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 xiiiAcknowledgements xviiList of Figures xixList of Tables xxiiiNomenclature xxvPart I FUNDAMENTALS1 Introduction 31.1 Motivational Illustrations 31.2 Previous Work 41.2.1 Diagnosis Techniques 41.2.2 Monitoring Techniques 71.3 Book Outline 121.3.1 Problem Overview and Illustrative Example 121.3.2 Overview of Proposed Work 12References 162 Prerequisite Fundamentals 192.1 Introduction 192.2 Bayesian Inference and Parameter Estimation 192.2.1 Tutorial on Bayesian Inference 242.2.2 Tutorial on Bayesian Inference with Time Dependency 272.2.3 Bayesian Inference vs. Direct Inference 322.2.4 Tutorial on Bayesian Parameter Estimation 332.3 The EM Algorithm 382.4 Techniques for Ambiguous Modes 442.4.1 Tutorial on Θ Parameters in the Presence of Ambiguous Modes 462.4.2 Tutorial on Probabilities Using Θ Parameters 472.4.3 Dempster–Shafer Theory 482.5 Kernel Density Estimation 512.5.1 From Histograms to Kernel Density Estimates 522.5.2 Bandwidth Selection 542.5.3 Kernel Density Estimation Tutorial 552.6 Bootstrapping 562.6.1 Bootstrapping Tutorial 572.6.2 Smoothed Bootstrapping Tutorial 572.7 Notes and References 60References 613 Bayesian Diagnosis 623.1 Introduction 623.2 Bayesian Approach for Control Loop Diagnosis 623.2.1 Mode M 623.2.2 Evidence E 633.2.3 Historical Dataset D 643.3 Likelihood Estimation 653.4 Notes and References 67References 674 Accounting for Autodependent Modes and Evidence 684.1 Introduction 684.2 Temporally Dependent Evidence 684.2.1 Evidence Dependence 684.2.2 Estimation of Evidence-transition Probability 704.2.3 Issues in Estimating Dependence in Evidence 744.3 Temporally Dependent Modes 754.3.1 Mode Dependence 754.3.2 Estimating Mode Transition Probabilities 774.4 Dependent Modes and Evidence 814.5 Notes and References 82References 825 Accounting for Incomplete Discrete Evidence 835.1 Introduction 835.2 The Incomplete Evidence Problem 835.3 Diagnosis with Incomplete Evidence 855.3.1 Single Missing Pattern Problem 865.3.2 Multiple Missing Pattern Problem 925.3.3 Limitations of the Single and Multiple Missing Pattern Solutions 935.4 Notes and References 94References 946 Accounting for Ambiguous Modes: A Bayesian Approach 966.1 Introduction 966.2 Parametrization of Likelihood Given Ambiguous Modes 966.2.1 Interpretation of Proportion Parameters 966.2.2 Parametrizing Likelihoods 976.2.3 Informed Estimates of Likelihoods 986.3 Fagin–Halpern Combination 996.4 Second-order Approximation 1006.4.1 Consistency of Θ Parameters 1016.4.2 Obtaining a Second-order Approximation 1016.4.3 The Second-order Bayesian Combination Rule 1036.5 Brief Comparison of Combination Methods 1046.6 Applying the Second-order Rule Dynamically 1056.6.1 Unambiguous Dynamic Solution 1056.6.2 The Second-order Dynamic Solution 1066.7 Making a Diagnosis 1076.7.1 Simple Diagnosis 1076.7.2 Ranged Diagnosis 1076.7.3 Expected Value Diagnosis 1076.8 Notes and References 111References 1117 Accounting for Ambiguous Modes: A Dempster–Shafer Approach 1127.1 Introduction 1127.2 Dempster–Shafer Theory 1127.2.1 Basic Belief Assignments 1127.2.2 Probability Boundaries 1147.2.3 Dempster’s Rule of Combination 1147.2.4 Short-cut Combination for Unambiguous Priors 1157.3 Generalizing Dempster–Shafer Theory 1167.3.1 Motivation: Difficulties with BBAs 1177.3.2 Generalizing the BBA 1197.3.3 Generalizing Dempster’s Rule 1227.3.4 Short-cut Combination for Unambiguous Priors 1237.4 Notes and References 124References 1258 Making Use of Continuous Evidence Through Kernel Density Estimation 1268.1 Introduction 1268.2 Performance: Continuous vs. Discrete Methods 1278.2.1 Average False Negative Diagnosis Criterion 1278.2.2 Performance of Discrete and Continuous Methods 1298.3 Kernel Density Estimation 1328.3.1 From Histograms to Kernel Density Estimates 1328.3.2 Defining a Kernel Density Estimate 1348.3.3 Bandwidth Selection Criterion 1358.3.4 Bandwidth Selection Techniques 1368.4 Dimension Reduction 1378.4.1 Independence Assumptions 1388.4.2 Principal and Independent Component Analysis 1398.5 Missing Values 1398.5.1 Kernel Density Regression 1408.5.2 Applying Kernel Density Regression for a Solution 1418.6 Dynamic Evidence 1428.7 Notes and References 143References 1439 Accounting for Sparse Data Within a Mode 1449.1 Introduction 1449.2 Analytical Estimation of the Monitor Output Distribution Function 1459.2.1 Control Performance Monitor 1459.2.2 Process Model Monitor 1469.2.3 Sensor Bias Monitor 1489.3 Bootstrap Approach to Estimating Monitor Output Distribution Function 1509.3.1 Valve Stiction Identification 1509.3.2 The Bootstrap Method 1539.3.3 Illustrative Example 1569.3.4 Applications 1609.4 Experimental Example 1649.4.1 Process Description 1649.4.2 Diagnostic Settings and Results 1679.5 Notes and References 170References 17010 Accounting for Sparse Modes Within the Data 17210.1 Introduction 17210.2 Approaches and Algorithms 17210.2.1 Approach for Component Diagnosis 17310.2.2 Approach for Bootstrapping New Modes 17610.3 Illustration 18110.3.1 Component-based Diagnosis 18410.3.2 Bootstrapping for Additional Modes 18810.4 Application 19410.4.1 Monitor Selection 19510.4.2 Component Diagnosis 19510.5 Notes and References 198References 199Part II APPLICATIONS11 Introduction to Testbed Systems 20311.1 Simulated System 20311.1.1 Monitor Design 20311.2 Bench-scale System 20511.3 Industrial Scale System 207References 20712 Bayesian Diagnosis with Discrete Data 20912.1 Introduction 20912.2 Algorithm 21012.3 Tutorial 21312.4 Simulated Case 21612.5 Bench-scale Case 21712.6 Industrial-scale Case 21912.7 Notes and References 220References 22013 Accounting for Autodependent Modes and Evidence 22113.1 Introduction 22113.2 Algorithms 22213.2.1 Evidence Transition Probability 22213.2.2 Mode Transition Probability 22613.3 Tutorial 22813.4 Notes and References 231References 23114 Accounting for Incomplete Discrete Evidence 23214.1 Introduction 23214.2 Algorithm 23214.2.1 Single Missing Pattern Problem 23214.2.2 Multiple Missing Pattern Problem 23614.3 Tutorial 23814.4 Simulated Case 24114.5 Bench-scale Case 24214.6 Industrial-scale Case 24414.7 Notes and References 246References 24615 Accounting for Ambiguous Modes in Historical Data: A Bayesian Approach 24715.1 Introduction 24715.2 Algorithm 24815.2.1 Formulating the Problem 24815.2.2 Second-order Taylor Series Approximation of p(E|M,Θ) 24815.2.3 Second-order Bayesian Combination 25015.2.4 Optional Step: Separating Monitors into Independent Groups 25215.2.5 Grouping Methodology 25315.3 Illustrative Example of Proposed Methodology 25415.3.1 Introduction 25415.3.2 Offline Step 1: Historical Data Collection 25515.3.3 Offline Step 2: Mutual Information Criterion (Optional) 25515.3.4 Offline Step 3: Calculate Reference Values 25615.3.5 Online Step 1: Calculate Support 25715.3.6 Online Step 2: Calculate Second-order Terms 25815.3.7 Online Step 3: Perform Combinations 26015.3.8 Online Step 4: Make a Diagnosis 26215.4 Simulated Case 26515.5 Bench-scale Case 26815.6 Industrial-scale Case 26915.7 Notes and References 270References 27116 Accounting for Ambiguous Modes in Historical Data: A Dempster–Shafer Approach 27216.1 Introduction 27216.2 Algorithm 27216.2.1 Parametrized Likelihoods 27216.2.2 Basic Belief Assignments 27316.2.3 The Generalized Dempster’s Rule of Combination 27516.3 Example of Proposed Methodology 27616.3.1 Introduction 27616.3.2 Offline Step 1: Historical Data Collection 27716.3.3 Offline Step 2: Mutual Information Criterion (Optional) 27716.3.4 Offline Step 3: Calculate Reference Value 27816.3.5 Online Step 1: Calculate Support 27916.3.6 Online Step 2: Calculate the GBBA 28016.3.7 Online Step 3: Combine BBAs and Diagnose 28316.4 Simulated Case 28316.5 Bench-scale Case 28416.6 Industrial System 28616.7 Notes and References 287References 28717 Making use of Continuous Evidence through Kernel Density Estimation 28817.1 Introduction 28817.2 Algorithm 28917.2.1 Kernel Density Estimation 28917.2.2 Bandwidth Selection 28917.2.3 Adaptive Bandwidths 29017.2.4 Optional Step: Dimension Reduction by Multiplying Independent Likelihoods 29117.2.5 Optional Step: Creating Independence via Independent Component Analysis 29117.2.6 Optional Step: Replacing Missing Values 29217.3 Example of Proposed Methodology 29317.3.1 Offline Step 1: Historical Data Collection 29517.3.2 Offline Step 3: Mutual Information Criterion (Optional) 29617.3.3 Offline Step 4: Independent Component Analysis (Optional) 29817.3.4 Offline Step 5: Obtain Bandwidths 29817.3.5 Online Step 1: Calculate Likelihood of New Data 30117.3.6 Online Step 2: Calculate Posterior Probability 30217.3.7 Online Step 3: Make a Diagnosis 30217.4 Simulated Case 30217.5 Bench-scale Case 30417.6 Industrial-scale Case 30417.7 Notes and References 307References 307Appendix 30817.A Code for Kernel Density Regression 30817.A.1 Kernel Density Regression 30817.A.2 Three-dimensional Matrix Toolbox 31018 Dynamic Application of Continuous Evidence and Ambiguous Mode Solutions 31318.1 Introduction 31318.2 Algorithm for Autodependent Modes 31318.2.1 Transition Probability Matrix 31418.2.2 Review of Second-order Method 31418.2.3 Second-order Probability Transition Rule 31518.3 Algorithm for Dynamic Continuous Evidence and Autodependent Modes 31618.3.1 Algorithm for Dynamic Continuous Evidence 31618.3.2 Combining both Solutions 31818.3.3 Comments on Usefulness 31918.4 Example of Proposed Methodology 32018.4.1 Introduction 32018.4.2 Offline Step 1: Historical Data Collection 32018.4.3 Offline Step 2: Create Temporal Data 32018.4.4 Offline Step 3: Mutual Information Criterion (Optional, but Recommended) 32118.4.5 Offline Step 5: Calculate Reference Values 32218.4.6 Online Step 1: Obtain Prior Second-order Terms 32218.4.7 Online Step 2: Calculate Support 32318.4.8 Online Step 3: Calculate Second-order Terms 32318.4.9 Online Step 4: Combining Prior and Likelihood Terms 32418.5 Simulated Case 32518.6 Bench-scale Case 32618.7 Industrial-scale Case 32618.8 Notes and References 327References 327Index 329

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