Process Control System Fault Diagnosis E-Book

Ruben Gonzalez

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Series in Dynamics and Control of Electromechanical Systems
• Sprache: Englisch

Seitenzahl: 428

Veröffentlichungsjahr: 2016

Beschreibung

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.

Leseprobe

Table of Contents

Title Page

Copyright

Preface

Background

Control Performance Diagnosis and Control System Fault Diagnosis

Book Objective, Organization and Readership

Acknowledgements

List of Figures

List of Tables

Nomenclature

Part One: Fundamentals

Chapter 1: Introduction

1.1 Motivational Illustrations

1.2 Previous Work

1.3 Book Outline

References

Chapter 2: Prerequisite Fundamentals

2.1 Introduction

2.2 Bayesian Inference and Parameter Estimation

2.3 The EM Algorithm

2.4 Techniques for Ambiguous Modes

2.5 Kernel Density Estimation

2.6 Bootstrapping

2.7 Notes and References

References

Chapter 3: Bayesian Diagnosis

3.1 Introduction

3.2 Bayesian Approach for Control Loop Diagnosis

3.3 Likelihood Estimation

3.4 Notes and References

References

Chapter 4: Accounting for Autodependent Modes and Evidence

4.1 Introduction

4.2 Temporally Dependent Evidence

4.3 Temporally Dependent Modes

4.4 Dependent Modes and Evidence

4.5 Notes and References

References

Chapter 5: Accounting for Incomplete Discrete Evidence

5.1 Introduction

5.2 The Incomplete Evidence Problem

5.3 Diagnosis with Incomplete Evidence

5.4 Notes and References

References

Chapter 6: Accounting for Ambiguous Modes: A Bayesian Approach

6.1 Introduction

6.2 Parametrization of Likelihood Given Ambiguous Modes

6.3 Fagin–Halpern Combination

6.4 Second-order Approximation

6.5 Brief Comparison of Combination Methods

6.6 Applying the Second-order Rule Dynamically

6.7 Making a Diagnosis

6.8 Notes and References

References

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

7.1 Introduction

7.2 Dempster–Shafer Theory

7.3 Generalizing Dempster–Shafer Theory

7.4 Notes and References

References

Chapter 8: Making use of Continuous Evidence Through Kernel Density Estimation

8.1 Introduction

8.2 Performance: Continuous vs. Discrete Methods

8.3 Kernel Density Estimation

8.4 Dimension Reduction

8.5 Missing Values

8.6 Dynamic Evidence

8.7 Notes and References

References

Chapter 9: Accounting for Sparse Data Within a Mode

9.1 Introduction

9.2 Analytical Estimation of the Monitor Output Distribution Function

9.3 Bootstrap Approach to Estimating Monitor Output Distribution Function

9.4 Experimental Example

9.5 Notes and References

References

Chapter 10: Accounting for Sparse Modes Within the Data

10.1 Introduction

10.2 Approaches and Algorithms

10.3 Illustration

10.4 Application

10.5 Notes and References

References

Part Two: Applications

Chapter 11: Introduction to Testbed Systems

11.1 Simulated System

11.2 Bench-scale System

11.3 Industrial Scale System

References

Chapter 12: Bayesian Diagnosis with Discrete Data

12.1 Introduction

12.2 Algorithm

12.3 Tutorial

12.4 Simulated Case

12.5 Bench-scale Case

12.6 Industrial-scale Case

12.7 Notes and References

References

Chapter 13: Accounting for Autodependent Modes and Evidence

13.1 Introduction

13.2 Algorithms

13.3 Tutorial

13.4 Notes and References

References

Chapter 14: Accounting for Incomplete Discrete Evidence

14.1 Introduction

14.2 Algorithm

14.3 Tutorial

14.4 Simulated Case

14.5 Bench-scale Case

14.6 Industrial-scale Case

14.7 Notes and References

References

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

15.1 Introduction

15.2 Algorithm

15.3 Illustrative Example of Proposed Methodology

15.4 Simulated Case

15.5 Bench-scale Case

15.6 Industrial-scale Case

15.7 Notes and References

References

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

16.1 Introduction

16.2 Algorithm

16.3 Example of Proposed Methodology

16.4 Simulated Case

16.5 Bench-scale Case

16.6 Industrial System

16.7 Notes and References

References

Chapter 17: Making use of Continuous Evidence through Kernel Density Estimation

17.1 Introduction

17.2 Algorithm

17.3 Example of Proposed Methodology

17.4 Simulated Case

17.5 Bench-scale Case

17.6 Industrial-scale Case

17.7 Notes and References

References

Appendix

17.A Code for Kernel Density Regression

Chapter 18: Dynamic Application of Continuous Evidence and Ambiguous Mode Solutions

18.1 Introduction

18.2 Algorithm for Autodependent Modes

18.3 Algorithm for Dynamic Continuous Evidence and Autodependent Modes

18.4 Example of Proposed Methodology

18.5 Simulated Case

18.6 Bench-scale Case

18.7 Industrial-scale Case

18.8 Notes and References

References

Index

End User License Agreement

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Guide

Table of Contents

Preface

Begin Reading

List of Illustrations

Chapter 1: Introduction

Figure 1.1 Typical control loop

Figure 1.2 Overview of proposed solutions

Chapter 2: Prerequisite Fundamentals

Figure 2.1 Bayesian parameter result

Figure 2.2 Comparison of inference methods

Figure 2.3 Illustrative process

Figure 2.4 Evidence space with only prior samples

Figure 2.5 Evidence space with prior and historical data

Figure 2.6 Mode dependence (hidden Markov model)

Figure 2.7 Evidence dependence

Figure 2.8 Evidence and mode dependence

Figure 2.9 Histogram of distribution

Figure 2.10 Centered histogram of distribution

Figure 2.11 Gaussian kernel density estimate

Figure 2.12 Data for kernel density estimation

Figure 2.13 Data points with kernels

Figure 2.14 Kernel density estimate from data

Figure 2.15 Distribution of estimate

Figure 2.16 Sampling distribution for bootstrapping

Figure 2.17 Smoothed sampling distribution for bootstrapping

Figure 2.18 Distribution of estimate

Chapter 3: Bayesian Diagnosis

Figure 3.1 Typical control system structure

Chapter 4: Accounting for Autodependent Modes and Evidence

Figure 4.1 Bayesian model with independent evidence data samples

Figure 4.2 Monitor outputs of the illustrative problem

Figure 4.3 Bayesian model considering dependent evidence

Figure 4.4 Illustration of evidence transition samples

Figure 4.5 Bayesian model considering dependent mode

Figure 4.6 Historical composite mode dataset for mode transition probability estimation

Figure 4.7 Dynamic Bayesian model that considers both mode and evidence dependence

Chapter 6: Accounting for Ambiguous Modes: A Bayesian Approach

Figure 6.1 Diagnosis result for support in Table 6.1

Chapter 8: Making use of Continuous Evidence Through Kernel Density Estimation

Figure 8.1 Grouping approaches for kernel density method

Figure 8.2 Discrete method performance

Figure 8.3 Two-dimensional system with dependent evidence

Figure 8.4 Two-dimensional discretization schemes

Figure 8.5 Histogram of distribution

Figure 8.6 Centered histogram of distribution

Figure 8.7 Gaussian kernel density estimate

Figure 8.8 Kernels summing to a kernel density estimate

Chapter 9: Accounting for Sparse Data Within a Mode

Figure 9.1 Operation diagram of sticky valve

Figure 9.2 Stiction model flow diagram

Figure 9.3 Bounded stiction parameter search space

Figure 9.4 Bootstrap method flow diagram

Figure 9.5 Histogram of simulated

Figure 9.6 Histogram of simulated

Figure 9.7 Auto-correlation coefficient of residuals

Figure 9.8 Histogram of residual distribution

Figure 9.9 Histogram of

Figure 9.10 Histogram of

Figure 9.11 Histogram of bootstrapped for Chemical 55

Figure 9.18 Histogram of bootstrapped for Paper 9

Figure 9.19 Schematic diagram of the distillation column

Figure 9.20 Distillation column diagnosis with all historical data

Figure 9.23 Distillation column diagnosis with only one sample from mode

Figure 9.24 Distillation column diagnosis with only one sample from mode

Chapter 10: Accounting for Sparse Modes Within the Data

Figure 10.1 Overall algorithm

Figure 10.2 Hybrid tank system

Figure 10.3 Hybrid tank control system

Figure 10.4 Diagnosis results for component-space approach

Figure 10.5 Diagnosis results for mode-space approach

Chapter 11: Introduction to Testbed Systems

Figure 11.1 Tennessee Eastman process

Figure 11.2 Hybrid tank system

Figure 11.3 Solids handling system

Chapter 12: Bayesian Diagnosis with Discrete Data

Figure 12.1 Bayesian diagnosis process

Figure 12.2 Illustrative process

Figure 12.3 Evidence space with only prior samples

Figure 12.4 Evidence space with prior samples and historical samples

Figure 12.5 Evidence space with historical data

Figure 12.6 Posterior probability assigned to each mode for TE simulation problem

Figure 12.7 Posterior probability assigned to each mode

Figure 12.8 Posterior probability assigned to each mode for industrial process

Chapter 13: Accounting for Autodependent Modes and Evidence

Figure 13.1 Dynamic Bayesian model that considers both mode and evidence dependence

Figure 13.2 Illustration of evidence transition samples

Figure 13.3 Historical composite mode dataset for mode transition probability estimation

Chapter 14: Accounting for Incomplete Discrete Evidence

Figure 14.1 Estimation of expected complete evidence numbers out of the incomplete samples

Figure 14.2 Bayesian diagnosis process with incomplete evidences

Figure 14.3 Evidence space with all samples

Figure 14.4 Comparison of complete evidence numbers

Figure 14.5 Diagnostic results with different dataset

Figure 14.6 Diagnostic rate with different datasets

Figure 14.7 Posterior probability assigned to each mode

Figure 14.8 Diagnostic rate with different dataset

Figure 14.9 Posterior probability assigned to each mode for industrial process

Figure 14.10 Diagnostic rate with different dataset

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

Figure 15.1 Typical control loop

Figure 15.2 An illustration of diagnosis results with uncertainty region

Figure 15.3 Probability bounds at 30% ambiguity

Figure 15.4 Probability bounds at 70% ambiguity

Figure 15.5 Tennessee Eastman problem mode-diagnosis error

Figure 15.6 Tennessee Eastman component-diagnosis error

Figure 15.7 Hybrid tank system mode-diagnosis error

Figure 15.8 Hybrid tank system component-diagnosis error

Figure 15.9 Industrial system mode-diagnosis error

Figure 15.10 Industrial system component-diagnosis error

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

Figure 16.1 Typical control loop

Figure 16.2 Tennessee Eastman problem mode-diagnosis error

Figure 16.3 Tennessee Eastman problem component-diagnosis error

Figure 16.4 Hybrid tank system mode-diagnosis error

Figure 16.5 Hybrid tank system component-diagnosis error

Figure 16.6 Industrial system mode-diagnosis error

Figure 16.7 Industrial system component-diagnosis error

Chapter 17: Making use of Continuous Evidence through Kernel Density Estimation

Figure 17.1 Typical control loop

Figure 17.2 Tennessee Eastman problem: discrete vs. kernel density estimation

Figure 17.3 Grouping approaches for discrete method

Figure 17.4 Grouping approaches for kernel density method

Figure 17.5 Hybrid tank problem: discrete vs. kernel density estimation

Figure 17.6 Grouping approaches for discrete method

Figure 17.7 Grouping approaches for kernel density method

Figure 17.8 Solids-handling problem: discrete vs. kernel density estimation

Figure 17.9 Grouping approaches for discrete method

Figure 17.10 Grouping approaches for kernel density method

Figure 17.11 Function

Figure 17.12 Function

Figure 17.13 Converting matrices depth-wise

Chapter 18: Dynamic Application of Continuous Evidence and Ambiguous Mode Solutions

Figure 18.1 Mode autodependence

Figure 18.2 Evidence autodependence

Figure 18.3 Evidence and mode autodependence

Figure 18.4 Typical control loop

Figure 18.5 Comparison of dynamic methods

Figure 18.6 Comparison of dynamic methods

Figure 18.7 Comparison of dynamic methods

List of Tables

Chapter 1: Introduction

Table 1.1 List of monitors for each system

Chapter 2: Prerequisite Fundamentals

Table 2.1 Counts of historical evidence

Table 2.2 Counts of combined historical and prior evidence

Table 2.3 Likelihoods of evidence

Table 2.4 Likelihoods of dynamic evidence

Table 2.5 Counts of combined historical and prior evidence

Table 2.6 List of conjugate priors (Fink 1997)

Table 2.7 Biased sensor mode

Table 2.8 Modes and their corresponding labels

Table 2.9 Ambiguous modes and their corresponding labels

Table 2.10 Historical data for all modes

Chapter 4: Accounting for Autodependent Modes and Evidence

Table 4.1 Likelihood estimation of the illustrative problem

Chapter 6: Accounting for Ambiguous Modes: A Bayesian Approach

Table 6.1 Support from example scenario

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

Table 7.1 Frequency counts from example

Chapter 8: Making use of Continuous Evidence Through Kernel Density Estimation

Table 8.1 Comparison between discrete and kernel methods

Table 8.2 The curse of dimensionality

Chapter 9: Accounting for Sparse Data Within a Mode

Table 9.1 Comparison of sample standard deviations

Table 9.2 Confidence intervals of the identified stiction parameters

Table 9.3 Dimensions of the distillation column

Table 9.4 Operating modes for the column

Table 9.5 Commissioned monitors for the column

Table 9.6 Summary of Bayesian diagnostic parameters

Chapter 10: Accounting for Sparse Modes Within the Data

Table 10.1 Included monitors for component space approach

Table 10.2 Misdiagnosis rates for modes

Chapter 11: Introduction to Testbed Systems

Table 11.1 List of simulated modes

Chapter 12: Bayesian Diagnosis with Discrete Data

Table 12.1 Numbers of historical evidences

Table 12.2 Updated likelihood with historical data

Table 12.3 Summary of Bayesian diagnostic parameters for TE simulation problem

Table 12.4 Correct diagnosis rate

Table 12.5 Summary of Bayesian diagnostic parameters for pilot experimental problem

Table 12.6 Summary of Bayesian diagnostic parameters for industrial problem

Table 12.7 Correct diagnosis rate

Chapter 14: Accounting for Incomplete Discrete Evidence

Table 14.1 Number of historical evidence samples

Table 14.2 Numbers of estimated sample numbers

Table 14.3 Summary of historical and prior samples

Table 14.4 Estimated likelihood with different strategy

Table 14.5 Summary of historical and prior samples

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

Table 15.1 Probability of evidence given Mode (1)

Table 15.2 Prior probabilities

Table 15.3 Frequency of modes containing

Table 15.4 Support of modes containing

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

Table 16.1 Probability of evidence given Mode (1)

Table 16.2 Frequency of modes containing

Table 16.3 Support of modes containing

Process Control System Fault Diagnosis

A Bayesian Approach

Ruben Gonzalez

Fei Qi

Biao Huang

This edition first published 2016

© 2016, John Wiley & Sons, Ltd

First edition published in 2016

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Library of Congress Cataloging-in-Publication Data

Names: Gonzalez, Ruben, 1985- author. | Qi, Fei, 1983- author | Huang, Biao, 1962- author.

Title: Process control system fault diagnosis : a Bayesian approach / Ruben Gonzalez, Fei Qi, Biao Huang.

Description: First edition. | Chichester, West Sussex, United Kingdom : John Wiley & Sons, 2016. | Includes bibliographical references and index.

Identifiers: LCCN 2016010340| ISBN 9781118770610 (cloth) | ISBN 9781118770597 (epub)

Subjects: LCSH: Chemical process control–Statistical methods. | Bayesian statistical decision theory. | Fault location (Engineering)

Classification: LCC TP155.75 .G67 2016 | DDC 660/.2815–dc23 LC record available at https://lccn.loc.gov/2016010340

A catalogue record for this book is available from the British Library.

Preface

Background

Control performance monitoring (CPM) has been and continues to be one of the most active research areas in the process control community. A number of CPM technologies have been developed since the late 1980s. It is estimated that several hundred papers have been published in this or related areas. CPM techniques have also been widely applied in industry. A number of commercial control performance assessment software packages are available off the shelf.

CPM techniques include controller monitoring, sensor monitoring, actuator monitoring, oscillation detection, model validation, nonlinearity detection and so on. All of these techniques have been designed to target a specific problem source in a control system. The common practice is that one monitoring technique (or monitor) is developed for a specific problem source. However, a specific problem source can show its signatures in more than one monitor, thereby inducing alarm flooding. There is a need to consider all monitors simultaneously in a systematic manner.

There are a number of challenging issues:

There are interactions between monitors. A monitor cannot be designed to just monitor one problem source in isolation from other problem sources. While each monitor may work well when only the targeted problem occurs, relying on a single monitor can be misleading when other problems also occur.

The causal relations between a problem source and a monitor are not obvious for industrial-scale problems. First-principles knowledge, including the process flowchart, cannot always provide an accurate causal relation.

Disturbances and uncertainties exist everywhere in industrial settings.

Most monitors are either model-based or data-driven; it is uncommon for monitor results to be combined with prior process knowledge.

Clearly, there is a need to develop a systematic framework, including theory and practical guidelines, to tackle the these monitoring problems.

Control Performance Diagnosis and Control System Fault Diagnosis

Control systems play a critical role in modern process industries. Malfunctioning components in control systems, including sensors, actuators and other components, are not uncommon in industrial environments. Their effects introduce excess variation throughout the process, thereby reducing machine operability, increasing costs and emissions, and disrupting final product quality control. It has been reported in the literature that as many as 60% of industrial controllers may have some kind of problem.

The motivation behind this book arises from the important task of isolating and diagnosing control performance abnormalities in complex industrial processes. A typical modern process operation consists of hundreds or even thousands of control loops, which is too many for plant personnel to monitor. Even if poor performance is detected in some control loops, because a problem in a single component can invoke a wide range of control problems, locating the underlying problem source is not a trivial task. Without an advanced information synthesis and decision-support system, it is difficult to handle the flood of process alarms to determine the source of the underlying problem. Human beings' inability to synthesize high-dimensional process data is the main reason behind these problems. The purpose of control performance diagnosis is to provide an automated procedure that aids plant personnel to determine whether specified performance targets are being met, evaluate the performance of control loops, and suggest possible problem sources and a troubleshooting sequence.

To understand the development of control performance diagnosis, it is necessary to review the historical evolution of CPM. From the 1990s and 2000s, there was a significant development in CPM and, from the 2000s to the 2010s, control performance diagnosis. CPM focuses on determining how well the controller is performing with respect to a given benchmark, while CPD focuses on diagnosing the causes of poor performance. CPM and CPD are of significant interest for process industries that have growing safety, environmental and efficiency requirements. The classical method of CPM was first proposed in 1989 by Harris, who used the minimum variance control (MVC) benchmark as a general indicator of control loop performance. The MVC benchmark can be obtained using the filtering and correlation (FCOR) algorithm, as proposed by Huang et al. in 1997; this technique can be easily generalized to obtain benchmarks for multivariate systems. Minimum variance control is generally aggressive, with potential for poor robustness, and is not a suitable benchmark for CPM of model predictive control, as itdoes not take input action into account. Thus the linear quadratic Gaussian (LQG) benchmark was proposed in the PhD dissertation of Huang in 1997. In order to extend beyond simple benchmark comparisons, a new family of methods was developed to monitor specific instruments within control loops for diagnosing poor performance (by Horch, Huang, Jelali, Kano, Qin, Scali, Shah, Thornhill, etc). As a result, various CPD approaches have appeared since 2000.

To address the CPD problem systematically, Bayesian diagnosis methods were introduced by Huang in 2008. Due to their ability to incorporate both prior knowledge and data, Bayesian methods are a powerful tool for CPD. They have been proven to be useful for a variety of monitoring and predictive maintenance purposes. Successful applications of the Bayesian approach have also been reported in medical science, image processing, target recognition, pattern matching, information retrieval, reliability analysis and engineering diagnosis. It provides a flexible structure for modelling and evaluating uncertainties. In the presence of noise and disturbances, Bayesian inference provides a good way to solve the monitoring and diagnosis problem, providing a quantifiable measure of uncertainty for decision making. It is one of the most widely applied techniques in statistical inference, as well being used to diagnose engineering problems.

The Bayesian approach was applied to fault detection and diagnosis (FDI) in the mechanical components of transport vehicles by Pernestal in 2007, and Huang applied it to CPD in 2008. CPD techniques bear some resemblance to FDI. Faults usually refer to failure events, while control performance abnormality does not necessarily imply a failure. Thus, CPD is performance-related, often focusing on detecting control related problems that affect control system performance, including economic and environmental performance, while FDI focuses on the failure of components. Under the Bayesian framework, both can be considered as an abnormal event or fault diagnosis for control systems. Thus control system fault diagnosis is a more appropriate term that covers both.

Book Objective, Organization and Readership

The main objectives of this book are to establish a Bayesian framework for control system fault diagnosis, to synthesize observations of different monitors with prior knowledge, and to pinpoint possible abnormal sources on the basis of Bayesian theory. To achieve these objectives, this book provides comprehensive coverage of various Bayesian methods for control system fault diagnosis. The book starts with a tutorial introduction of Bayesian theory and its applications for general diagnosis problems, and an introduction to the existing control loop performance-monitoring techniques. Based upon these fundamentals, the book turns to a general data-driven Bayesian framework for control system fault diagnosis. This is followed by presentation of various practicalproblems and solutions. To extend beyond traditional CPM with discrete outputs, this book also explores how control loop performance monitors with continuous outputs can be directly incorporated into the Bayesian diagnosis framework, thus improving diagnosis performance. Furthermore, to deal with historical data taken from ambiguous operating conditions, two approaches are explored:

Dempster–Shafer theory, which is often used in other applications when ambiguity is present

a parametrized Bayesian approach.

Finally, to demonstrate the practical relevance of the methodology, the proposed solutions are demonstrated through a number of practical engineering examples.

This book attempts to consolidate results developed or published by the authors over the last few years and to compile them together with their fundamentals in a systematic way. In this respect, the book is likely to be of use for graduate students and researchers as a monograph, and as a place to look for basic as well as 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 practising engineers to look for solutions to their daily monitoring and diagnosis problems. In addition, the book has comprehensive coverage of Bayesian theory and its application in fault diagnosis, and thus it will be of interest to mathematically oriented readers who are interested in applying theory to practice. On the other hand, due to the combination of theory and applications, it will also be beneficial to applied researchers and practitioners who are interested in giving themselves a sound theoretical foundation. The readers of this book will include graduate students and researchers in chemical engineering, mechanical engineering and electrical engineering, specializing in process control, control systems and process systems engineering. It is expected that readers will be acquainted with some fundamental knowledge of undergraduate probability and statistics.

Acknowledgements

The material in this book is the outcome of several years of research efforts by the authors and many other graduate students and post-doctoral fellows at the University of Alberta. In particular, we would like to acknowledge those who have contributed directly to the general area of Bayesian statistics that has now become one of the most active research subjects in our group: Xingguang Shao, Shima Khatibisepehr, Marziyeh Keshavarz, Kangkang Zhang, Swanand Khare, Aditya Tulsyan, Nima Sammaknejad and Ming Ma. We would also like to thank our colleagues and collaborators in the computer process control group at the University of Alberta, who have provided a stimulating environment for process control research. The broad range of talent within the Department of Chemical and Materials Engineering at the University of Alberta has allowed cross-fertilization and nurturing of many different ideas that have made this book possible. We are indebted to industrial practitioners Aris Espejo, Ramesh Kadali, Eric Lau and Dan Brown, who have inspired us with practical relevance in broad areas of process control research. We would also like to thank our laboratory support from Artin Afacan, computing support from Jack Gibeau, and other supporting staff in the Department of Chemical and Materials Engineering at the University of Alberta. The support of the Natural Sciences and Engineering Research Council of Canada and Alberta Innovates Technology Futures for this and related research work is gratefully acknowledged. Last, but not least, we would like to acknowledge Kangkang Zhang, Yuri Shardt and Sun Zhou for their detailed review of and comments on the book.

Some of the figures presented in this book are taken from our previous work that has been published in journals. We would like to acknowledge the journal publishers who have allowed us to re-use these figures:

Figures 3.1 and 14.1 are adapted with permission from AIChE Journal, Vol. 56, Qi F, Huang B and Tamayo EC, ‘A Bayesian approach for control loop diagnosis with missing data’, pp. 179–195. ©2010 John Wiley and Sons.

Figures 4.4 and 13.2 are adapted with permission from Automatica, Vol. 47, Qi F and Huang B, ‘Bayesian methods for control loop diagnosis in the presence of temporal dependent evidences’, pp. 1349–1356. ©2011 Elsevier.

Figures 4.1, 4.3, 4.5–4.7, 13.1 and 13.3 are adapted with permission from Industrial & Engineering Chemistry Research, Vol. 49, Qi F and Huang B, ‘Dynamic Bayesian approach for control loop diagnosis with underlying mode dependency’, pp. 8613–8623. © 2010 American Chemical Society.

Figures 8.1–8.4 are adapted with permission from Journal of Process Control,Vol. 24, Gonzalez R and Huang B, ‘Control loop diagnosis using continuous evidence through kernel density estimation’, pp. 640–651. ©2014 Elsevier.

List of Figures

1.1 Typical control loop

1.2 Overview of proposed solutions

2.1 Bayesian parameter result

2.2 Comparison of inference methods

2.3 Illustrative process

2.4 Evidence space with only prior samples

2.5 Evidence space with prior and historical data

2.6 Mode dependence (hidden Markov model)

2.7 Evidence dependence

2.8 Evidence and mode dependence

2.9 Histogram of distribution

2.10 Centered histogram of distribution

2.11 Gaussian kernel density estimate

2.12 Data for kernel density estimation

2.13 Data points with kernels

2.14 Kernel density estimate from data

2.15 Distribution of estimate

2.16 Sampling distribution for bootstrapping

2.17 Smoothed sampling distribution for bootstrapping

2.18 Distribution of estimate

3.1 Typical control system structure

4.1 Bayesian model with independent evidence data samples

4.2 Monitor outputs of the illustrative problem

4.3 Bayesian model considering dependent evidence

4.4 Illustration of evidence transition samples

4.5 Bayesian model considering dependent mode

4.6 Historical composite mode dataset for mode transition probability estimation

4.7 Dynamic Bayesian model that considers both mode and evidence dependence

6.1 Diagnosis result for support in Table 6.1

8.1 Grouping approaches for kernel density method

8.2 Discrete method performance

8.3 Two-dimensional system with dependent evidence

8.4 Two-dimensional discretization schemes

8.5 Histogram of distribution

8.6 Centered histogram of distribution

8.7 Gaussian kernel density estimate

8.8 Kernels summing to a kernel density estimate

9.1 Operation diagram of sticky valve

9.2 Stiction model flow diagram

9.3 Bounded stiction parameter search space

9.4 Bootstrap method flow diagram

9.5 Histogram of simulated

9.6 Histogram of simulated

9.7 Auto-correlation coefficient of residuals

9.8 Histogram of residual distribution

9.9 Histogram of

9.10 Histogram of

9.11 Histogram of bootstrapped for Chemical 55

9.12 Histogram of bootstrapped

for Chemical 55

9.13 Histogram of bootstrapped

for Chemical 60

9.14 Histogram of bootstrapped

for Chemical 60

9.15 Histogram of bootstrapped

for Paper 1

9.16 Histogram of bootstrapped

for Paper 1

9.17 Histogram of bootstrapped

for Paper 9

9.18 Histogram of bootstrapped for Paper 9

9.19 Schematic diagram of the distillation column

9.20 Distillation column diagnosis with all historical data

9.21 Distillation column diagnosis with only one sample from mode

9.22 Distillation column diagnosis with only one sample from mode

9.23 Distillation column diagnosis with only one sample from mode

9.24 Distillation column diagnosis with only one sample from mode

10.1 Overall algorithm

10.2 Hybrid tank system

10.3 Hybrid tank control system

10.4 Diagnosis results for component-space approach

10.5 Diagnosis results for mode-space approach

11.1 Tennessee Eastman process

11.2 Hybrid tank system

11.3 Solids handling system

12.1 Bayesian diagnosis process

12.2 Illustrative process

12.3 Evidence space with only prior samples

12.4 Evidence space with prior samples and historical samples

12.5 Evidence space with historical data

12.6 Posterior probability assigned to each mode for TE simulation problem

12.7 Posterior probability assigned to each mode

12.8 Posterior probability assigned to each mode for industrial process

13.1 Dynamic Bayesian model that considers both mode and evidence dependence

13.2 Illustration of evidence transition samples

13.3 Historical composite mode dataset for mode transition probability estimation

14.1 Estimation of expected complete evidence numbers out of the incomplete samples

14.2 Bayesian diagnosis process with incomplete evidences

14.3 Evidence space with all samples

14.4 Comparison of complete evidence numbers

14.5 Diagnostic results with different dataset

14.6 Diagnostic rate with different datasets

14.7 Posterior probability assigned to each mode

14.8 Diagnostic rate with different dataset

14.9 Posterior probability assigned to each mode for industrial process

14.10 Diagnostic rate with different dataset

15.1 Typical control loop

15.2 An illustration of diagnosis results with uncertainty region

15.3 Probability bounds at 30% ambiguity

15.4 Probability bounds at 70% ambiguity

15.5 Tennessee Eastman problem mode-diagnosis error

15.6 Tennessee Eastman component-diagnosis error

15.7 Hybrid tank system mode-diagnosis error

15.8 Hybrid tank system component-diagnosis error

15.9 Industrial system mode-diagnosis error

15.10 Industrial system component-diagnosis error

16.1 Typical control loop

16.2 Tennessee Eastman problem mode-diagnosis error

16.3 Tennessee Eastman problem component-diagnosis error

16.4 Hybrid tank system mode-diagnosis error

16.5 Hybrid tank system component-diagnosis error

16.6 Industrial system mode-diagnosis error

16.7 Industrial system component-diagnosis error

17.1 Typical control loop

17.2 Tennessee Eastman problem: discrete vs. kernel density estimation

17.3 Grouping approaches for discrete method

17.4 Grouping approaches for kernel density method

17.5 Hybrid tank problem: discrete vs. kernel density estimation

17.6 Grouping approaches for discrete method

17.7 Grouping approaches for kernel density method

17.8 Solids-handling problem: discrete vs. kernel density estimation

17.9 Grouping approaches for discrete method

17.10 Grouping approaches for kernel density method

17.11 Function

17.12 Function

17.13 Converting matrices depth-wise

18.1 Mode autodependence

18.2 Evidence autodependence

18.3 Evidence and mode autodependence

18.4 Typical control loop

18.5 Comparison of dynamic methods

18.6 Comparison of dynamic methods

18.7 Comparison of dynamic methods

List of Tables

1.1 List of monitors for each system

2.1 Counts of historical evidence

2.2 Counts of combined historical and prior evidence

2.3 Likelihoods of evidence

2.4 Likelihoods of dynamic evidence

2.5 Counts of combined historical and prior evidence

2.6 List of conjugate priors (Fink 1997)

2.7 Biased sensor mode

2.8 Modes and their corresponding labels

2.9 Ambiguous modes and their corresponding labels

2.10 Historical data for all modes

4.1 Likelihood estimation of the illustrative problem

6.1 Support from example scenario

7.1 Frequency counts from example

8.1 Comparison between discrete and kernel methods

8.2 The curse of dimensionality

9.1 Comparison of sample standard deviations

9.2 Confidence intervals of the identified stiction parameters

9.3 Dimensions of the distillation column

9.4 Operating modes for the column

9.5 Commissioned monitors for the column

9.6 Summary of Bayesian diagnostic parameters

10.1 Included monitors for component space approach

10.2 Misdiagnosis rates for modes

10.3 Misdiagnosis rates for component faults

11.1 List of simulated modes

12.1 Numbers of historical evidences

12.2 Updated likelihood with historical data

12.3 Summary of Bayesian diagnostic parameters for TE simulation problem

12.4 Correct diagnosis rate

12.5 Summary of Bayesian diagnostic parameters for pilot experimental problem

12.6 Summary of Bayesian diagnostic parameters for industrial problem

12.7 Correct diagnosis rate

14.1 Number of historical evidence samples

14.2 Numbers of estimated sample numbers

14.3 Summary of historical and prior samples

14.4 Estimated likelihood with different strategy

14.5 Summary of historical and prior samples

15.1 Probability of evidence given Mode (1)

15.2 Prior probabilities

15.3 Frequency of modes containing

15.4 Support of modes containing

16.1 Probability of evidence given Mode (1)

16.2 Frequency of modes containing

16.3 Support of modes containing

Nomenclature

Symbol

Description

Frequency parameter for the Dirichlet distribution

Frequency parameters pertaining to the ambiguous mode

Population mean

Population covariance

Population standard deviation

Complete set of probability/proportion parameters

The set of elements in

pertaining to the ambiguous mode

Informed estimate of

Complete set of probability/proportion parameters (matrix form)

Inclusive estimate of

(matrix form)

Exclusive estimate of

(matrix form)

A probability/proportion parameter

Proportion of data in ambiguous mode

belonging to mode

Lower-bound probability of mode

State of the component of interest (random variable)

State of the component of interest (observation)

The event where mode

was diagnosed

The event where mode

was diagnosed and

was true

The event where a mode other than

was diagnosed and

was true

Historical record of evidence

th element of historical evidence data record

Evidence (random variable)

Evidence (observation)

False negative diagnosis rate

Generalized BBA

th column of

(MATLAB notation)

th row of

(MATLAB notation)

Bandwidth matrix (Kernel density estimation)

Hessian matrix

i.i.d.

Independent and identically distributed

Jacobian matrix

Support for conflict (Dempster–Shafer theory)

Kernel function (kernel density estimation)

Operational mode (random variable)

Potentially ambiguous operational mode (random variable)

Operational mode (observation)

Part One

Fundamentals

Chapter 1Introduction

1.1 Motivational Illustrations

Consider the following scenarios:

Scenario A

You are a plant operator, and a gas analyser reading triggers an alarm for a low level of a vital reaction component, but from experience you know that this gas analyser is prone to error. The difficulty is, however, that if the vital reaction component is truly scarce, its scarcity could cause plugging and corrosion downstream that could cost over $120 million in plant downtime and repairs, but if the reagent is not low, shutting down the plant would result in $30 million in downtime. Now, imagine that you have a diagnosis system that has recorded several events like this in the past, using information from both upstream and downstream, is able to generate a list of possible causes of this alarm reading, and displays the probability of each scenario. The diagnosis system indicates that the most possible cause is a scenario that happened three years ago, when the vital reagent concentration truly dropped, and by quickly taking action to bypass the downstream section of the plant a $120-million incident was successfully avoided. Finally, imagine that you are the manager of this plant and discover that after implementing this diagnosis system, the incidents of unscheduled downtime are reduced by 60% and that incidents of false alarms are reduced by 80%.

Scenario B

You are the head of a maintenance team of another section of the plant with over 40 controllers and 30 actuators. Oscillation has been detected in this plant, where any of these controllers or actuators could be the cause. Because these oscillations can push the system into risky operating regions, caution must be exercised to keep the plant in a safer region, but at the cost of poorer product quality. Now, imagine you have a diagnosis tool that has data recorded from previous incidents, their troubleshooting solutions, and the probabilities of each incident. With this tool, we see that the most probable cause (at 45%) was fixed by replacing the stem packing on Valve 23, and that the second most probable cause (at 22%) was a tank level controller that in the past was sometimes overtuned by poor application of tuning software. By looking at records, you find out that a young engineer recently used tuning software to re-tune the level controller. Because of this information, and because changing the valve packing costs more, you re-tune the controller during scheduled maintenance, and at startup find that the oscillations are gone and you can now safely move the system to a point that produces better product quality. Now that the problem has been solved, you update the diagnosis tool with the historical data to improve the tool's future diagnostic performance. Now imagine, that as the head engineer of this plant, you find out that 30% of the most experienced people on your maintenance team are retiring this year, but because the diagnostic system has documented a large amount of their experience, new operators are better equipped to figure out where the problems in the system truly are.

Overview

These stories paint a picture of why there has been so much research interest in fault and control loop diagnosis systems in the process control community. The strong demand for better safety practices, decreased downtime, and fewer costly incidents (coupled with the increasing availability of computational power) all fuel this active area of research. Traditionally, a major area of interest has been in detection algorithms (or monitors as they will be called in this book) that focus on the behaviour of the system component. The end goal of implementing a monitor is to create an alarm that would sound if the target behaviour is observed. As more and more alarms are developed, it becomes increasingly probable that a single problem source will set off a large number of alarms, resulting in an alarm flood. Such scenarios in industry have caused many managers to develop alarm management protocols within their organizations. Scenarios such as those presented in scenarios A and B can be realized and in some instances have already been realized by research emphasizing the best use of information obtained from monitors and historical troubleshooting results.

1.2 Previous Work

1.2.1 Diagnosis Techniques

The principal objective in this book is to diagnose the operational mode of the process, where the mode consists of the operational state of all components within the process. For example, if a system comprises a controller, a sensor and a valve, themode would contain information about the controller (e.g. well tuned or poorly tuned), the sensor (e.g. biased or unbiased) and the valve (e.g. normal or sticky). As such, the main problem presented in this book falls within the scope of fault detection and diagnosis.

Fault detection and diagnosis has a vast (and often times overwhelming) amount of literature devoted to it for two important reasons:

The problem of fault detection and diagnosis is a legitimately difficult problem due to the sheer size and complexity of most practical systems.

There is great demand for fault detection and diagnosis as it is estimated that poor fault management has cost the United States alone more than $20 billion annually as of 2003 (Nimmo 2003).

In a three-part publication, Venkatasubramanian et al. (2003b) review the major contributions to this area and classify them under the following broad families: quantitative model-driven approaches (Venkatasubramanian et al. 2003b), qualitative model-driven approaches (Venkatasubramanian et al. 2003a), and process data-driven approaches (Venkatasubramanian et al. 2003c). Each type of approach has been shown to have certain challenges. Quantitative model-driven approaches require very accurate models that cover a wide array of operating conditions; such models can be very difficult to obtain. Qualitative model-driven approaches require attention to detail when developing heuristics, or else one runs the risk of a spurious result. Process data-driven approaches have been shown to be quite powerful in terms of detection, but most techniques tend to yield results that make fault isolation difficult to perform. In this book, particular interest is taken in the quantitative model-driven and the process data-driven approaches.

Quantitative Model-driven Approaches

Quantitative model-driven approaches focus on constructing the models of a process and using these models to diagnose different problems within a process (Lerner 2002) (Romessis and Mathioudakis 2006). These techniques bear some resemblance to some of the monitoring techniques described in Section 1.2.2 applied to specific elements in a control loop. Many different types of model-driven techniques exist, and have been broken down according to Frank (1990) as follows:

1.

The parity space approach

looks at analytical redundancy in equations that govern the system (Desai and Ray 1981).

2.

The dedicated observer and innovations approach

filters residual errors from the Parity Space Approach using an observer (Jones 1973).

3.

The Fault Detection Filter Approach

augments the State Space models with fault-related variables (Clark et al. 1975; Willsky 1976)

4.

The Parameter Identification Approach

is traditionally performed offline (Frank 1990). Here, modeling techniques are used to estimate the model parameters, and the parameters themselves are used to indicate faults.

A popular subclass of these techniques is deterministic fault diagnosis methods. One popular method in this subclass is the parity space approach (Desai and Ray 1981), which set up parity equations having analytical redundancy to look at error directions that could correspond to faults. Another popular method is the observer-based approach (Garcia and Frank 1997), which uses an observer to compare differences in the predicted and observed states.

Stochastic techniques, in contrast to deterministic techniques, use fault-related parameters as augmented states; these methods enjoy the advantage of being less sensitive to process noise (Hagenblad et al. 2004), being able to determine the size and precise cause of the fault, but are very difficult to implement in large-scale systems and often require some excitement (Frank 1996). Including physical fault parameters in the state often requires a nonlinear form of the Kalman filter (such as the extended Kalman filer (EKF), unscented Kalman filter (UKF) or particle filter) because these fault-related parameters often have nonlinear relationships with respect to the states. Such techniques were pioneered by Isermann (Isermann and Freyermuth 1991), (Isermann 1993) with other important contributions coming from Rault et al. (1984). The motivation for including fault parameters in the state is the stochastic Kalman filter's ability to estimate state distributions. By including fault parameters in the state, fault parameter distributions are automatically estimated in parallel with the state. Examples of this technique include that of Gonzalez et al. (2012), which made use of continuous augmented bias states, while Lerner et al. (2000) made use of discrete augmented fault states.

Process Data-driven Approaches

A popular class of techniques for process monitoring are data-driven modeling methods, where one of the more popular techniques is principal component analysis (PCA) (Ge and Song 2010). These techniques create black-box models assuming that the data can be explained using a linear combination of independent Gaussian latent variables (Tipping and Bishop 1998); a transformation method is used to calculate values of these independent Gaussian variables, and abnormal operation is detected by performing a significance test. The relationship between abnormal latent variables and the real system variables is then used to help the user determine what the possible causes of abnormality could be. There have also been modifications of the PCA model to include multiple Gaussian models (Ge and Song 2010; Tipping and Bishop 1999) where the best local model is used to calculate the underlying latent variables used for testing.