InhaltsangabePreface 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 Nonnegative 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 Errorinvariable estimate for known See 218 6.2.5 Errorinvariable 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 6.4 Small sample sets 232 6.5 Tutorial session 237 7 Monitoring multivariate time-varying processes 240 7.1 Problem analysis 241 7.2 Recursive principal component analysis 242 7.3 Moving window principal component analysis 244 7.3.1 Adapting the data correlation matrix 244 7.3.2 Adapting the eigendecomposition 247 7.3.3 Computational analysis of the adaptation procedure 251 7.3.4 Adaptation of control limits 252 7.3.5 Process monitoring using an application delay 253 7.3.6 Minimum window lengt

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

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