Fault detection and isolation with robust principal component analysis

Yvon Tharrault; Gilles Mourot; José Ragot; Didier Maquin

International Journal of Applied Mathematics and Computer Science (2008)

  • Volume: 18, Issue: 4, page 429-442
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Yvon Tharrault, et al. "Fault detection and isolation with robust principal component analysis." International Journal of Applied Mathematics and Computer Science 18.4 (2008): 429-442. <http://eudml.org/doc/207897>.

@article{YvonTharrault2008,
abstract = {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.},
author = {Yvon Tharrault, Gilles Mourot, José Ragot, Didier Maquin},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {principal component analysis; robustness; outliers; fault detection and isolation; structured residual vector; variable reconstruction},
language = {eng},
number = {4},
pages = {429-442},
title = {Fault detection and isolation with robust principal component analysis},
url = {http://eudml.org/doc/207897},
volume = {18},
year = {2008},
}

TY - JOUR
AU - Yvon Tharrault
AU - Gilles Mourot
AU - José Ragot
AU - Didier Maquin
TI - Fault detection and isolation with robust principal component analysis
JO - International Journal of Applied Mathematics and Computer Science
PY - 2008
VL - 18
IS - 4
SP - 429
EP - 442
AB - 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.
LA - eng
KW - principal component analysis; robustness; outliers; fault detection and isolation; structured residual vector; variable reconstruction
UR - http://eudml.org/doc/207897
ER -

References

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  14. Rousseeuw P. (1987). Robust Regression and Outliers Detection, Wiley, New York, NY. Zbl0711.62030
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