Process Control System Fault Diagnosis

Ruben Gonzalez completed his Bachelor's degree in chemical engineering in 2008 at the University of New Brunswick. Under the supervision of Dr. Biao Huang, he completed his Master's degree in 2010 and his Doctorate in 2014, both in chemical engineering, at the University of Alberta. His research interests include Bayesian diagnosis, fault detection and diagnosis, data reconciliation, and applied kernel density estimation. Fei Qi obtained his Ph.D. degree in Process Control from the University of Alberta, Canada, in 2011. He had his M.Sc. degree (2006) and B.Sc. degree (2003) in Automation from the University of Science and Technology of China. Fei Qi joined Suncor Energy Inc. in 2010 as an Advance Process Control Engineer. He has extensive experiences in applying system identification, model predictive control, and control performance monitoring in real industrial processes. His Ph.D. research was on applying Bayesian statistics to control loop diagnosis. His current research interests include model predictive control, soft sensor, fault detection, and process optimization. Biao Huang obtained his PhD degree in Process Control from the University of Alberta, Canada, in 1997. He is currently a Professor in the Department of Chemical and Materials Engineering, University of Alberta, NSERC Industrial Research Chair in Control of Oil Sands Processes and AITF Industry Chair in Process Control. He is a Fellow of the Canadian Academy of Engineering, Fellow of the Chemical Institute of Canada, and recipient of numerous awards including Germany’s Alexander von Humboldt Research Fellowship, Bantrel Award in Design and Industrial Practice, APEGA Summit Award in Research Excellence, best paper award from Journal of Process Control etc. Biao Huang’s main research interests include: Bayesian inference, control performance assessment, fault detection and isolation. Biao Huang has applied his expertise extensively in industrial practice. He also serves as the Deputy Editor-in-Chief for Control Engineering Practice, the Associate Editor for Canadian Journal of Chemical Engineering and the Associate Editor for Journal of Process Control.

Preface xiii

Acknowledgements xvii

List of Figures xix

List of Tables xxiii

Nomenclature xxv

Part I FUNDAMENTALS

1 Introduction 3

1.1 Motivational Illustrations 3

1.2 Previous Work 4

1.2.1 Diagnosis Techniques 4

1.2.2 Monitoring Techniques 7

1.3 Book Outline 12

1.3.1 Problem Overview and Illustrative Example 12

1.3.2 Overview of Proposed Work 12

References 16

2 Prerequisite Fundamentals 19

2.1 Introduction 19

2.2 Bayesian Inference and Parameter Estimation 19

2.2.1 Tutorial on Bayesian Inference 24

2.2.2 Tutorial on Bayesian Inference with Time Dependency 27

2.2.3 Bayesian Inference vs. Direct Inference 32

2.2.4 Tutorial on Bayesian Parameter Estimation 33

2.3 The EM Algorithm 38

2.4 Techniques for Ambiguous Modes 44

2.4.1 Tutorial on Θ Parameters in the Presence of Ambiguous Modes 46

2.4.2 Tutorial on Probabilities Using Θ Parameters 47

2.4.3 Dempster–Shafer Theory 48

2.5 Kernel Density Estimation 51

2.5.1 From Histograms to Kernel Density Estimates 52

2.5.2 Bandwidth Selection 54

2.5.3 Kernel Density Estimation Tutorial 55

2.6 Bootstrapping 56

2.6.1 Bootstrapping Tutorial 57

2.6.2 Smoothed Bootstrapping Tutorial 57

2.7 Notes and References 60

References 61

3 Bayesian Diagnosis 62

3.1 Introduction 62

3.2 Bayesian Approach for Control Loop Diagnosis 62

3.2.1 Mode M 62

3.2.2 Evidence E 63

3.2.3 Historical Dataset D 64

3.3 Likelihood Estimation 65

3.4 Notes and References 67

References 67

4 Accounting for Autodependent Modes and Evidence 68

4.1 Introduction 68

4.2 Temporally Dependent Evidence 68

4.2.1 Evidence Dependence 68

4.2.2 Estimation of Evidence-transition Probability 70

4.2.3 Issues in Estimating Dependence in Evidence 74

4.3 Temporally Dependent Modes 75

4.3.1 Mode Dependence 75

4.3.2 Estimating Mode Transition Probabilities 77

4.4 Dependent Modes and Evidence 81

4.5 Notes and References 82

References 82

5 Accounting for Incomplete Discrete Evidence 83

5.1 Introduction 83

5.2 The Incomplete Evidence Problem 83

5.3 Diagnosis with Incomplete Evidence 85

5.3.1 Single Missing Pattern Problem 86

5.3.2 Multiple Missing Pattern Problem 92

5.3.3 Limitations of the Single and Multiple Missing Pattern Solutions 93

5.4 Notes and References 94

References 94

6 Accounting for Ambiguous Modes: A Bayesian Approach 96

6.1 Introduction 96

6.2 Parametrization of Likelihood Given Ambiguous Modes 96

6.2.1 Interpretation of Proportion Parameters 96

6.2.2 Parametrizing Likelihoods 97

6.2.3 Informed Estimates of Likelihoods 98

6.3 Fagin–Halpern Combination 99

6.4 Second-order Approximation 100

6.4.1 Consistency of Θ Parameters 101

6.4.2 Obtaining a Second-order Approximation 101

6.4.3 The Second-order Bayesian Combination Rule 103

6.5 Brief Comparison of Combination Methods 104

6.6 Applying the Second-order Rule Dynamically 105

6.6.1 Unambiguous Dynamic Solution 105

6.6.2 The Second-order Dynamic Solution 106

6.7 Making a Diagnosis 107

6.7.1 Simple Diagnosis 107

6.7.2 Ranged Diagnosis 107

6.7.3 Expected Value Diagnosis 107

6.8 Notes and References 111

References 111

7 Accounting for Ambiguous Modes: A Dempster–Shafer Approach 112

7.1 Introduction 112

7.2 Dempster–Shafer Theory 112

7.2.1 Basic Belief Assignments 112

7.2.2 Probability Boundaries 114

7.2.3 Dempster’s Rule of Combination 114

7.2.4 Short-cut Combination for Unambiguous Priors 115

7.3 Generalizing Dempster–Shafer Theory 116

7.3.1 Motivation: Difficulties with BBAs 117

7.3.2 Generalizing the BBA 119

7.3.3 Generalizing Dempster’s Rule 122

7.3.4 Short-cut Combination for Unambiguous Priors 123

7.4 Notes and References 124

References 125

8 Making Use of Continuous Evidence Through Kernel Density Estimation 126

8.1 Introduction 126

8.2 Performance: Continuous vs. Discrete Methods 127

8.2.1 Average False Negative Diagnosis Criterion 127

8.2.2 Performance of Discrete and Continuous Methods 129

8.3 Kernel Density Estimation 132

8.3.1 From Histograms to Kernel Density Estimates 132

8.3.2 Defining a Kernel Density Estimate 134

8.3.3 Bandwidth Selection Criterion 135

8.3.4 Bandwidth Selection Techniques 136

8.4 Dimension Reduction 137

8.4.1 Independence Assumptions 138

8.4.2 Principal and Independent Component Analysis 139

8.5 Missing Values 139

8.5.1 Kernel Density Regression 140

8.5.2 Applying Kernel Density Regression for a Solution 141

8.6 Dynamic Evidence 142

8.7 Notes and References 143

References 143

9 Accounting for Sparse Data Within a Mode 144

9.1 Introduction 144

9.2 Analytical Estimation of the Monitor Output Distribution Function 145

9.2.1 Control Performance Monitor 145

9.2.2 Process Model Monitor 146

9.2.3 Sensor Bias Monitor 148

9.3 Bootstrap Approach to Estimating Monitor Output Distribution Function 150

9.3.1 Valve Stiction Identification 150

9.3.2 The Bootstrap Method 153

9.3.3 Illustrative Example 156

9.3.4 Applications 160

9.4 Experimental Example 164

9.4.1 Process Description 164

9.4.2 Diagnostic Settings and Results 167

9.5 Notes and References 170

References 170

10 Accounting for Sparse Modes Within the Data 172

10.1 Introduction 172

10.2 Approaches and Algorithms 172

10.2.1 Approach for Component Diagnosis 173

10.2.2 Approach for Bootstrapping New Modes 176

10.3 Illustration 181

10.3.1 Component-based Diagnosis 184

10.3.2 Bootstrapping for Additional Modes 188

10.4 Application 194

10.4.1 Monitor Selection 195

10.4.2 Component Diagnosis 195

10.5 Notes and References 198

References 199

Part II APPLICATIONS

11 Introduction to Testbed Systems 203

11.1 Simulated System 203

11.1.1 Monitor Design 203

11.2 Bench-scale System 205

11.3 Industrial Scale System 207

References 207

12 Bayesian Diagnosis with Discrete Data 209

12.1 Introduction 209

12.2 Algorithm 210

12.3 Tutorial 213

12.4 Simulated Case 216

12.5 Bench-scale Case 217

12.6 Industrial-scale Case 219

12.7 Notes and References 220

References 220

13 Accounting for Autodependent Modes and Evidence 221

13.1 Introduction 221

13.2 Algorithms 222

13.2.1 Evidence Transition Probability 222

13.2.2 Mode Transition Probability 226

13.3 Tutorial 228

13.4 Notes and References 231

References 231

14 Accounting for Incomplete Discrete Evidence 232

14.1 Introduction 232

14.2 Algorithm 232

14.2.1 Single Missing Pattern Problem 232

14.2.2 Multiple Missing Pattern Problem 236

14.3 Tutorial 238

14.4 Simulated Case 241

14.5 Bench-scale Case 242

14.6 Industrial-scale Case 244

14.7 Notes and References 246

References 246

15 Accounting for Ambiguous Modes in Historical Data: A Bayesian Approach 247

15.1 Introduction 247

15.2 Algorithm 248

15.2.1 Formulating the Problem 248

15.2.2 Second-order Taylor Series Approximation of p(E|M,Θ) 248

15.2.3 Second-order Bayesian Combination 250

15.2.4 Optional Step: Separating Monitors into Independent Groups 252

15.2.5 Grouping Methodology 253

15.3 Illustrative Example of Proposed Methodology 254

15.3.1 Introduction 254

15.3.2 Offline Step 1: Historical Data Collection 255

15.3.3 Offline Step 2: Mutual Information Criterion (Optional) 255

15.3.4 Offline Step 3: Calculate Reference Values 256

15.3.5 Online Step 1: Calculate Support 257

15.3.6 Online Step 2: Calculate Second-order Terms 258

15.3.7 Online Step 3: Perform Combinations 260

15.3.8 Online Step 4: Make a Diagnosis 262

15.4 Simulated Case 265

15.5 Bench-scale Case 268

15.6 Industrial-scale Case 269

15.7 Notes and References 270

References 271

16 Accounting for Ambiguous Modes in Historical Data: A Dempster–Shafer Approach 272

16.1 Introduction 272

16.2 Algorithm 272

16.2.1 Parametrized Likelihoods 272

16.2.2 Basic Belief Assignments 273

16.2.3 The Generalized Dempster’s Rule of Combination 275

16.3 Example of Proposed Methodology 276

16.3.1 Introduction 276

16.3.2 Offline Step 1: Historical Data Collection 277

16.3.3 Offline Step 2: Mutual Information Criterion (Optional) 277

16.3.4 Offline Step 3: Calculate Reference Value 278

16.3.5 Online Step 1: Calculate Support 279

16.3.6 Online Step 2: Calculate the GBBA 280

16.3.7 Online Step 3: Combine BBAs and Diagnose 283

16.4 Simulated Case 283

16.5 Bench-scale Case 284

16.6 Industrial System 286

16.7 Notes and References 287

References 287

17 Making use of Continuous Evidence through Kernel Density Estimation 288

17.1 Introduction 288

17.2 Algorithm 289

17.2.1 Kernel Density Estimation 289

17.2.2 Bandwidth Selection 289

17.2.3 Adaptive Bandwidths 290

17.2.4 Optional Step: Dimension Reduction by Multiplying Independent Likelihoods 291

17.2.5 Optional Step: Creating Independence via Independent Component Analysis 291

17.2.6 Optional Step: Replacing Missing Values 292

17.3 Example of Proposed Methodology 293

17.3.1 Offline Step 1: Historical Data Collection 295

17.3.2 Offline Step 3: Mutual Information Criterion (Optional) 296

17.3.3 Offline Step 4: Independent Component Analysis (Optional) 298

17.3.4 Offline Step 5: Obtain Bandwidths 298

17.3.5 Online Step 1: Calculate Likelihood of New Data 301

17.3.6 Online Step 2: Calculate Posterior Probability 302

17.3.7 Online Step 3: Make a Diagnosis 302

17.4 Simulated Case 302

17.5 Bench-scale Case 304

17.6 Industrial-scale Case 304

17.7 Notes and References 307

References 307

Appendix 308

17.A Code for Kernel Density Regression 308

17.A.1 Kernel Density Regression 308

17.A.2 Three-dimensional Matrix Toolbox 310

18 Dynamic Application of Continuous Evidence and Ambiguous Mode Solutions 313

18.1 Introduction 313

18.2 Algorithm for Autodependent Modes 313

18.2.1 Transition Probability Matrix 314

18.2.2 Review of Second-order Method 314

18.2.3 Second-order Probability Transition Rule 315

18.3 Algorithm for Dynamic Continuous Evidence and Autodependent Modes 316

18.3.1 Algorithm for Dynamic Continuous Evidence 316

18.3.2 Combining both Solutions 318

18.3.3 Comments on Usefulness 319

18.4 Example of Proposed Methodology 320

18.4.1 Introduction 320

18.4.2 Offline Step 1: Historical Data Collection 320

18.4.3 Offline Step 2: Create Temporal Data 320

18.4.4 Offline Step 3: Mutual Information Criterion (Optional, but Recommended) 321

18.4.5 Offline Step 5: Calculate Reference Values 322

18.4.6 Online Step 1: Obtain Prior Second-order Terms 322

18.4.7 Online Step 2: Calculate Support 323

18.4.8 Online Step 3: Calculate Second-order Terms 323

18.4.9 Online Step 4: Combining Prior and Likelihood Terms 324

18.5 Simulated Case 325

18.6 Bench-scale Case 326

18.7 Industrial-scale Case 326

18.8 Notes and References 327

References 327

Index 329