Efficient recursive principal component analysis algorithms for process monitoring

Industrial and Engineering Chemistry Research

Volumn 49, Issue 1, 2010, Pages 252-259

  Elshenawy, Lamiaa M ^a   Yin, Shen ^b   Naik, Amol S ^b   Ding, Steven X ^b  

^a MENOUFIA UNIVERSITY   (Egypt)

^b UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE SUBSPACE TRACKING; COMPUTATION COSTS; CONTINUOUS STIRRED TANK REACTOR; DATA PROJECTION; EIGENVALUE DECOMPOSITION; EIGENVALUES; EIGENVECTORS; FALSE ALARMS; FIRST-ORDER; MONITORING SYSTEM; NONISOTHERMAL; PERTURBATION ANALYSIS; PRINCIPAL COMPONENTS; SAMPLE COVARIANCE MATRIX;

ALGORITHMS; COMPUTATIONAL EFFICIENCY; COST REDUCTION; COVARIANCE MATRIX; EIGENVALUES AND EIGENFUNCTIONS; ERRORS; MESH GENERATION; PROCESS CONTROL; PROCESS MONITORING; SINGULAR VALUE DECOMPOSITION;

PRINCIPAL COMPONENT ANALYSIS;

EID: 74249108882     PISSN: 08885885     EISSN: None     Source Type: Journal    
DOI: 10.1021/ie900720w     Document Type: Article

References (31)

1. Pearson, K. On Lines and Planes of Closest Fit to Systems of Points in Space. Philos. Mag. 1901, 2, 559-572.
2. Hotelling, H. Analysis of a complex of statistical variables into principal components. J. Educ. Psych. 1933, 24, 417-441.
3. Chiang, L. H.; Russel, E.; Braatz, R. Fault Detection and Diagnosis in Industrial Systems; Springer: London, 2001.
4. Liu, X.; Chen, T.; Thornton, S. Eigenspace Updating for Non- Stationary Process and Its Application to Face Recognition. Pattern Recognit. 2003, 36, 1945-1959.
5. Malinowski, E. R. Factor Analysis in Chemistry; Wiley: New York, 1991.
6. Jackson, J. E. A User's Guide to Principal Components; John Wiley & Sons, Inc: New York, 1991.
7. Raich, A. C.; Çinar, A. Multivariate statistical methods for monitoring continuous processes: assessment of discrimination power of disturbance models and diagnosis of multiple disturbances. Chemom. Intell. Lab. Syst. 1995, 30, 37-48.
8. Dong, D.; McAvoy, T. J. Batch tracking via nonlinear principal component analysis. AIChE J. 1996, 42, 2199-2208.
9. Wold, S. Exponentially weighted moving principal component analysis and projection to latent structures. Chemom. Intell. Lab. Syst. 1994, 23, 149-161.
10. Li, W.; Yue, H.; Valle-Cervantes, S.; Qin, S. Recursive PCA for adaptive process monitoring. J. Process Control 2000, 10, 471-486.
11. Wang, X.; Kruger, U.; Lennox, B. Recursive partial least squares algorithms for monitoring complex industrial processes. Control Eng. Practice 2003, 11, 613-632.
12. Jin., H.; Lee, Y.-H.; Lee, G.; Han, C. Robust Recursive Principal Component Analysis Modeling for Adaptive Monitoring. Ind. Eng. Chem. Res. 2006, 45, 696-703.
13. Choi, S. W.; Martin, E. B.; Morris, A. J.; Lee, I.-B. Adaptive Multivariate Statistical Process Control for Monitoring Time-Varying Processes. Ind. Eng. Chem. Res. 2006, 45, 3108-3118.
14. He, X. B.; Yang, Y. P. Variable MWPCA for Adaptive Process Monitoring. Ind. Eng. Chem. Res. 2008, 47, 419-427.
15. Naik, A. S.; Yin, S.; Ding, S. X. Recursive identification algorithm for parity space based fault detection systems. Preprints of the 7th IFAC SafeProcess, Jun 30-Jul 3, 2009, Barcelona, Spain.
16. Yin, S.; Naik, A. S.; Ding, S. X. Adaptive process monitoring based on parity space methods. Preprints of the 7th IFAC SafeProcess, Jun 30- Jul 3, 2009, Barcelona, Spain.
17. Wang, X.; Kruger, U.; Irwin, G. Process monitoring approach using fast moving window PCA. Ind. Eng. Chem. Res. 2005, 44, 5691-5702.
18. Liu, X.; Kruger, U.; Littler, T.; Xie, L.; Wang, S. Moving window kernel PCA for adaptive monitoring of nonlinear processes. Chemom. Intell. Lab. Syst. 2009, 96, 132-143.
19. Hall, P.; Marshall, D.; Martin, R. Incrementally Computing Eigenspace Models. Proc. Br. Machine Vision Conf. 1998, 286-295.
20. Hall, P.; Marshall, D.; Martin, R. Merging and Splitting Eigenspace Models. IEEE Trans. Pattern Anal. Machine Intell. 2000, 22, 1042-1049.
21. Hall, P.; Marshall, D.; Martin, R. Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition. Image Vision Comput. 2002, 20, 1009-1016.
22. Champagne, B. Adaptive Eigendecomposition of Data Covariance Matrices Based on First-Order Perturbations. IEEE Trans. Signal Process. 1994, 42, 2758-2770.
23. Willink, T. Efficient Adaptive SVD Algorithm for MIMO Applications. IEEE Trans. Signal Process. 2008, 56, 615-622.
24. Doukopoulos, X. G.; Moustakides, G. V. Fast and Stable Subspace Tracking. IEEE Trans. Signal Process. 2008, 56, 1452-1465.
25. Qin, S. J. Statistical process monitoring: basics and beyond. J. Chemom. 2003, 17, 480-502.
26. Stewart, G.; Sun, J. Matrix perturbation theory; Academic Press, San Diego, 1990.
27. Golub, G.; Loan., C. V. Matrix computations, 3rd ed.; Johns Hopkins Press Ltd.: London, 1996.
28. Himes, D.; Storer, R.; Georgakis, C. Determination of the number of principal components for disturbance detection and isolation. Proc. Am. Control Conf. 1994, 1279-1283.
29. Valle, S.; Li, W.; Qin, S. Selection of the Number of Principal Components: The Variance of the Reconstruction Error Criterion with a Comparison to other Methods. Ind. Eng. Chem. Res. 1999, 38, 4389-4401.
30. Jackson, J. E.; Mudholkar, G. Control procedures for residuals associated with principal component analysis. J. Process Control 1979, 21, 341-349.
31. Yoon, S.; MacGregor, J. F. Fault Diagnosis With Multivariate Statistical Models Part I: Using Steady State Fault Signatures. J. Process Control 2001, 11, 387-400.