Principal component analysis (PCA) is a powerful fault detection and isolation method. However, the classical PCA, which is based on the estimation of the sample mean and covariance matrix of the data, is very sensitive to outliers in the training data set. Usually robust principal component analysis is applied to remove the effect of outliers on the PCA model. In this paper, a fast two-step algorithm is proposed. First, the objective was to find an accurate estimate of the covariance matrix of the data so that a PCA model might be developed that could then be used for fault detection and isolation. A very simple estimate derived from a one-step weighted variance-covariance estimate is used (Ruiz-Gazen, 1996). This is a “local” matrix of variance which tends to emphasize the contribution of close observations in comparison with distant observations (outliers). Second, structured residuals are used for multiple fault detection and isolation. These structured residuals are based on the reconstruction principle, and the existence condition of such residuals is used to determine the detectable faults and the isolable faults. The proposed scheme avoids the combinatorial explosion of faulty scenarios related to multiple faults to be considered. Then, this procedure for outliers detection and isolation is successfully applied to an example with multiple faults.
@article{bwmeta1.element.bwnjournal-article-amcv18i4p429bwm,
author = {Yvon Tharrault and Gilles Mourot and Jos\'e Ragot and Didier Maquin},
title = {Fault detection and isolation with robust principal component analysis},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {18},
year = {2008},
pages = {429-442},
zbl = {1156.93399},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv18i4p429bwm}
}
Yvon Tharrault; Gilles Mourot; José Ragot; Didier Maquin. Fault detection and isolation with robust principal component analysis. International Journal of Applied Mathematics and Computer Science, Tome 18 (2008) pp. 429-442. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv18i4p429bwm/
[000] Chiang L. H. and Colegrove L. F. (2007). Industrial implementation of on-line multivariate quality control, Chemometrics and Intelligent Laboratory Systems 88(2): 143-153.
[001] Croux C., Filzmoser P. and Oliveira M. (2007). Algorithms for projection-pursuit robust principal component analysis, Chemometrics and Intelligent Laboratory Systems 87(2): 218-225.
[002] Croux C. and Ruiz-Gazen A. (2005). High breakdown estimators for principal components: The projectionpursuit approach revisited, Journal of Multivariate Analysis 95(1): 206-226. | Zbl 1065.62040
[003] Dunia R. and Qin S. (1998). A subspace approach to multidimensional fault identification and reconstruction, American Institute of Chemical Engineers Journal 44 (8): 1813-1831.
[004] Harkat M.-F., Mourot G. and Ragot J. (2006). An improved PCA scheme for sensor FDI: Application to an air quality monitoring network, Journal of Process Control 16(6): 625-634.
[005] Hubert M., Rousseeuw P. and Van den Branden, K. (2005). RobPCA: A new approach to robust principal component analysis, Technometrics 47 (1): 64-79.
[006] Hubert M., Rousseeuw P. and Verboven S. (2002). A fast method for robust principal components with applications to chemometrics, Chemometrics and Intelligent Laboratory Systems 60(1-2): 101-111.
[007] Jackson J. and Mudholkar G. S. (1979). Control procedures for residuals associated with principal component analysis, Technometrics 21(3): 341-349. | Zbl 0439.62039
[008] Kano M. and Nakagawa Y. (2008). Data-based process monitoring, process control, and quality improvement: Recent developments and applications in steel industry, Computers & Chemical Engineering 32(1-2): 12-24.
[009] Li G. and Chen Z. (1985). Projection-pursuit approach to robust dispersion matrices and principal components: Primary theory and Monte Carlo, Journal of the American Statistical Association 80(391): 759-766. | Zbl 0595.62060
[010] Li W. and Qin S. J. (2001). Consistent dynamic PCA based on errors-in-variables subspace identification, Journal of Process Control 11(6): 661-678.
[011] Maronna R. A., Martin R. and Yohai V. J. (2006). Robust Statistics: Theory and Methods, Wiley, New York, NY. | Zbl 1094.62040
[012] Qin S. J. (2003). Statistical process monitoring: Basics and beyond, Journal of Chemometrics 17(8-9): 480-502.
[013] Rousseeuw P. (1987). Robust Regression and Outliers Detection, Wiley, New York, NY. | Zbl 0711.62030
[014] Rousseeuw P. and Van Driessen K. (1999). Fast algorithm for the minimum covariance determinant estimator, Technometrics 41(3): 212-223.
[015] Ruiz-Gazen, A. (1996). A very simple robust estimator of a dispersion matrix, Computational Statistics and Data Analysis 21(2): 149-162. | Zbl 0900.62274
[016] Yue, H. and Qin, S. (2001). Reconstruction-based fault identification using a combined index, Industrial and Engineering Chemistry Research 40(20): 4403-4414.