Statistical Monitoring of Complex Multivariate Processes

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

• Preface xiiiAcknowledgements xviiAbbreviations xixSymbols xxiNomenclature xxiiiIntroduction xxvPart I Fundamentals of Multivariate Statistical Process Control 11 Motivation for multivariate statistical process control 31.1 Summary of statistical process control 31.1.1 Roots and evolution of statistical process control 41.1.2 Principles of statistical process control 51.1.3 Hypothesis testing, Type I and II errors 121.2 Why multivariate statistical process control 151.2.1 Statistically uncorrelated variables 161.2.2 Perfectly correlated variables 171.2.3 Highly correlated variables 191.2.4 Type I and II errors and dimension reduction 241.3 Tutorial session 262 Multivariate data modeling methods 282.1 Principal component analysis 302.1.1 Assumptions for underlying data structure 302.1.2 Geometric analysis of data structure 332.1.3 A simulation example 342.2 Partial least squares 382.2.1 Assumptions for underlying data structure 392.2.2 Deflation procedure for estimating data models 412.2.3 A simulation example 432.3 Maximum redundancy partial least squares 492.3.1 Assumptions for underlying data structure 492.3.2 Source signal estimation 502.3.3 Geometric analysis of data structure 522.3.4 A simulation example 582.4 Estimating the number of source signals 652.4.1 Stopping rules for PCA models 652.4.2 Stopping rules for PLS models 762.5 Tutorial Session 793 Process monitoring charts 813.1 Fault detection 833.1.1 Scatter diagrams 843.1.2 Non-negative quadratic monitoring statistics 853.2 Fault isolation and identification 933.2.1 Contribution charts 953.2.2 Residual-based tests 983.2.3 Variable reconstruction 1003.3 Geometry of variable projections 1113.3.1 Linear dependency of projection residuals 1113.3.2 Geometric analysis of variable reconstruction 1123.4 Tutorial session 119Part II Application Studies 1214 Application to a chemical reaction process 1234.1 Process description 1234.2 Identification of a monitoring model 1244.3 Diagnosis of a fault condition 1335 Application to a distillation process 1415.1 Process description 1415.2 Identification of a monitoring model 1445.3 Diagnosis of a fault condition 153Part III Advances in Multivariate Statistical Process Control 1656 Further modeling issues 1676.1 Accuracy of estimating PCA models 1686.1.1 Revisiting the eigendecomposition of Sz0z0 1686.1.2 Two illustrative examples 1716.1.3 Maximum likelihood PCA for known Sgg 1726.1.4 Maximum likelihood PCA for unknown Sgg 1776.1.5 A simulation example 1826.1.6 A stopping rule for maximum likelihood PCA models 1876.1.7 Properties of model and residual subspace estimates 1896.1.8 Application to a chemical reaction process – revisited 1946.2 Accuracy of estimating PLS models 2026.2.1 Bias and variance of parameter estimation 2036.2.2 Comparing accuracy of PLS and OLS regression models 2056.2.3 Impact of error-in-variables structure upon PLS models 2126.2.4 Error-in-variable estimate for known See 2186.2.5 Error-in-variable estimate for unknown See 2196.2.6 Application to a distillation process – revisited 2236.3 Robust model estimation 2266.3.1 Robust parameter estimation 2286.3.2 Trimming approaches 2316.4 Small sample sets 2326.5 Tutorial session 2377 Monitoring multivariate time-varying processes 2407.1 Problem analysis 2417.2 Recursive principal component analysis 2427.3 Moving window principal component analysis 2447.3.1 Adapting the data correlation matrix 2447.3.2 Adapting the eigendecomposition 2477.3.3 Computational analysis of the adaptation procedure 2517.3.4 Adaptation of control limits 2527.3.5 Process monitoring using an application delay 2537.3.6 Minimum window length 2547.4 A simulation example 2577.4.1 Data generation 2577.4.2 Application of PCA 2587.4.3 Utilizing MWPCA based on an application delay 2617.5 Application to a Fluid Catalytic Cracking Unit 2657.5.1 Process description 2667.5.2 Data generation 2687.5.3 Pre-analysis of simulated data 2727.5.4 Application of PCA 2737.5.5 Application of MWPCA 2757.6 Application to a furnace process 2787.6.1 Process description 2787.6.2 Description of sensor bias 2797.6.3 Application of PCA 2807.6.4 Utilizing MWPCA based on an application delay 2827.7 Adaptive partial least squares 2867.7.1 Recursive Adaptation of SX0X0 and Sx0y0 2877.7.2 Moving Window Adaptation of SX0X0 and Sx0y0 2877.7.3 Adapting the number of source signals 2877.7.4 Adaptation of the PLS model 2907.8 Tutorial Session 2928 Monitoring changes in covariance structure 2938.1 Problem analysis 2948.1.1 First intuitive example 2948.1.2 Generic statistical analysis 2978.1.3 Second intuitive example 2998.2 Preliminary discussion of related techniques 3048.3 Definition of primary and improved residuals 3058.3.1 Primary residuals for eigenvectors 3068.3.2 Primary residuals for eigenvalues 3078.3.3 Comparing both types of primary residuals 3078.3.4 Statistical properties of primary residuals 3128.3.5 Improved residuals for eigenvalues 3158.4 Revisiting the simulation examples of Section 8.1 3178.4.1 First simulation example 3188.4.2 Second simulation example 3218.5 Fault isolation and identification 3248.5.1 Diagnosis of step-type fault conditions 3258.5.2 Diagnosis of general deterministic fault conditions 3288.5.3 A simulation example 3288.6 Application study of a gearbox system 3318.6.1 Process description 3328.6.2 Fault description 3328.6.3 Identification of a monitoring model 3348.6.4 Detecting a fault condition 3388.7 Analysis of primary and improved residuals 3418.7.1 Central limit theorem 3418.7.2 Further statistical properties of primary residuals 3448.7.3 Sensitivity of statistics based on improved residuals 3498.8 Tutorial session 353Part IV Description of Modeling Methods 3559 Principal component analysis 3579.1 The core algorithm 3579.2 Summary of the PCA algorithm 3629.3 Properties of a PCA model 36310 Partial least squares 37510.1 Preliminaries 37510.2 The core algorithm 37710.3 Summary of the PLS algorithm 38010.4 Properties of PLS 38110.5 Properties of maximum redundancy PLS 396References 410Index 427