Process Control System Fault Diagnosis
-15%
portes grátis
Process Control System Fault Diagnosis
A Bayesian Approach
; ;
John Wiley & Sons Inc
09/2016
360
Dura
Inglês
9781118770610
15 a 20 dias
Descrição não disponível.
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 Parameters in the Presence of Ambiguous Modes 46 2.4.2 Tutorial on Probabilities Using 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 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, ) 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
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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 Parameters in the Presence of Ambiguous Modes 46 2.4.2 Tutorial on Probabilities Using 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 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, ) 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
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