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E-raamat: Process Control System Fault Diagnosis: A Bayesian Approach

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Process Control System Fault Diagnosis: A Bayesian Approach

Ruben T. Gonzalez, University of Alberta, Canada

Fei Qi, Suncor Energy Inc., Canada

Biao Huang, University of Alberta, Canada

 

Data-driven Inferential Solutions for Control System Fault Diagnosis

 

A typical modern process system consists of hundreds or even thousands of control loops, which are overwhelming for plant personnel to monitor. The main objectives of this book are to establish a new framework for control system fault diagnosis, to synthesize observations of different monitors with a prior knowledge, and to pinpoint possible abnormal sources on the basis of Bayesian theory.

Process Control System Fault Diagnosis: A Bayesian Approach consolidates results developed by the authors, along with the fundamentals, and presents them in a systematic way. The book provides a comprehensive coverage of various Bayesian methods for control system fault diagnosis, along with a detailed tutorial. The book is useful for graduate students and researchers as a monograph and as a reference for state-of-the-art techniques in control system performance monitoring and fault diagnosis. Since several self-contained practical examples are included in the book, it also provides a place for practicing engineers to look for solutions to their daily monitoring and diagnosis problems.

 

Key features:

             A comprehensive coverage of Bayesian Inference for control system fault diagnosis.

             Theory and applications are self-contained.

             Provides detailed algorithms and sample Matlab codes.

             Theory is illustrated through benchmark simulation examples, pilot-scale experiments and industrial application.

 

Process Control System Fault Diagnosis: A Bayesian Approach is a comprehensive guide for graduate students, practicing engineers, and researchers who are interests in applying theory to practice.
Preface xiii
Acknowledgements xvii
List of Figures xix
List of Tables xxiii
Nomenclature xxv
Part I Fundamentals
1 Introduction
3(16)
1.1 Motivational Illustrations
3(1)
1.2 Previous Work
4(8)
1.2.1 Diagnosis Techniques
4(3)
1.2.2 Monitoring Techniques
7(5)
1.3 Book Outline
12(4)
1.3.1 Problem Overview and Illustrative Example
12(1)
1.3.2 Overview of Proposed Work
12(4)
References
16(3)
2 Prerequisite Fundamentals
19(43)
2.1 Introduction
19(1)
2.2 Bayesian Inference and Parameter Estimation
19(19)
2.2.1 Tutorial on Bayesian Inference
24(3)
2.2.2 Tutorial on Bayesian Inference with Time Dependency
27(5)
2.2.3 Bayesian Inference vs. Direct Inference
32(1)
2.2.4 Tutorial on Bayesian Parameter Estimation
33(5)
2.3 The EM Algorithm
38(6)
2.4 Techniques for Ambiguous Modes
44(7)
2.4.1 Tutorial on Θ Parameters in the Presence of Ambiguous Modes
46(1)
2.4.2 Tutorial on Probabilities Using Θ Parameters
47(1)
2.4.3 Dempster—Shafer Theory
48(3)
2.5 Kernel Density Estimation
51(5)
2.5.1 From Histograms to Kernel Density Estimates
52(2)
2.5.2 Bandwidth Selection
54(1)
2.5.3 Kernel Density Estimation Tutorial
55(1)
2.6 Bootstrapping
56(4)
2.6.1 Bootstrapping Tutorial
57(1)
2.6.2 Smoothed Bootstrapping Tutorial
57(3)
2.7 Notes and References
60(1)
References
61(1)
3 Bayesian Diagnosis
62(6)
3.1 Introduction
62(1)
3.2 Bayesian Approach for Control Loop Diagnosis
62(3)
3.2.1 Mode M
62(1)
3.2.2 Evidence E
63(1)
3.2.3 Historical Dataset D
64(1)
3.3 Likelihood Estimation
65(2)
3.4 Notes and References
67(1)
References
67(1)
4 Accounting for Autodependent Modes and Evidence
68(15)
4.1 Introduction
68(1)
4.2 Temporally Dependent Evidence
68(7)
4.2.1 Evidence Dependence
68(2)
4.2.2 Estimation of Evidence-transition Probability
70(4)
4.2.3 Issues in Estimating Dependence in Evidence
74(1)
4.3 Temporally Dependent Modes
75(6)
4.3.1 Mode Dependence
75(2)
4.3.2 Estimating Mode Transition Probabilities
77(4)
4.4 Dependent Modes and Evidence
81(1)
4.5 Notes and References
82(1)
References
82(1)
5 Accounting for Incomplete Discrete Evidence
83(13)
5.1 Introduction
83(1)
5.2 The Incomplete Evidence Problem
83(2)
5.3 Diagnosis with Incomplete Evidence
85(9)
5.3.1 Single Missing Pattern Problem
86(6)
5.3.2 Multiple Missing Pattern Problem
92(1)
5.3.3 Limitations of the Single and Multiple Missing Pattern Solutions
93(1)
5.4 Notes and References
94(1)
References
94(2)
6 Accounting for Ambiguous Modes: A Bayesian Approach
96(16)
6.1 Introduction
96(1)
6.2 Parametrization of Likelihood Given Ambiguous Modes
96(3)
6.2.1 Interpretation of Proportion Parameters
96(1)
6.2.2 Parametrizing Likelihoods
97(1)
6.2.3 Informed Estimates of Likelihoods
98(1)
6.3 Fagin—Halpern Combination
99(1)
6.4 Second-order Approximation
100(4)
6.4.1 Consistency of Θ Parameters
101(1)
6.4.2 Obtaining a Second-order Approximation
101(2)
6.4.3 The Second-order Bayesian Combination Rule
103(1)
6.5 Brief Comparison of Combination Methods
104(1)
6.6 Applying the Second-order Rule Dynamically
105(2)
6.6.1 Unambiguous Dynamic Solution
105(1)
6.6.2 The Second-order Dynamic Solution
106(1)
6.7 Making a Diagnosis
107(4)
6.7.1 Simple Diagnosis
107(1)
6.7.2 Ranged Diagnosis
107(1)
6.7.3 Expected Value Diagnosis
107(4)
6.8 Notes and References
111(1)
References
111(1)
7 Accounting for Ambiguous Modes: A Dempster—Shafer Approach
112(14)
7.1 Introduction
112(1)
7.2 Dempster—Shafer Theory
112(4)
7.2.1 Basic Belief Assignments
112(2)
7.2.2 Probability Boundaries
114(1)
7.2.3 Dempster's Rule of Combination
114(1)
7.2.4 Short-cut Combination for Unambiguous Priors
115(1)
7.3 Generalizing Dempster—Shafer Theory
116(8)
7.3.1 Motivation: Difficulties with BBAs
117(2)
7.3.2 Generalizing the BBA
119(3)
7.3.3 Generalizing Dempster's Rule
122(1)
7.3.4 Short-cut Combination for Unambiguous Priors
123(1)
7.4 Notes and References
124(1)
References
125(1)
8 Making Use of Continuous Evidence Through Kernel Density Estimation
126(18)
8.1 Introduction
126(1)
8.2 Performance: Continuous vs. Discrete Methods
127(5)
8.2.1 Average False Negative Diagnosis Criterion
127(2)
8.2.2 Performance of Discrete and Continuous Methods
129(3)
8.3 Kernel Density Estimation
132(5)
8.3.1 From Histograms to Kernel Density Estimates
132(2)
8.3.2 Defining a Kernel Density Estimate
134(1)
8.3.3 Bandwidth Selection Criterion
135(1)
8.3.4 Bandwidth Selection Techniques
136(1)
8.4 Dimension Reduction
137(2)
8.4.1 Independence Assumptions
138(1)
8.4.2 Principal and Independent Component Analysis
139(1)
8.5 Missing Values
139(3)
8.5.1 Kernel Density Regression
140(1)
8.5.2 Applying Kernel Density Regression for a Solution
141(1)
8.6 Dynamic Evidence
142(1)
8.7 Notes and References
143(1)
References
143(1)
9 Accounting for Sparse Data Within a Mode
144(28)
9.1 Introduction
144(1)
9.2 Analytical Estimation of the Monitor Output Distribution Function
145(5)
9.2.1 Control Performance Monitor
145(1)
9.2.2 Process Model Monitor
146(2)
9.2.3 Sensor Bias Monitor
148(2)
9.3 Bootstrap Approach to Estimating Monitor Output Distribution Function
150(14)
9.3.1 Valve Stiction Identification
150(3)
9.3.2 The Bootstrap Method
153(3)
9.3.3 Illustrative Example
156(4)
9.3.4 Applications
160(4)
9.4 Experimental Example
164(6)
9.4.1 Process Description
164(3)
9.4.2 Diagnostic Settings and Results
167(3)
9.5 Notes and References
170(1)
References
170(2)
10 Accounting for Sparse Modes Within the Data
172(31)
10.1 Introduction
172(1)
10.2 Approaches and Algorithms
172(9)
10.2.1 Approach for Component Diagnosis
173(3)
10.2.2 Approach for Bootstrapping New Modes
176(5)
10.3 Illustration
181(13)
10.3.1 Component-based Diagnosis
184(4)
10.3.2 Bootstrapping for Additional Modes
188(6)
10.4 Application
194(4)
10.4.1 Monitor Selection
195(1)
10.4.2 Component Diagnosis
195(3)
10.5 Notes and References
198(1)
References
199(4)
Part II Applications
11 Introduction to Testbed Systems
203(6)
11.1 Simulated System
203(2)
11.1.1 Monitor Design
203(2)
11.2 Bench-scale System
205(2)
11.3 Industrial Scale System
207(1)
References
207(2)
12 Bayesian Diagnosis with Discrete Data
209(12)
12.1 Introduction
209(1)
12.2 Algorithm
210(3)
12.3 Tutorial
213(3)
12.4 Simulated Case
216(1)
12.5 Bench-scale Case
217(2)
12.6 Industrial-scale Case
219(1)
12.7 Notes and References
220(1)
References
220(1)
13 Accounting for Autodependent Modes and Evidence
221(11)
13.1 Introduction
221(1)
13.2 Algorithms
222(6)
13.2.1 Evidence Transition Probability
222(4)
13.2.2 Mode Transition Probability
226(2)
13.3 Tutorial
228(3)
13.4 Notes and References
231(1)
References
231(1)
14 Accounting for Incomplete Discrete Evidence
232(15)
14.1 Introduction
232(1)
14.2 Algorithm
232(6)
14.2.1 Single Missing Pattern Problem
232(4)
14.2.2 Multiple Missing Pattern Problem
236(2)
14.3 Tutorial
238(3)
14.4 Simulated Case
241(1)
14.5 Bench-scale Case
242(2)
14.6 Industrial-scale Case
244(2)
14.7 Notes and References
246(1)
References
246(1)
15 Accounting for Ambiguous Modes in Historical Data: A Bayesian Approach
247(25)
15.1 Introduction
247(1)
15.2 Algorithm
248(6)
15.2.1 Formulating the Problem
248(1)
15.2.2 Second-order Taylor Series Approximation of p(E|M, Θ)
248(2)
15.2.3 Second-order Bayesian Combination
250(2)
15.2.4 Optional Step: Separating Monitors into Independent Groups
252(1)
15.2.5 Grouping Methodology
253(1)
15.3 Illustrative Example of Proposed Methodology
254(11)
15.3.1 Introduction
254(1)
15.3.2 Offline Step 1: Historical Data Collection
255(1)
15.3.3 Offline Step 2: Mutual Information Criterion (Optional)
255(1)
15.3.4 Offline Step 3: Calculate Reference Values
256(1)
15.3.5 Online Step 1: Calculate Support
257(1)
15.3.6 Online Step 2: Calculate Second-order Terms
258(2)
15.3.7 Online Step 3: Perform Combinations
260(2)
15.3.8 Online Step 4: Make a Diagnosis
262(3)
15.4 Simulated Case
265(3)
15.5 Bench-scale Case
268(1)
15.6 Industrial-scale Case
269(1)
15.7 Notes and References
270(1)
References
271(1)
16 Accounting for Ambiguous Modes in Historical Data: A Dempster—Shafer Approach
272(16)
16.1 Introduction
272(1)
16.2 Algorithm
272(4)
16.2.1 Parametrized Likelihoods
272(1)
16.2.2 Basic Belief Assignments
273(2)
16.2.3 The Generalized Dempster's Rule of Combination
275(1)
16.3 Example of Proposed Methodology
276(7)
16.3.1 Introduction
276(1)
16.3.2 Offline Step 1: Historical Data Collection
277(1)
16.3.3 Offline Step 2: Mutual Information Criterion (Optional)
277(1)
16.3.4 Offline Step 3: Calculate Reference Value
278(1)
16.3.5 Online Step 1: Calculate Support
279(1)
16.3.6 Online Step 2: Calculate the GBBA
280(3)
16.3.7 Online Step 3: Combine BBAs and Diagnose
283(1)
16.4 Simulated Case
283(1)
16.5 Bench-scale Case
284(2)
16.6 Industrial System
286(1)
16.7 Notes and References
287(1)
References
287(1)
17 Making use of Continuous Evidence through Kernel Density Estimation
288(25)
17.1 Introduction
288(1)
17.2 Algorithm
289(4)
17.2.1 Kernel Density Estimation
289(1)
17.2.2 Bandwidth Selection
289(1)
17.2.3 Adaptive Bandwidths
290(1)
17.2.4 Optional Step: Dimension Reduction by Multiplying Independent Likelihoods
291(1)
17.2.5 Optional Step: Creating Independence via Independent Component Analysis
291(1)
17.2.6 Optional Step: Replacing Missing Values
292(1)
17.3 Example of Proposed Methodology
293(9)
17.3.1 Offline Step 1: Historical Data Collection
295(1)
17.3.2 Offline Step 3: Mutual Information Criterion (Optional)
296(2)
17.3.3 Offline Step 4: Independent Component Analysis (Optional)
298(1)
17.3.4 Offline Step 5: Obtain Bandwidths
298(3)
17.3.5 Online Step 1: Calculate Likelihood of New Data
301(1)
17.3.6 Online Step 2: Calculate Posterior Probability
302(1)
17.3.7 Online Step 3: Make a Diagnosis
302(1)
17.4 Simulated Case
302(2)
17.5 Bench-scale Case
304(1)
17.6 Industrial-scale Case
304(3)
17.7 Notes and References
307(1)
References
307(1)
Appendix
308(5)
17.A Code for Kernel Density Regression
308(5)
17.A.1 Kernel Density Regression
308(2)
17.A.2 Three-dimensional Matrix Toolbox
310(3)
18 Dynamic Application of Continuous Evidence and Ambiguous Mode Solutions
313(16)
18.1 Introduction
313(1)
18.2 Algorithm for Autodependent Modes
313(3)
18.2.1 Transition Probability Matrix
314(1)
18.2.2 Review of Second-order Method
314(1)
18.2.3 Second-order Probability Transition Rule
315(1)
18.3 Algorithm for Dynamic Continuous Evidence and Autodependent Modes
316(4)
18.3.1 Algorithm for Dynamic Continuous Evidence
316(2)
18.3.2 Combining both Solutions
318(1)
18.3.3 Comments on Usefulness
319(1)
18.4 Example of Proposed Methodology
320(5)
18.4.1 Introduction
320(1)
18.4.2 Offline Step 1: Historical Data Collection
320(1)
18.4.3 Offline Step 2: Create Temporal Data
320(1)
18.4.4 Offline Step 3: Mutual Information Criterion (Optional, but Recommended)
321(1)
18.4.5 Offline Step 5: Calculate Reference Values
322(1)
18.4.6 Online Step 1: Obtain Prior Second-order Terms
322(1)
18.4.7 Online Step 2: Calculate Support
323(1)
18.4.8 Online Step 3: Calculate Second-order Terms
323(1)
18.4.9 Online Step 4: Combining Prior and Likelihood Terms
324(1)
18.5 Simulated Case
325(1)
18.6 Bench-scale Case
326(1)
18.7 Industrial-scale Case
326(1)
18.8 Notes and References
327(1)
References
327(2)
Index 329
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 Germanys 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 Huangs 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.
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