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International Journal of Applied Mathematics and Computer Science

Journal of University of Zielona Gora and Lubuskie Scientific Society

IMPACT FACTOR 2015: 1.037
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Rank 83 out of 254 in category Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

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Fault Detection and Isolation with Robust Principal Component Analysis

Yvon Tharrault1 / Gilles Mourot1 / José Ragot1 / Didier Maquin1

Centre de Recherche en Automatique de Nancy (CRAN), Nancy Université, UMR 7039, CNRS 2, Avenue de la forět de Haye, F-54 516 Vandoeuvre-lès-Nancy, France1

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Citation Information: International Journal of Applied Mathematics and Computer Science. Volume 18, Issue 4, Pages 429–442, ISSN (Print) 1641-876X, DOI: 10.2478/v10006-008-0038-3, December 2008

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Fault Detection and Isolation with Robust Principal Component Analysis

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.

Keywords: principal component analysis; robustness; outliers; fault detection and isolation; structured residual vector; variable reconstruction

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