Diagnosis of process nonlinearities and valve stiction : data driven approaches

were published in the series as the contributed volume, Process Control Performance Assessment: From Theory to Implementation with Andrzej Ordys, Damian Uduehi, and Michael Johnson as Editors (ISBN 978-1-84628-623-0, 2007). Along with this good progress in process controller assessment methods, researchers have also been investigating techniques to diagnose what is causing the process or control loop degradation. This requires the use of on-line data to identify faults via new diagnostic indicators of typical process problems. A significant focus of some of this research has been the issue of valve problems; a research direction that has been motivated by some industrial statistics that show up to 40% of control loops having performance degradation attributable to valve problems. Shoukat Choudhury, Sirish Shah, and Nina Thornhill have been very active in this research field for a number of years and have written a coherent and consistent presentation of their many research results as this monograph, Diagnosis of Process Nonlinearities and Valve Stiction. The Advances in Industrial Control series is pleased to welcome this new and substantial contribution to the process diagnostic literature. The reader will find the exploitation of the extensive process data archives created by today's process computer systems one theme in the monograph. From another viewpoint, the use of higher-order statistics could be considered to provide a continuing link to the earlier methods of the statistical process control paradigm.

Author Notes

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 fellowin 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.

1 Introduction	p. 1
1.1 Concepts in Data-Driven Analysis of Chemical Processes	p. 2
1.1.1 Linear and Nonlinear Time Series	p. 3
1.1.2 Statistics and Randomness	p. 3
1.1.3 Frequency Content and Spectral Methods	p. 6
1.2 Nonlinearity in Control Valves	p. 8
1.3 The Layout of the Book	p. 10
1.3.1 Part I Higher-Order Statistics	p. 10
1.3.2 Part II Data Quality - Compression and Quantization	p. 10
1.3.3 Part III Nonlinearity and Control Performance	p. 11
1.3.4 Part IV Control Valve Stiction - Definition, Modelling, Detection and Quantification	p. 12
1.3.5 Part V Plant-wide Oscillations - Detection and Diagnosis	p. 13
1.3.6 References	p. 14
1.4 Summary	p. 14
Part I Higher-Order Statistics
2 Higher-Order Statistics: Preliminaries	p. 17
2.1 Introduction	p. 17
2.2 Time Domain Analysis	p. 18
2.2.1 Moments	p. 18
2.2.2 Cumulants	p. 20
2.2.3 The Relationship Between Moments and Cumulants	p. 22
2.2.4 Properties of Moments and Cumulants	p. 22
2.2.5 Moments and Cumulants of Stationary Signals	p. 25
2.3 Spectral Analysis	p. 25
2.3.1 Power Spectrum, n=2	p. 26
2.3.2 Bispectrum, n=3	p. 27
2.4 Summary	p. 28
3 Bispectrum and Biocherence	p. 29
3.1 Bispectrum	p. 29
3.1.1 Estimation of the Bispectrum	p. 30
3.1.2 Properties of Estimators and Asymptotic Behaviour	p. 32
3.1.3 Bicoherence or Normalized Bispectrum	p. 34
3.1.4 Properties of Bispectrum and Bicoherence	p. 35
3.2 Bispectrum or Bicoherence Estimation Issues	p. 37
3.2.1 Choice of Window Function	p. 38
3.2.2 Choice of Data Length, Segment Length and Fourier Transform Length	p. 40
3.3 Summary	p. 41
Part II Data Quality - Compression and Quantization
4 Impact of Data Compression and Quantization on Data-Driven Process Analyses	p. 45
4.1 Introduction	p. 45
4.2 Data Compression Methods	p. 47
4.2.1 Overview of Data Compression	p. 47
4.2.2 Box-Car (BC) Algorithm	p. 47
4.2.3 Backward-Slope (BS) Algorithm	p. 47
4.2.4 Combined Box-Car and Backward-Slope (BCBS) Method	p. 49
4.2.5 Swinging Door Compression Algorithm	p. 49
4.2.6 The Compression Factor	p. 49
4.3 Measures of Data Quality	p. 50
4.3.1 Statistical Measures	p. 50
4.3.2 Nonlinearity Measures	p. 51
4.3.3 Performance Index (Harris) Measures	p. 51
4.4 Process Data for Compression Comparison	p. 52
4.4.1 Industrial Example 1	p. 52
4.4.2 Industrial Example 2	p. 55
4.5 Results and Discussions for Industrial Example 2	p. 56
4.5.1 Visual Observations	p. 56
4.5.2 Statistical Properties	p. 57
4.5.3 Nonlinearity Assessment	p. 58
4.5.4 Performance (Harris) Index	p. 58
4.6 Summary of Data Quality Measures	p. 59
4.7 Automated Detection of Compression	p. 59
4.7.1 Motivation	p. 59
4.7.2 Compression Detection Procedure	p. 60
4.7.3 Implementation Considerations	p. 61
4.8 A Recommendation for Harmless Storing of Data	p. 63
4.9 Quantization	p. 63
4.10 Summary	p. 65
Part III Nonlinearity and Control Performance
5 Measures of Nonlinearity - A Review	p. 69
5.1 Definition of Nonlinear Systems	p. 69
5.2 Nonlinearity in Process Time Trends	p. 70
5.3 Various Measures of Nonlinearity	p. 70
5.3.1 Model-Based Measures of Nonlinearity	p. 71
5.3.2 Time Series-Based Measures of Nonlinearity	p. 71
5.4 Summary	p. 75
6 Linear or Nonlinear? A Bicoherence-Based Measure of Nonlinearity	p. 77
6.1 Introduction	p. 77
6.2 Bispectrum and Biocherence	p. 78
6.2.1 Spurious Peaks in the Estimated Bicoherence	p. 78
6.2.2 Illustrative Example 1	p. 79
6.2.3 How to Choose [epsilon]?	p. 80
6.3 Test of Gaussianity and Linearity of a Signal	p. 81
6.3.1 Total Nonlinearity Index (TNLI)	p. 85
6.4 Illustrative Example 2: Bicoherence of a Linear and a Nonlinear Signal	p. 85
6.5 Illustrative Example 3: Bicoherence of a Nonlinear Sinusoid Signal with Noise	p. 87
6.5.1 Mild Nonlinearity (n[subscript l] = 0.05)	p. 88
6.5.2 Strong Nonlinearity (n[subscript l] = 0.25)	p. 89
6.5.3 Extent of Nonlinearity and Effect of Noise	p. 90
6.6 Summary	p. 91
7 A Nonlinearity Measure Based on Surrogate Data Analysis	p. 93
7.1 Surrogate Time Series	p. 93
7.1.1 Nonlinearity Detection Using Surrogates	p. 93
7.1.2 Predictability in Nonlinear Time Series	p. 93
7.2 Algorithm for Nonlinearity Diagnosis	p. 95
7.2.1 Construction of the Data Matrix for Nonlinear Prediction	p. 95
7.2.2 Calculation of Prediction Error	p. 96
7.2.3 Calculation of Surrogate Data	p. 96
7.2.4 Statistical Testing	p. 98
7.2.5 Algorithm Summary	p. 98
7.3 Selection of the Parameter Values	p. 99
7.3.1 Recommended Default Parameter Values	p. 99
7.3.2 Choice of Embedding Parameters E and H	p. 99
7.3.3 Choice of Parameters C and k	p. 100
7.3.4 Default Data Ensemble Size, Q and Number of Samples Per Feature, S	p. 101
7.3.5 Choice of the Number of Surrogates, M	p. 101
7.4 Data-Preprocessing and End-Matching	p. 102
7.4.1 False-Positive Results with Cyclic Data	p. 102
7.4.2 End-Matching	p. 103
7.4.3 Summary of the Data-Preprocessing Steps	p. 104
7.4.4 Application to Oscillating Time Grends	p. 104
7.5 Worked Examples	p. 106
7.5.1 Identification of Nonlinear Root Causes	p. 106
7.5.2 Application to the SE Asia Data Set	p. 106
7.5.3 The Mechanisms of Propagation in the SE Asia Process	p. 106
7.5.4 An Example with No Nonlinearity	p. 108
7.6 Summary	p. 110
8 Nonlinearities in Control Loops	p. 111
8.1 Process Nonlinearity	p. 111
8.1.1 Nonlinearity of a Spherical Tank	p. 111
8.1.2 Nonlinearities of a Continuous Stirred Tank Reactor (CSTR)	p. 115
8.2 Nonlinear Valve Characteristic	p. 117
8.2.1 Linear Valves	p. 118
8.2.2 Equal Percentage Valves	p. 118
8.2.3 Square-Root Valve	p. 119
8.2.4 Remarks on Nonlinear Valve Characteristic	p. 120
8.3 Nonlinear Disturbances	p. 121
8.4 Summary	p. 121
9 Diagnosis of Poor Control Performance	p. 123
9.1 Introduction	p. 123
9.2 Problem Description	p. 124
9.3 Usual Causes of Poor Performance	p. 125
9.4 Diagnosis of Poor Control Performance	p. 126
9.4.1 Well Tuned Controller	p. 127
9.4.2 Tightly Tuned Controller or Excessive Integral Action	p. 128
9.4.3 Presence of an External Oscillatory Disturbance	p. 129
9.4.4 Presence of Stiction	p. 129
9.5 Industrial Case Studies	p. 129
9.5.1 Stiction in a Furnace Dryer Temperature Control Valve	p. 130
9.5.2 Valve Saturation	p. 131
9.5.3 Valve Problems in Some Flow Control Loops	p. 132
9.6 Summary	p. 134
Part IV Control Valve Stiction - Definition, Modelling, Detection and Quantification
10 Different Types of Faults in Control Valves	p. 137
10.1 What Is a Control Valve	p. 137
10.2 Faults in Control Valve	p. 138
10.2.1 Oversized Valve	p. 139
10.2.2 Undersized Valve	p. 139
10.2.3 Corroded Valve Seat	p. 139
10.2.4 Faulty Diaphragm	p. 139
10.2.5 Packing Leakage	p. 139
10.2.6 Valve Hysteresis	p. 140
10.2.7 Valve Stiction	p. 140
10.2.8 Large Deadband	p. 140
10.2.9 Valve Saturation	p. 141
10.3 Summary	p. 141
11 Stiction: Definition and Discussions	p. 143
11.1 Introduction	p. 143
11.2 What Is Stiction?	p. 143
11.2.1 Definition of Terms Relating to Valve Nonlinearity	p. 144
11.2.2 Discussion of the Term 'Stiction'	p. 145
11.2.3 A Formal Definition of Stiction	p. 146
11.3 Practical Examples of Valve Stiction	p. 148
11.4 Summary	p. 151
12 Physics-Based Model of Control Valve Stiction	p. 153
12.1 Introduction	p. 153
12.2 Physical Modelling of Valve Friction	p. 153
12.2.1 Physics of a Control Valve	p. 153
12.2.2 Friction Model	p. 154
12.2.3 Model Parameters	p. 155
12.2.4 Detection of Zero Velocity	p. 156
12.2.5 Model of the Pressure Chamber	p. 156
12.3 Valve Simulation	p. 157
12.3.1 Open-Loop Response	p. 157
12.3.2 Closed-Loop Response	p. 158
12.4 Summary	p. 160
13 Data-Driven Model of Valve Stiction	p. 161
13.1 One-Parameter Data-Driven Stiction Model	p. 161
13.2 Two-Parameter Data-Driven Model of Valve Stiction	p. 163
13.2.1 Model Formulation	p. 163
13.2.2 Dealing with Stochastic or Noisy Control Signals	p. 166
13.2.3 Open-Loop Response of the Model Under a Sinusoidal Input	p. 166
13.2.4 Stiction in Reality	p. 167
13.2.5 Closed-Loop Behaviour of the Model	p. 167
13.3 Comparison of Physics-Based Model and Data-Driven Model	p. 171
13.4 Summary	p. 171
14 Describing Function Analysis	p. 173
14.1 Introduction	p. 173
14.2 Describing Function Analysis for Two-Parameter Stiction Model	p. 174
14.2.1 Derivation of the Describing Function	p. 174
14.3 Asymptotes of the Describing Function	p. 177
14.4 Insights Gained from the Describing Function	p. 178
14.4.1 The Impact of the Controller on the Limit Cycle	p. 179
14.5 Summary	p. 180
15 Automatic Detection and Quantification of Valve Stiction	p. 181
15.1 Introduction	p. 181
15.2 Stiction Detection - A Literature Review	p. 182
15.3 Detection of Stiction Using Nonlinearity Information and the pv-op Mapping	p. 183
15.3.1 Detection of Loop Nonlinearity	p. 184
15.3.2 Use of pv-op Plot	p. 185
15.4 Stiction Quantification	p. 187
15.4.1 Clustering Techniques of Quantifying Stiction	p. 187
15.4.2 Fitted Ellipse Technique for Quantifying Stiction	p. 190
15.5 An Illustrative Example	p. 192
15.5.1 Validation of the Results	p. 193
15.6 Automation of the Method	p. 193
15.7 Simulation Results	p. 195
15.7.1 A Worked Example	p. 195
15.7.2 Distinguishing Limit Cycles Caused by Stiction and Those Caused by a Sinusoidal Disturbance	p. 196
15.7.3 Detecting Stiction When Its Impact Propagates as Disturbance	p. 198
15.8 Practical Implementation Issues	p. 201
15.8.1 Bicoherence Estimation	p. 201
15.8.2 Nonstationarity of the Data	p. 201
15.8.3 Problems of Outliers and Abrupt Changes	p. 201
15.8.4 Dealing with Short Length Data	p. 202
15.8.5 Dealing with Longer Oscillations	p. 202
15.8.6 Valve Nonlinearity	p. 202
15.8.7 Filtering of the Data	p. 203
15.8.8 Segmenting Data for pv-op Plot	p. 204
15.9 Summary	p. 204
16 Industrial Applications of the Stiction Quantification Algorithm	p. 205
16.1 Industrial Case Studies	p. 205
16.1.1 Loop 1: A Level Loop	p. 205
16.1.2 Loop 2: A Linear-Level Control Loop	p. 207
16.1.3 Loop 3: A Flow Control Loop	p. 208
16.1.4 Loop 4: Flow Control Loop Cascaded with Level Control	p. 209
16.1.5 Loop 5: A Pressure Control Loop	p. 210
16.1.6 Loop 6: A Composition Control Loop	p. 210
16.1.7 Loop 7: A Cascaded Flow Control Loop	p. 211
16.1.8 Loop 8: A Temperature Control Loop	p. 212
16.1.9 Loops 9 and 10	p. 212
16.2 Online Compensation for Stiction	p. 213
16.3 Summary	p. 215
17 Confirming Valve Stiction	p. 217
17.1 Methods to Confirm Valve Stiction	p. 217
17.2 Gain Change Method for Confirming Valve Stiction	p. 218
17.2.1 Distinguishing Stiction from External Oscillatory Disturbance	p. 218
17.3 Describing Function Analysis	p. 222
17.3.1 Comparison of Describing Function Analysis (DFA) Results with Simulation Results	p. 225
17.4 Industrial Example	p. 225
17.5 Summary	p. 226
Part V Plant-wide Oscillations - Detection and Diagnosis
18 Detection of Plantwide Oscillations	p. 229
18.1 Introduction	p. 229
18.2 What is an Oscillation?	p. 230
18.2.1 Units of Frequency	p. 230
18.2.2 Examples of Oscillatory Signals	p. 230
18.3 Detection of Oscillation(s) in a Single Time Series	p. 231
18.3.1 The Power Spectrum	p. 231
18.3.2 Hagglund's IAE Method	p. 231
18.3.3 Autocovariance (ACF) Based Method	p. 232
18.3.4 Other Methods	p. 237
18.4 What are Plant-wide Oscillations?	p. 237
18.5 Classification of Plant-wide Oscillations or Disturbances	p. 237
18.5.1 Time scales	p. 237
18.5.2 Oscillating and Non-oscillating Disturbances	p. 238
18.6 Detection of Plant-wide Oscillations	p. 238
18.6.1 High-Density Plots	p. 238
18.6.2 ACF-Based Method	p. 239
18.6.3 Power Spectral Correlation Map (PSCMAP)	p. 239
18.6.4 Spectral Envelope Method	p. 240
18.6.5 Spectral Decomposition Methods	p. 241
18.7 Summary	p. 250
19 Diagnosis of Plant-wide Oscillations	p. 253
19.1 Root Cause Diagnosis of Plant-wide Oscillation	p. 253
19.1.1 Finding a Nonlinear Root Cause of a Plant-Wide Disturbance	p. 253
19.1.2 Finding a Linear Root Cause of a Plant-wide Disturbance	p. 256
19.2 Industrial Case Study 1 - Eastman Chemical Plant	p. 257
19.2.1 Data Description	p. 258
19.2.2 Reduction of the Problem Size	p. 258
19.2.3 Detection of Plant-wide Oscillation by PSCMAP	p. 259
19.2.4 Nonlinearity Analysis Using Biocherence-Based Indices	p. 260
19.2.5 Diagnosis of the Problem in Loop LC2	p. 262
19.3 Industrial Case Study 2 - SE Asia Refinery Data Analysis	p. 263
19.3.1 Oscillation Detection by PSCMAP	p. 264
19.3.2 Oscillation Detection by Spectral Envelope	p. 265
19.3.3 Oscillation Diagnosis	p. 266
19.4 Industrial Case Study 3 - Mitshubishi Chemical Corporation	p. 266
19.4.1 Scope of the Analysis and Data Set	p. 268
19.4.2 Oscillation-Detection Results	p. 268
19.4.3 Oscillation Diagnosis	p. 268
19.4.4 The Results of Maintenance on the PC1 and LI1 Loops	p. 271
19.5 Summary	p. 272
References	p. 273
Copyright Acknowledgements	p. 281
Index	p. 283

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