Rajamani Doraiswami, Maryhelen Stevenson, Chris Diduch

Identification of Physical Systems (eBook, ePUB)

Applications to Condition Monitoring, Fault Diagnosis, Soft Sensor and Controller Design

• Format: ePub

Produktbeschreibung

Identification of a physical system deals with the problem of identifying its mathematical model using the measured input and output data. As the physical system is generally complex, nonlinear, and its input-output data is corrupted noise, there are fundamental theoretical and practical issues that need to be considered. Identification of Physical Systems addresses this need, presenting a systematic, unified approach to the problem of physical system identification and its practical applications. Starting with a least-squares method, the authors develop various schemes to address the issues of accuracy, variation in the operating regimes, closed loop, and interconnected subsystems. Also presented is a non-parametric signal or data-based scheme to identify a means to provide a quick macroscopic picture of the system to complement the precise microscopic picture given by the parametric model-based scheme. Finally, a sequential integration of totally different schemes, such as non-parametric, Kalman filter, and parametric model, is developed to meet the speed and accuracy requirement of mission-critical systems. Key features: * Provides a clear understanding of theoretical and practical issues in identification and its applications, enabling the reader to grasp a clear understanding of the theory and apply it to practical problems * Offers a self-contained guide by including the background necessary to understand this interdisciplinary subject * Includes case studies for the application of identification on physical laboratory scale systems, as well as number of illustrative examples throughout the book Identification of Physical Systems is a comprehensive reference for researchers and practitioners working in this field and is also a useful source of information for graduate students in electrical, computer, biomedical, chemical, and mechanical engineering.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 536
• Erscheinungstermin: 29. Juli 2014
• Englisch
• ISBN-13: 9781118536490
• Artikelnr.: 41330781

Autorenporträt

Rajamani Doraiswami, Professor Emeritus, Electrical and Computer Engineering Department, University of New Brunswick, USA Rajamani Doraiswami is Professor Emeritus in the Department of Electrical and Computer Engineering at the University of New Brunswick. Dr. Doraiswami is known internationally as an excellent researcher, has held an NSERC operating grant continually since 1981 and has published more than 60 papers in refereed journals and 90 conference papers. Dr. Doraiswami's research interests focus on control, signal processing, pattern classification and algorithms. One of his most successful collaborations has been in the development of laboratories for the teaching of analysis and design of control and signal processing systems in real-time. Chris Diduch is a Professor in the Department of Electrical and Computer Engineering at the University of New Brunswick. His research is in the fields of control systems and digital systems. Maryhelen Stevenson is a Professor in the Department of Electrical and Computer Engineering at the University of New Brunswick. Her research is in the fields of pattern classification, speech and signal processing, adaptive systems and time-frequency representations.

Inhaltsangabe

Preface xv

Nomenclature xxi

1 Modeling of Signals and Systems 1

1.1 Introduction 1

1.2 Classification of Signals 2

1.3 Model of Systems and Signals 5

1.4 Equivalence of Input-Output and State-Space Models 8

1.5 Deterministic Signals 11

1.6 Introduction to Random Signals 23

1.7 Model of Random Signals 28

1.8 Model of a System with Disturbance and Measurement Noise 41

1.9 Summary 50

References 54

Further Readings 54

2 Characterization of Signals: Correlation and Spectral Density 57

2.1 Introduction 57

2.2 Definitions of Auto- and Cross-Correlation (and Covariance) 58

2.3 Spectral Density: Correlation in the Frequency Domain 67

2.4 Coherence Spectrum 74

2.5 Illustrative Examples in Correlation and Spectral Density 76

2.6 Input-Output Correlation and Spectral Density 91

2.7 Illustrative Examples: Modeling and Identification 98

2.8 Summary 109

2.9 Appendix 112

References 116

3 Estimation Theory 117

3.1 Overview 117

3.2 Map Relating Measurement and the Parameter 119

3.3 Properties of Estimators 123

3.4 Cramér-Rao Inequality 127

3.5 Maximum Likelihood Estimation 139

3.6 Summary 154

3.7 Appendix: Cauchy-Schwarz Inequality 157

3.8 Appendix: Cram´er-Rao Lower Bound 157

3.9 Appendix: Fisher Information: Cauchy PDF 161

3.10 Appendix: Fisher Information for i.i.d. PDF 161

3.11 Appendix: Projection Operator 162

3.12 Appendix: Fisher Information: Part Gauss-Part Laplace 164

Problem 165

References 165

Further Readings 165

4 Estimation of Random Parameter 167

4.1 Overview 167

4.2 Minimum Mean-Squares Estimator (MMSE): Scalar Case 167

4.3 MMSE Estimator: Vector Case 169

4.4 Expression for Conditional Mean 172

4.5 Summary 183

4.6 Appendix: Non-Gaussian Measurement PDF 184

References 188

Further Readings 188

5 Linear Least-Squares Estimation 189

5.1 Overview 189

5.2 Linear Least-Squares Approach 189

5.3 Performance of the Least-Squares Estimator 195

5.4 Illustrative Examples 205

5.5 Cram´er-Rao Lower Bound 209

5.6 Maximum Likelihood Estimation 210

5.7 Least-Squares Solution of Under-Determined System 212

5.8 Singular Value Decomposition 213

5.9 Summary 218

5.10 Appendix: Properties of the Pseudo-Inverse and the Projection Operator 221

5.11 Appendix: Positive Definite Matrices 222

5.12 Appendix: Singular Value Decomposition of a Matrix 223

5.13 Appendix: Least-Squares Solution for Under-Determined System 228

5.14 Appendix: Computation of Least-Squares Estimate Using the SVD 229

References 229

Further Readings 230

6 Kalman Filter 231

6.1 Overview 231

6.2 Mathematical Model of the System 233

6.3 Internal Model Principle 236

6.4 Duality Between Controller and an Estimator Design 244

6.5 Observer: Estimator for the States of a System 246

6.6 Kalman Filter: Estimator of the States of a Stochastic System 250

6.7 The Residual of the Kalman Filter with Model Mismatch and Non-Optimal Gain 267

6.8 Summary 274

6.9 Appendix: Estimation Error Covariance and the Kalman Gain 277

6.10 Appendix: The Role of the Ratio of Plant and the Measurement Noise Variances 279

6.11 Appendix: Orthogonal Properties of the Kalman Filter 279

6.12 Appendix: Kalman Filter Residual with Model Mismatch 285

References 287

7 System Identification 289

7.1 Overview 289

7.2 System Model 291

7.3 Kalman Filter-Based Identification Model Structure 297

7.4 Least-Squares Method 307

7.5 High-Order Least-Squares Method 318

7.6 The Prediction Error Method 327

7.7 Comparison of High-Order Least-Squares and the Prediction Error Methods 330

7.8 Subspace Identification Method 334

7.9 Summary 340

7.10 Appendix: Performance of the Least-Squares Approach 347

7.11 Appendix: Frequency-Weighted Model Order Reduction 352

References 354

8 Closed Loop Identification 357

8.1 Overview 357

8.2 Closed-Loop System 359

8.3 Model of the Single Input Multi-Output System 360

8.4 Kalman Filter-Based Identification Model 364

8.5 Closed-Loop Identification Schemes 366

8.6 Second Stage of the Two-Stage Identification 372

8.7 Evaluation on a Simulated Closed-Loop Sensor Net 372

8.8 Summary 374

References 377

9 Fault Diagnosis 379

9.1 Overview 379

9.2 Mathematical Model of the System 381

9.3 Model of the Kalman Filter 382

9.4 Modeling of Faults 383

9.5 Diagnostic Parameters and the Feature Vector 384

9.6 Illustrative Example 386

9.7 Residual of the Kalman Filter 388

9.8 Fault Diagnosis 390

9.9 Fault Detection: Bayes Decision Strategy 390

9.10 Evaluation of Detection Strategy on Simulated System 396

9.11 Formulation of Fault Isolation Problem 396

9.12 Estimation of the Influence Vectors and Additive Fault 399

9.13 Fault Isolation Scheme 401

9.14 Isolation of a Single Fault 403

9.15 Emulators for Offline Identification 406

9.16 Illustrative Example 409

9.17 Overview of Fault Diagnosis Scheme 414

9.18 Evaluation on a Simulated Example 414

9.19 Summary 418

9.20 Appendix: Bayesian Multiple Composite Hypotheses Testing Problem 422

9.21 Appendix: Discriminant Function for Fault Isolation 423

9.22 Appendix: Log-Likelihood Ratio for a Sinusoid and a Constant 424

References 426

10 Modeling and Identification of Physical Systems 427

10.1 Overview 427

10.2 Magnetic Levitation System 427

10.3 Two-Tank Process Control System 436

10.4 Position Control System 442

10.5 Summary 444

References 446

11 Fault Diagnosis of Physical Systems 447

11.1 Overview 447

11.2 Two-Tank Physical Process Control System 448

11.3 Position Control System 452

11.4 Summary 457

References 457

12 Fault Diagnosis of a Sensor Network 459

12.1 Overview 459

12.2 Problem Formulation 461

12.3 Fault Diagnosis Using a Bank of Kalman Filters 461

12.4 Kalman Filter for Pairs of Measurements 462

12.5 Kalman Filter for the Reference Input-Measurement Pair 463

12.6 Kalman Filter Residual: A Model Mismatch Indicator 463

12.7 Bayes Decision Strategy 464

12.8 Truth Table of Binary Decisions 465

12.9 Illustrative Example 467

12.10 Evaluation on a Physical Process Control System 469

12.11 Fault Detection and Isolation 470

12.12 Summary 474

12.13 Appendix 475

References 477

13 Soft Sensor 479

13.1 Review 479

13.2 Mathematical Formulation 481

13.3 Identification of the System 483

13.4 Model of the Kalman Filter 488

13.5 Robust Controller Design 489

13.6 High Performance and Fault Tolerant Control System 494

13.7 Evaluation on a Simulated System: Soft Sensor 496

13.8 Evaluation on a Physical Velocity Control System 500

13.9 Conclusions 502

13.10 Summary 503

References 507

Index 509