Statistical Monitoring of Complex Multivatiate Processes

The development and application of multivariate statistical
techniques in process monitoring has gained substantial interest
over the past two decades in academia and industry alike.
Initially developed for monitoring and fault diagnosis in complex
systems, such techniques have been refined and applied in various
engineering areas, for example mechanical and manufacturing,
chemical, electrical and electronic, and power engineering.
The recipe for the tremendous interest in multivariate statistical
techniques lies in its simplicity and adaptability for developing
monitoring applications. In contrast, competitive model,
signal or knowledge based techniques showed their potential only
whenever cost-benefit economics have justified the required effort
in developing applications.

Statistical Monitoring of Complex Multivariate Processes
presents recent advances in statistics based process monitoring,
explaining how these processes can now be used in areas such as
mechanical and manufacturing engineering for example, in addition
to the traditional chemical industry.

This book:

• Contains a detailed theoretical background of the component
  technology.

• Brings together a large body of work to address the
  field's drawbacks, and develops methods for their
  improvement.

• Details cross-disciplinary utilization, exemplified by examples
  in chemical, mechanical and manufacturing engineering.

• Presents real life industrial applications, outlining
  deficiencies in the methodology and how to address them.

• Includes numerous examples, tutorial questions and homework
  assignments in the form of individual and team-based projects, to
  enhance the learning experience.

• Features a supplementary website including Matlab algorithms
  and data sets.

This book provides a timely reference text to the rapidly
evolving area of multivariate statistical analysis for academics,
advanced level students, and practitioners alike.

Autorentext

Uwe Kruger, The Petroleum Institute, Abu Dhabi, United Arab Emirates
Lei Xie, Institute of Cyber-Systems & Control, Zhejiang University, China

Zusammenfassung

The development and application of multivariate statistical techniques in process monitoring has gained substantial interest over the past two decades in academia and industry alike. Initially developed for monitoring and fault diagnosis in complex systems, such techniques have been refined and applied in various engineering areas, for example mechanical and manufacturing, chemical, electrical and electronic, and power engineering. The recipe for the tremendous interest in multivariate statistical techniques lies in its simplicity and adaptability for developing monitoring applications. In contrast, competitive model, signal or knowledge based techniques showed their potential only whenever cost-benefit economics have justified the required effort in developing applications.

Statistical Monitoring of Complex Multivariate Processes presents recent advances in statistics based process monitoring, explaining how these processes can now be used in areas such as mechanical and manufacturing engineering for example, in addition to the traditional chemical industry.

This book:

• Contains a detailed theoretical background of the component technology.
• Brings together a large body of work to address the field's drawbacks, and develops methods for their improvement.
• Details cross-disciplinary utilization, exemplified by examples in chemical, mechanical and manufacturing engineering.
• Presents real life industrial applications, outlining deficiencies in the methodology and how to address them.
• Includes numerous examples, tutorial questions and homework assignments in the form of individual and team-based projects, to enhance the learning experience.
• Features a supplementary website including Matlab algorithms and data sets.
  This book provides a timely reference text to the rapidly evolving area of multivariate statistical analysis for academics, advanced level students, and practitioners alike.

Inhalt

Preface xiii

Acknowledgements xvii

Abbreviations xix

Symbols xxi

Nomenclature xxiii

Introduction xxv

Part I Fundamentals of Multivariate Statistical Process Control 1

1 Motivation for multivariate statistical process control 3

1.1 Summary of statistical process control 3

1.1.1 Roots and evolution of statistical process control 4

1.1.2 Principles of statistical process control 5

1.1.3 Hypothesis testing, Type I and II errors 12

1.2 Why multivariate statistical process control 15

1.2.1 Statistically uncorrelated variables 16

1.2.2 Perfectly correlated variables 17

1.2.3 Highly correlated variables 19

1.2.4 Type I and II errors and dimension reduction 24

1.3 Tutorial session 26

2 Multivariate data modeling methods 28

2.1 Principal component analysis 30

2.1.1 Assumptions for underlying data structure 30

2.1.2 Geometric analysis of data structure 33

2.1.3 A simulation example 34

2.2 Partial least squares 38

2.2.1 Assumptions for underlying data structure 39

2.2.2 Deflation procedure for estimating data models 41

2.2.3 A simulation example 43

2.3 Maximum redundancy partial least squares 49

2.3.1 Assumptions for underlying data structure 49

2.3.2 Source signal estimation 50

2.3.3 Geometric analysis of data structure 52

2.3.4 A simulation example 58

2.4 Estimating the number of source signals 65

2.4.1 Stopping rules for PCA models 65

2.4.2 Stopping rules for PLS models 76

2.5 Tutorial Session 79

3 Process monitoring charts 81

3.1 Fault detection 83

3.1.1 Scatter diagrams 84

3.1.2 Non-negative quadratic monitoring statistics 85

3.2 Fault isolation and identification 93

3.2.1 Contribution charts 95

3.2.2 Residual-based tests 98

3.2.3 Variable reconstruction 100

3.3 Geometry of variable projections 111

3.3.1 Linear dependency of projection residuals 111

3.3.2 Geometric analysis of variable reconstruction 112

3.4 Tutorial session 119

Part II Application Studies 121

4 Application to a chemical reaction process 123

4.1 Process description 123

4.2 Identification of a monitoring model 124

4.3 Diagnosis of a fault condition 133

5 Application to a distillation process 141

5.1 Process description 141

5.2 Identification of a monitoring model 144

5.3 Diagnosis of a fault condition 153

Part III Advances in Multivariate Statistical Process Control 165

6 Further modeling issues 167

6.1 Accuracy of estimating PCA models 168

6.1.1 Revisiting the eigendecomposition of Sz0z0 168

6.1.2 Two illustrative examples 171

6.1.3 Maximum likelihood PCA for known Sgg 172

6.1.4 Maximum likelihood PCA for unknown Sgg 177

6.1.5 A simulation example 182

6.1.6 A stopping rule for maximum likelihood PCA models 187

6.1.7 Properties of model and residual subspace estimates 189

6.1.8 Application to a chemical reaction process revisited 194

6.2 Accuracy of estimating PLS models 202

6.2.1 Bias and variance of parameter estimation 203

6.2.2 Comparing accuracy of PLS and OLS regression models 205

6.2.3 Impact of error-in-variables structure upon PLS models 212

6.2.4 Error-in-variable estimate for known See 218

6.2.5 Error-in-variable estimate for unknown See 219

6.2.6 Application to a distillation process revisited 223

6.3 Robust model estimation 226

6.3.1 Robust parameter estimation 228

6.3.2 Trimming approaches 231 ...