Jump to ContentJump to Main Navigation
Show Summary Details
More options …

International Journal of Applied Mathematics and Computer Science

Journal of University of Zielona Gora and Lubuskie Scientific Society

4 Issues per year


IMPACT FACTOR 2016: 1.420
5-year IMPACT FACTOR: 1.597

CiteScore 2016: 1.81

SCImago Journal Rank (SJR) 2016: 0.524
Source Normalized Impact per Paper (SNIP) 2016: 1.440

Mathematical Citation Quotient (MCQ) 2016: 0.08

Open Access
Online
ISSN
2083-8492
See all formats and pricing
More options …
Volume 18, Issue 4 (Dec 2008)

Issues

Fault Detection and Isolation with Robust Principal Component Analysis

Yvon Tharrault
  • 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, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Gilles Mourot
  • 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, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ José Ragot
  • 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, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Didier Maquin
  • 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, France
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2008-12-30 | DOI: https://doi.org/10.2478/v10006-008-0038-3

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

  • 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.Web of ScienceCrossrefGoogle Scholar

  • 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.Web of ScienceCrossrefGoogle Scholar

  • Croux C. and Ruiz-Gazen A. (2005). High breakdown estimators for principal components: The projection-pursuit approach revisited, Journal of Multivariate Analysis 95(1): 206-226.CrossrefGoogle Scholar

  • 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.Google Scholar

  • 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.CrossrefGoogle Scholar

  • Hubert M., Rousseeuw P. and Van den Branden K. (2005). RobPCA: A new approach to robust principal component analysis, Technometrics 47 (1): 64-79.CrossrefGoogle Scholar

  • 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.CrossrefGoogle Scholar

  • Jackson J. and Mudholkar G. S. (1979). Control procedures for residuals associated with principal component analysis, Technometrics 21(3): 341-349.CrossrefGoogle Scholar

  • 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.Web of ScienceCrossrefGoogle Scholar

  • 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.Google Scholar

  • 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.CrossrefGoogle Scholar

  • Maronna R. A., Martin R. and Yohai V. J. (2006). Robust Statistics: Theory and Methods, Wiley, New York, NY.Google Scholar

  • Qin S. J. (2003). Statistical process monitoring: Basics and beyond, Journal of Chemometrics 17(8-9): 480-502.CrossrefGoogle Scholar

  • Rousseeuw P. (1987). Robust Regression and Outliers Detection, Wiley, New York, NY.Google Scholar

  • Rousseeuw P. and Van Driessen K. (1999). Fast algorithm for the minimum covariance determinant estimator, Technometrics 41(3): 212-223.CrossrefGoogle Scholar

  • Ruiz-Gazen A. (1996). A very simple robust estimator of a dispersion matrix, Computational Statistics and Data Analysis 21(2): 149-162.Google Scholar

  • Yue H. and Qin S. (2001). Reconstruction-based fault identification using a combined index, Industrial and Engineering Chemistry Research 40(20): 4403-4414.Google Scholar

About the article


Published Online: 2008-12-30

Published in Print: 2008-12-01


Citation Information: International Journal of Applied Mathematics and Computer Science, ISSN (Print) 1641-876X, DOI: https://doi.org/10.2478/v10006-008-0038-3.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Hajer Lahdhiri, Ilyes Elaissi, Okba Taouali, Mohamed Faouzi Harakat, and Hassani Messaoud
Stochastic Environmental Research and Risk Assessment, 2017
[2]
J Marzat, H Piet-Lahanier, F Damongeot, and E Walter
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2012, Volume 226, Number 10, Page 1329
[3]
Imen Gueddi, Othman Nasri, Kamal Benothman, and Philippe Dague
International Journal of Control, Automation and Systems, 2017, Volume 15, Number 2, Page 776
[4]
Przemyslaw Baranski, Piotr Pietrzak, and Xiaosong Hu
PLOS ONE, 2016, Volume 11, Number 3, Page e0150787
[5]
M.-F. HARKAT, G. MOUROT, and J. RAGOT
IFAC Proceedings Volumes, 2009, Volume 42, Number 8, Page 828
[6]
Baligh Mnassri, El Mostafa El Adel, and Mustapha Ouladsine
IFAC Proceedings Volumes, 2011, Volume 44, Number 1, Page 2851
[7]
Baligh Mnassri, El Mostafa El Adel, and Mustapha Ouladsine
IFAC Proceedings Volumes, 2012, Volume 45, Number 20, Page 421
[8]
Majdi Mansouri, Mohamed Nounou, Hazem Nounou, and Nazmul Karim
Journal of Loss Prevention in the Process Industries, 2016, Volume 40, Page 334
[9]
Raoudha Baklouti, Majdi Mansouri, Mohamed Nounou, Hazem Nounou, and Ahmed Ben Hamida
Journal of Computational Science, 2016, Volume 15, Page 34
[10]
Okba Taouali, Ines Jaffel, Hajer Lahdhiri, Mohamed Faouzi Harkat, and Hassani Messaoud
The International Journal of Advanced Manufacturing Technology, 2016, Volume 85, Number 5-8, Page 1547
[11]
Baligh Mnassri, El Mostafa El Adel, and Mustapha Ouladsine
Journal of Process Control, 2015, Volume 33, Page 60
[12]
Tawfik Najeh, Achraf Jabeur Telmoudi, and Lotfi Nabli
Arabian Journal for Science and Engineering, 2015, Volume 40, Number 8, Page 2123
[13]
Othman Nasri, Imen Gueddi, Philippe Dague, and Kamal Benothman
Journal of Control Science and Engineering, 2015, Volume 2015, Page 1
[14]
Mohammad Mahdi Tafarroj, Hadi Kalani, Majid Moavenian, and Afshin Ghanbarzadeh
Journal of the Indian Academy of Wood Science, 2014, Volume 11, Number 1, Page 33
[15]
G. Georgoulas, M.O. Mustafa, I.P. Tsoumas, J.A. Antonino-Daviu, V. Climente-Alarcon, C.D. Stylios, and G. Nikolakopoulos
Expert Systems with Applications, 2013, Volume 40, Number 17, Page 7024
[16]
Baligh Mnassri, El Mostafa El Adel, and Mustapha Ouladsine
Annual Reviews in Control, 2013, Volume 37, Number 1, Page 154
[17]
Silvia M. Zanoli and Giacomo Astolfi
International Journal of Rotating Machinery, 2013, Volume 2013, Page 1
[18]
Jiusun Zeng, Jinhui Cai, Lei Xie, Jianming Zhang, and Yong Gu
Industrial & Engineering Chemistry Research, 2013, Volume 52, Number 5, Page 2000
[19]
Ahmed Khelassi, Didier Theilliol, and Philippe Weber
International Journal of Applied Mathematics and Computer Science, 2011, Volume 21, Number 3
[20]
Piero Baraldi, Antonio Cammi, Francesca Mangili, and Enrico E. Zio
IEEE Transactions on Nuclear Science, 2010, Volume 57, Number 2, Page 793

Comments (0)

Please log in or register to comment.
Log in