimum order residual generator, 154
null matrix, 153
unknown input diagnostic observer
(UIDO), 141
unknown input fault detection filter
(UIFDF), 128
unknown input observer (UIO), 142
unknown input parity space approach, 152
W
Weighting matrix, 451
Y
Youla parameterization
observer-based realization, 475
original form, 473
residual generation based realization, 476


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