Combination Method of Kernel Principal Component Analysis and Independent Component Analysis for Process Monitoring

Abstract:

A combination method of kernel principal component analysis (KPCA) and independent component analysis (ICA) for process monitoring is proposed. The new method is a two-phase algorithm: whitened KPCA plus ICA. KPCA spheres data and makes the data structure become as linearly separable as possible by virtue of an implicit nonlinear mapping determined by kernel. ICA seeks the projection directions in the KPCA whitened space, making the distribution of the projected data as non-gaussian as possible. The application to the Tennessee Eastman (TE) simulated process indicates that the proposed process monitoring method can effectively capture the nonlinear relationship in process variables. Its performance significantly outperforms monitoring method based on ICA or KPCA.

• Periodical: Applied Mechanics and Materials (Volumes 249-250)
• Pages: 153-158
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.249-250.153
• Online since: December 2012
• Authors: Ying Wang Xiao, Ying Du
• Keywords: Independent Component Analysis (ICA), Kernel Principal Component Analysis, Process Monitoring, Tennessee Eastman

References

[1] M.A. Bin Shams, H. M. Budman, T. A. Duever, Fault detection, identification and diagnosis using CUSUM based PCA, Chemical Engineering Science. 66(20) (2011) 4488-4498.

DOI: 10.1016/j.ces.2011.05.028

[2] Manuel Zarzo, Pau Martí, Modeling the variability of solar radiation data among weather stations by means of principal components analysis, Applied Energy. 88(8) (2011) 2775-2784.

DOI: 10.1016/j.apenergy.2011.01.070

[3] Chun-Chin Hsu, Mu-Chen Chen, Long-Sheng Chen, Intelligent ICA–SVM fault detector for non-Gaussian multivariate process monitoring, Expert Systems with Applications. 37(4) (2010) 3264-3273.

DOI: 10.1016/j.eswa.2009.09.053

[4] Hyvarinen A, Oja E, Independent Component Analysis: Algorithms and Applications, Neural Networks. 13(4) (2000) 411-430.

DOI: 10.1016/s0893-6080(00)00026-5

[5] Lee J M, Yoo C K, Lee I B, Statistical Process Monitoring with Independent Component Analysis, Journal of Process Control. 14(5) (2004) 467-485.

DOI: 10.1016/j.jprocont.2003.09.004

[6] Lee J M, Yoo C K, Choi S W, Nonlinear Process Monitoring Using Kernel Principal Component Analysis, Chemical Engineering Science. 59(1) (2004) 223-234.

DOI: 10.1016/j.ces.2003.09.012

[7] Matej Kristan, Aleš Leonardis, Danijel Skočaj, Multivariate online kernel density estimation with Gaussian kernels, Pattern Recognition. 44(10) (2011) 2630–2642.

DOI: 10.1016/j.patcog.2011.03.019

[8] Li XIONG, Jun LIANG, Jixin QIAN, Multivariate Statistical Process Monitoring of an Industrial Polypropylene Catalyzer Reactor with Component Analysis and Kernel Density Estimation, Chinese Journal of Chemical Engineering. 15(4) (2007) 524–532.

DOI: 10.1016/s1004-9541(07)60119-0

[9] Jidong Shao, Gang Rong, Jong Min Lee, Learning a data-dependent kernel function for KPCA-based nonlinear process monitoring, Chemical Engineering Research and Design. 87 (11) (2009) 1471–1480.

DOI: 10.1016/j.cherd.2009.04.011

[10] Zhiqiang Ge, Zhihuan Song, A distribution-free method for process monitoring, Expert Systems with Applications. 38(8) (2011) 9821–9829.

DOI: 10.1016/j.eswa.2011.02.048