Diagnosis of Process Nonlinearities and Valve Stiction

by Choudhury, M. A. A. Shoukat; Shah, Sirish L.; Thornhill, Nina F.

• ISBN13: 9783540792239
• ISBN10: 3540792236
• Format: Hardcover
• Copyright: 2008-11-13
• Publisher: Springer Nature

Summary

The subject matter of the book is concerned with the detection and diagnosis of process nonlinearities from routine process data. In general, processes can be treated as locally linear and measures of overall process performance can be monitored from routine operating data. However when process performance is not satisfactory then it is imperative that the cause of poor performance be diagnosed. Poor performance can be due to several reasons. Statistics abound on the cause of poor control performance. It has been documented that as many as 40% of the control loops in industry perform unsatisfactorily because of valve problems, a majority of them due to valve stiction, causing the closed loop system to become nonlinear. The development of signal processing methods to detect and quantify process nonlinearity from routine process data is the main subject matter of this book.

Author Biography

M. A. A. Shoukat Choudhury received his B. Sc. Engineering (Chemical) from Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh in 1996. He was awarded a gold medal for his outstanding results in B. Sc. Engineering. He obtained an M. Sc. Engineering (Chemical) in 1998 from the same university. He has completed his PhD degree in process control (Chemical Engineering) at the University of Alberta, Canada. For his outstanding research performance during the course of PhD program he has been awarded several awards such as University of Alberta PhD Dissertation Fellowship, Andrew Stewart Memorial Prize and ISA Educational Foundation Scholarship. He is the principal inventor of an internation patent (applied, 2005) on "Methods for Detection and Quantification of Control Valve Stiction". The methodologies and algorithms described in this patent are implemented and available in the commercial software ProcessDoctor from Matrikon Inc. His main research interests include diagnosis of poor control performance, stiction in control valves, data compression, control loop performance assessment and monitoring, and diagnosis of plant wide oscillations.Sirish Shah received his B.Sc. degree in control engineering from Leeds University in 1971, a M.Sc. degree in automatic control from UMIST, Manchester in 1972, and a Ph.D. degree in process control (chemical engineering) from the University of Alberta in 1976. During 1977 he worked as a computer applications engineer at Esso Chemicals in Sarnia, Ontario. Since 1978 he has been with the University of Alberta, where currently holds the NSERC-Matrikon-ASRA Senior Industrial Research Chair in Computer Process Control. In 1989, he was the recipient of the Albright & Wilson Americas Award of the Canadian Society for Chemical Engineering in recognition of distinguished contributions to chemical engineering. He has held visiting appointments at Oxford University and Balliol College as a SERC fellow in 1985-86 and at Kumamoto University, Japan as a senior research fellow of the Japan Society for the Promotion of Science (JSPS) in 1994. The main area of his current research is process and performance monitoring, system identification and design and implementation of softsensors. He has recently co-authored a book titled, Performance Assessment of Control Loops: Theory and Applications. He has held consulting appointments with a wide variety of process Industries and has also taught many industrial courses.

Table of Contents

Introduction	p. 1
Concepts in Data-Driven Analysis of Chemical Processes	p. 2
Linear and Nonlinear Time Series	p. 3
Statistics and Randomness	p. 3
Frequency Content and Spectral Methods	p. 6
Nonlinearity in Control Valves	p. 8
The Layout of the Book	p. 10
Part I Higher-Order Statistics	p. 10
Part II Data Quality - Compression and Quantization	p. 10
Part III Nonlinearity and Control Performance	p. 11
Part IV Control Valve Stiction - Definition, Modelling, Detection and Quantification	p. 12
Part V Plant-wide Oscillations - Detection and Diagnosis	p. 13
References	p. 14
Summary	p. 14
Higher-Order Statistics
Higher-Order Statistics: Preliminaries	p. 17
Introduction	p. 17
Time Domain Analysis	p. 18
Moments	p. 18
Cumulants	p. 20
The Relationship Between Moments and Cumulants	p. 22
Properties of Moments and Cumulants	p. 22
Moments and Cumulants of Stationary Signals	p. 25
Spectral Analysis	p. 25
Power Spectrum, n=2	p. 26
Bispectrum, n=3	p. 27
Summary	p. 28
Bispectrum and Biocherence	p. 29
Bispectrum	p. 29
Estimation of the Bispectrum	p. 30
Properties of Estimators and Asymptotic Behaviour	p. 32
Bicoherence or Normalized Bispectrum	p. 34
Properties of Bispectrum and Bicoherence	p. 35
Bispectrum or Bicoherence Estimation Issues	p. 37
Choice of Window Function	p. 38
Choice of Data Length, Segment Length and Fourier Transform Length	p. 40
Summary	p. 41
Data Quality - Compression and Quantization
Impact of Data Compression and Quantization on Data-Driven Process Analyses	p. 45
Introduction	p. 45
Data Compression Methods	p. 47
Overview of Data Compression	p. 47
Box-Car (BC) Algorithm	p. 47
Backward-Slope (BS) Algorithm	p. 47
Combined Box-Car and Backward-Slope (BCBS) Method	p. 49
Swinging Door Compression Algorithm	p. 49
The Compression Factor	p. 49
Measures of Data Quality	p. 50
Statistical Measures	p. 50
Nonlinearity Measures	p. 51
Performance Index (Harris) Measures	p. 51
Process Data for Compression Comparison	p. 52
Industrial Example 1	p. 52
Industrial Example 2	p. 55
Results and Discussions for Industrial Example 2	p. 56
Visual Observations	p. 56
Statistical Properties	p. 57
Nonlinearity Assessment	p. 58
Performance (Harris) Index	p. 58
Summary of Data Quality Measures	p. 59
Automated Detection of Compression	p. 59
Motivation	p. 59
Compression Detection Procedure	p. 60
Implementation Considerations	p. 61
A Recommendation for Harmless Storing of Data	p. 63
Quantization	p. 63
Summary	p. 65
Nonlinearity and Control Performance
Measures of Nonlinearity - A Review	p. 69
Definition of Nonlinear Systems	p. 69
Nonlinearity in Process Time Trends	p. 70
Various Measures of Nonlinearity	p. 70
Model-Based Measures of Nonlinearity	p. 71
Time Series-Based Measures of Nonlinearity	p. 71
Summary	p. 75
Linear or Nonlinear? A Bicoherence-Based Measure of Nonlinearity	p. 77
Introduction	p. 77
Bispectrum and Biocherence	p. 78
Spurious Peaks in the Estimated Bicoherence	p. 78
Illustrative Example 1	p. 79
How to Choose [epsilon]?	p. 80
Test of Gaussianity and Linearity of a Signal	p. 81
Total Nonlinearity Index (TNLI)	p. 85
Illustrative Example 2: Bicoherence of a Linear and a Nonlinear Signal	p. 85
Illustrative Example 3: Bicoherence of a Nonlinear Sinusoid Signal with Noise	p. 87
Mild Nonlinearity (n[subscript l] = 0.05)	p. 88
Strong Nonlinearity (n[subscript l] = 0.25)	p. 89
Extent of Nonlinearity and Effect of Noise	p. 90
Summary	p. 91
A Nonlinearity Measure Based on Surrogate Data Analysis	p. 93
Surrogate Time Series	p. 93
Nonlinearity Detection Using Surrogates	p. 93
Predictability in Nonlinear Time Series	p. 93
Algorithm for Nonlinearity Diagnosis	p. 95
Construction of the Data Matrix for Nonlinear Prediction	p. 95
Calculation of Prediction Error	p. 96
Calculation of Surrogate Data	p. 96
Statistical Testing	p. 98
Algorithm Summary	p. 98
Selection of the Parameter Values	p. 99
Recommended Default Parameter Values	p. 99
Choice of Embedding Parameters E and H	p. 99
Choice of Parameters C and k	p. 100
Default Data Ensemble Size, Q and Number of Samples Per Feature, S	p. 101
Choice of the Number of Surrogates, M	p. 101
Data-Preprocessing and End-Matching	p. 102
False-Positive Results with Cyclic Data	p. 102
End-Matching	p. 103
Summary of the Data-Preprocessing Steps	p. 104
Application to Oscillating Time Grends	p. 104
Worked Examples	p. 106
Identification of Nonlinear Root Causes	p. 106
Application to the SE Asia Data Set	p. 106
The Mechanisms of Propagation in the SE Asia Process	p. 106
An Example with No Nonlinearity	p. 108
Summary	p. 110
Nonlinearities in Control Loops	p. 111
Process Nonlinearity	p. 111
Nonlinearity of a Spherical Tank	p. 111
Nonlinearities of a Continuous Stirred Tank Reactor (CSTR)	p. 115
Nonlinear Valve Characteristic	p. 117
Linear Valves	p. 118
Equal Percentage Valves	p. 118
Square-Root Valve	p. 119
Remarks on Nonlinear Valve Characteristic	p. 120
Nonlinear Disturbances	p. 121
Summary	p. 121
Diagnosis of Poor Control Performance	p. 123
Introduction	p. 123
Problem Description	p. 124
Usual Causes of Poor Performance	p. 125
Diagnosis of Poor Control Performance	p. 126
Well Tuned Controller	p. 127
Tightly Tuned Controller or Excessive Integral Action	p. 128
Presence of an External Oscillatory Disturbance	p. 129
Presence of Stiction	p. 129
Industrial Case Studies	p. 129
Stiction in a Furnace Dryer Temperature Control Valve	p. 130
Valve Saturation	p. 131
Valve Problems in Some Flow Control Loops	p. 132
Summary	p. 134
Control Valve Stiction - Definition, Modelling, Detection and Quantification
Different Types of Faults in Control Valves	p. 137
What Is a Control Valve	p. 137
Faults in Control Valve	p. 138
Oversized Valve	p. 139
Undersized Valve	p. 139
Corroded Valve Seat	p. 139
Faulty Diaphragm	p. 139
Packing Leakage	p. 139
Valve Hysteresis	p. 140
Valve Stiction	p. 140
Large Deadband	p. 140
Valve Saturation	p. 141
Summary	p. 141
Stiction: Definition and Discussions	p. 143
Introduction	p. 143
What Is Stiction?	p. 143
Definition of Terms Relating to Valve Nonlinearity	p. 144
Discussion of the Term 'Stiction'	p. 145
A Formal Definition of Stiction	p. 146
Practical Examples of Valve Stiction	p. 148
Summary	p. 151
Physics-Based Model of Control Valve Stiction	p. 153
Introduction	p. 153
Physical Modelling of Valve Friction	p. 153
Physics of a Control Valve	p. 153
Friction Model	p. 154
Model Parameters	p. 155
Detection of Zero Velocity	p. 156
Model of the Pressure Chamber	p. 156
Valve Simulation	p. 157
Open-Loop Response	p. 157
Closed-Loop Response	p. 158
Summary	p. 160
Data-Driven Model of Valve Stiction	p. 161
One-Parameter Data-Driven Stiction Model	p. 161
Two-Parameter Data-Driven Model of Valve Stiction	p. 163
Model Formulation	p. 163
Dealing with Stochastic or Noisy Control Signals	p. 166
Open-Loop Response of the Model Under a Sinusoidal Input	p. 166
Stiction in Reality	p. 167
Closed-Loop Behaviour of the Model	p. 167
Comparison of Physics-Based Model and Data-Driven Model	p. 171
Summary	p. 171
Describing Function Analysis	p. 173
Introduction	p. 173
Describing Function Analysis for Two-Parameter Stiction Model	p. 174
Derivation of the Describing Function	p. 174
Asymptotes of the Describing Function	p. 177
Insights Gained from the Describing Function	p. 178
The Impact of the Controller on the Limit Cycle	p. 179
Summary	p. 180
Automatic Detection and Quantification of Valve Stiction	p. 181
Introduction	p. 181
Stiction Detection - A Literature Review	p. 182
Detection of Stiction Using Nonlinearity Information and the pv-op Mapping	p. 183
Detection of Loop Nonlinearity	p. 184
Use of pv-op Plot	p. 185
Stiction Quantification	p. 187
Clustering Techniques of Quantifying Stiction	p. 187
Fitted Ellipse Technique for Quantifying Stiction	p. 190
An Illustrative Example	p. 192
Validation of the Results	p. 193
Automation of the Method	p. 193
Simulation Results	p. 195
A Worked Example	p. 195
Distinguishing Limit Cycles Caused by Stiction and Those Caused by a Sinusoidal Disturbance	p. 196
Detecting Stiction When Its Impact Propagates as Disturbance	p. 198
Practical Implementation Issues	p. 201
Bicoherence Estimation	p. 201
Nonstationarity of the Data	p. 201
Problems of Outliers and Abrupt Changes	p. 201
Dealing with Short Length Data	p. 202
Dealing with Longer Oscillations	p. 202
Valve Nonlinearity	p. 202
Filtering of the Data	p. 203
Segmenting Data for pv-op Plot	p. 204
Summary	p. 204
Industrial Applications of the Stiction Quantification Algorithm	p. 205
Industrial Case Studies	p. 205
Loop 1: A Level Loop	p. 205
Loop 2: A Linear-Level Control Loop	p. 207
Loop 3: A Flow Control Loop	p. 208
Loop 4: Flow Control Loop Cascaded with Level Control	p. 209
Loop 5: A Pressure Control Loop	p. 210
Loop 6: A Composition Control Loop	p. 210
Loop 7: A Cascaded Flow Control Loop	p. 211
Loop 8: A Temperature Control Loop	p. 212
Loops 9 and 10	p. 212
Online Compensation for Stiction	p. 213
Summary	p. 215
Confirming Valve Stiction	p. 217
Methods to Confirm Valve Stiction	p. 217
Gain Change Method for Confirming Valve Stiction	p. 218
Distinguishing Stiction from External Oscillatory Disturbance	p. 218
Describing Function Analysis	p. 222
Comparison of Describing Function Analysis (DFA) Results with Simulation Results	p. 225
Industrial Example	p. 225
Summary	p. 226
Plant-wide Oscillations - Detection and Diagnosis
Detection of Plantwide Oscillations	p. 229
Introduction	p. 229
What is an Oscillation?	p. 230
Units of Frequency	p. 230
Examples of Oscillatory Signals	p. 230
Detection of Oscillation(s) in a Single Time Series	p. 231
The Power Spectrum	p. 231
Hagglund's IAE Method	p. 231
Autocovariance (ACF) Based Method	p. 232
Other Methods	p. 237
What are Plant-wide Oscillations?	p. 237
Classification of Plant-wide Oscillations or Disturbances	p. 237
Time scales	p. 237
Oscillating and Non-oscillating Disturbances	p. 238
Detection of Plant-wide Oscillations	p. 238
High-Density Plots	p. 238
ACF-Based Method	p. 239
Power Spectral Correlation Map (PSCMAP)	p. 239
Spectral Envelope Method	p. 240
Spectral Decomposition Methods	p. 241
Summary	p. 250
Diagnosis of Plant-wide Oscillations	p. 253
Root Cause Diagnosis of Plant-wide Oscillation	p. 253
Finding a Nonlinear Root Cause of a Plant-Wide Disturbance	p. 253
Finding a Linear Root Cause of a Plant-wide Disturbance	p. 256
Industrial Case Study 1 - Eastman Chemical Plant	p. 257
Data Description	p. 258
Reduction of the Problem Size	p. 258
Detection of Plant-wide Oscillation by PSCMAP	p. 259
Nonlinearity Analysis Using Biocherence-Based Indices	p. 260
Diagnosis of the Problem in Loop LC2	p. 262
Industrial Case Study 2 - SE Asia Refinery Data Analysis	p. 263
Oscillation Detection by PSCMAP	p. 264
Oscillation Detection by Spectral Envelope	p. 265
Oscillation Diagnosis	p. 266
Industrial Case Study 3 - Mitshubishi Chemical Corporation	p. 266
Scope of the Analysis and Data Set	p. 268
Oscillation-Detection Results	p. 268
Oscillation Diagnosis	p. 268
The Results of Maintenance on the PC1 and LI1 Loops	p. 271
Summary	p. 272
References	p. 273
Copyright Acknowledgements	p. 281
Index	p. 283
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