Research Article
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Fault Detection Using an Adapted Interval PCA Approach

Year 2025, Volume: 8 Issue: 1, 22 - 38, 03.07.2025
https://doi.org/10.53508/ijiam.1603442

Abstract

Principal Component Analysis (PCA) is a commonly employed technique in industrial systems for process monitoring and fault diagnosis, owing to its capability to efficiently process large datasets. Traditionally, it is applied to single-valued variables, where critical information can be lost in real scenarios with data uncertainties. Interval-valued PCA methods like Symbolic Covariance PCA (SCPCA) and Complete Information PCA (CIPCA) have been developed to enhance fault detection by incorporating data uncertainties in the PCA model. This paper presents a novel adaptation of SCPCA for detecting incertain sensor faults, marking the first correct implementation of SCPCA for fault detection and isolation (FDI). It aims to compare the performance of the new SCPCA with that of CIPCA, evaluating its reliability and accuracy in detecting sensor faults in a greenhouse prototype system.

References

  • Neal B Gallagher, Barry M Wise, Stephanie Watts Butler, Daniel D White Jr, and Gabriel G Barna. Development and benchmarking of multivariate statistical process control tools for a semiconductor etch process: improving robustness through model updating. IFAC Proceedings Volumes, 30(9):79–84, 1997.
  • S Joe Qin. Statistical process monitoring: basics and beyond. Journal of Chemometrics: A Journal of the Chemometrics Society, 17(8-9):480–502, 2003.
  • Lynne Billard and Edwin Diday. Symbolic data analysis: Conceptual statistics and data mining. John Wiley & Sons, 2012.
  • Tarek Ait-Izem, M-Faouzi Harkat, Messaoud Djeghaba, and Frédéric Kratz. On the application of interval pca to process monitoring: A robust strategy for sensor fdi with new efficient control statistics. Journal of Process Control, 63:29–46, 2018.
  • Chouaib Chakour, Azzedine Hamza, and Lamiaa M Elshenawy. Adaptive cipca based fault diagnosis scheme for uncertain time-varying processes. Neural Computing and Applications, 33(22):15413–15432, 2021.
  • Pierre Cazes, Ahlame Chouakria, Edwin Diday, and Yves Schektman. Extension de l’analyse en composantes principales à des données de type intervalle. Revue de Statistique appliquée, 45(3):5–24, 1997.
  • Francesco Palumbo and Carlo N Lauro. A pca for interval-valued data based on midpoints and radii. In New Developments in Psychometrics: Proceedings of the International Meeting of the Psychometric Society IMPS2001. Osaka, Japan, July 15–19, 2001, pages 641–648. Springer, 2003.
  • Lynne Billard. Sample covariance functions for complex quantitative data. In Proceedings of World IASC Conference, Yokohama, Japan, pages 157–163, 2008.
  • Jennifer Le-Rademacher and Lynne Billard. Symbolic covariance principal component analysis and visualization for interval-valued data. Journal of Computational and Graphical Statistics, 21(2):413–432, 2012.
  • Huiwen Wang, Rong Guan, and Junjie Wu. Cipca: Complete-information-based principal component analysis for interval-valued data. Neurocomputing, 86:158 169, 2012.
  • Chouaib Chakour, Abdelhafid Benyounes, and Mahmoud Boudiaf. Diagnosis of uncertain nonlinear systems using interval kernel principal components analysis: Application to a weather station. ISA transactions, 83:126–141, 2018.
  • Antonio Irpino and Rosanna Verde. Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9:143–175, 2015.
  • Ricardo Dunia and S Joe Qin. Joint diagnosis of process and sensor faults using principal component analysis. Control Engineering Practice, 6(4):457–469, 1998.
  • Francisco de AT De Carvalho, Paula Brito, and Hans-Hermann Bock. Dynamic clustering for interval data based on l 2 distance. Computational Statistics, 21:231 250, 2006.
  • Ramon E Moore. Interval analysis. Prentice-Hall, 1966.
  • Mohamed-Faouzi Harkat, Gilles Mourot, and José Ragot. An improved pca scheme for sensor fdi: Application to an air quality monitoring network. Journal of Process Control, 16(6):625–634, 2006.
  • J Edward Jackson and Govind S Mudholkar. Control procedures for residuals associated with principal component analysis. Technometrics, 21(3):341–349, 1979.
  • Mounir Guesbaya and Hassina Megherbi. Thermal modeling and prediction of soil less greenhouse in arid region based on particle swarm optimization. experimentally validated. In 2019 International Conference on Advanced Electrical Engineering (ICAEE), pages 1–6. IEEE, 2019.

Year 2025, Volume: 8 Issue: 1, 22 - 38, 03.07.2025
https://doi.org/10.53508/ijiam.1603442

Abstract

References

  • Neal B Gallagher, Barry M Wise, Stephanie Watts Butler, Daniel D White Jr, and Gabriel G Barna. Development and benchmarking of multivariate statistical process control tools for a semiconductor etch process: improving robustness through model updating. IFAC Proceedings Volumes, 30(9):79–84, 1997.
  • S Joe Qin. Statistical process monitoring: basics and beyond. Journal of Chemometrics: A Journal of the Chemometrics Society, 17(8-9):480–502, 2003.
  • Lynne Billard and Edwin Diday. Symbolic data analysis: Conceptual statistics and data mining. John Wiley & Sons, 2012.
  • Tarek Ait-Izem, M-Faouzi Harkat, Messaoud Djeghaba, and Frédéric Kratz. On the application of interval pca to process monitoring: A robust strategy for sensor fdi with new efficient control statistics. Journal of Process Control, 63:29–46, 2018.
  • Chouaib Chakour, Azzedine Hamza, and Lamiaa M Elshenawy. Adaptive cipca based fault diagnosis scheme for uncertain time-varying processes. Neural Computing and Applications, 33(22):15413–15432, 2021.
  • Pierre Cazes, Ahlame Chouakria, Edwin Diday, and Yves Schektman. Extension de l’analyse en composantes principales à des données de type intervalle. Revue de Statistique appliquée, 45(3):5–24, 1997.
  • Francesco Palumbo and Carlo N Lauro. A pca for interval-valued data based on midpoints and radii. In New Developments in Psychometrics: Proceedings of the International Meeting of the Psychometric Society IMPS2001. Osaka, Japan, July 15–19, 2001, pages 641–648. Springer, 2003.
  • Lynne Billard. Sample covariance functions for complex quantitative data. In Proceedings of World IASC Conference, Yokohama, Japan, pages 157–163, 2008.
  • Jennifer Le-Rademacher and Lynne Billard. Symbolic covariance principal component analysis and visualization for interval-valued data. Journal of Computational and Graphical Statistics, 21(2):413–432, 2012.
  • Huiwen Wang, Rong Guan, and Junjie Wu. Cipca: Complete-information-based principal component analysis for interval-valued data. Neurocomputing, 86:158 169, 2012.
  • Chouaib Chakour, Abdelhafid Benyounes, and Mahmoud Boudiaf. Diagnosis of uncertain nonlinear systems using interval kernel principal components analysis: Application to a weather station. ISA transactions, 83:126–141, 2018.
  • Antonio Irpino and Rosanna Verde. Basic statistics for distributional symbolic variables: a new metric-based approach. Advances in Data Analysis and Classification, 9:143–175, 2015.
  • Ricardo Dunia and S Joe Qin. Joint diagnosis of process and sensor faults using principal component analysis. Control Engineering Practice, 6(4):457–469, 1998.
  • Francisco de AT De Carvalho, Paula Brito, and Hans-Hermann Bock. Dynamic clustering for interval data based on l 2 distance. Computational Statistics, 21:231 250, 2006.
  • Ramon E Moore. Interval analysis. Prentice-Hall, 1966.
  • Mohamed-Faouzi Harkat, Gilles Mourot, and José Ragot. An improved pca scheme for sensor fdi: Application to an air quality monitoring network. Journal of Process Control, 16(6):625–634, 2006.
  • J Edward Jackson and Govind S Mudholkar. Control procedures for residuals associated with principal component analysis. Technometrics, 21(3):341–349, 1979.
  • Mounir Guesbaya and Hassina Megherbi. Thermal modeling and prediction of soil less greenhouse in arid region based on particle swarm optimization. experimentally validated. In 2019 International Conference on Advanced Electrical Engineering (ICAEE), pages 1–6. IEEE, 2019.
There are 18 citations in total.

Details

Primary Language English
Subjects Artificial Life and Complex Adaptive Systems
Journal Section Research Article
Authors

Anis El Maharat

Chakour Chouaib This is me

Azzedine Hamza This is me

Submission Date December 19, 2024
Acceptance Date April 21, 2025
Publication Date July 3, 2025
Published in Issue Year 2025 Volume: 8 Issue: 1

Cite

APA El Maharat, A., Chouaib, C., & Hamza, A. (2025). Fault Detection Using an Adapted Interval PCA Approach. International Journal of Informatics and Applied Mathematics, 8(1), 22-38. https://doi.org/10.53508/ijiam.1603442
AMA El Maharat A, Chouaib C, Hamza A. Fault Detection Using an Adapted Interval PCA Approach. IJIAM. July 2025;8(1):22-38. doi:10.53508/ijiam.1603442
Chicago El Maharat, Anis, Chakour Chouaib, and Azzedine Hamza. “Fault Detection Using an Adapted Interval PCA Approach”. International Journal of Informatics and Applied Mathematics 8, no. 1 (July 2025): 22-38. https://doi.org/10.53508/ijiam.1603442.
EndNote El Maharat A, Chouaib C, Hamza A (July 1, 2025) Fault Detection Using an Adapted Interval PCA Approach. International Journal of Informatics and Applied Mathematics 8 1 22–38.
IEEE A. El Maharat, C. Chouaib, and A. Hamza, “Fault Detection Using an Adapted Interval PCA Approach”, IJIAM, vol. 8, no. 1, pp. 22–38, 2025, doi: 10.53508/ijiam.1603442.
ISNAD El Maharat, Anis et al. “Fault Detection Using an Adapted Interval PCA Approach”. International Journal of Informatics and Applied Mathematics 8/1 (July2025), 22-38. https://doi.org/10.53508/ijiam.1603442.
JAMA El Maharat A, Chouaib C, Hamza A. Fault Detection Using an Adapted Interval PCA Approach. IJIAM. 2025;8:22–38.
MLA El Maharat, Anis et al. “Fault Detection Using an Adapted Interval PCA Approach”. International Journal of Informatics and Applied Mathematics, vol. 8, no. 1, 2025, pp. 22-38, doi:10.53508/ijiam.1603442.
Vancouver El Maharat A, Chouaib C, Hamza A. Fault Detection Using an Adapted Interval PCA Approach. IJIAM. 2025;8(1):22-38.

International Journal of Informatics and Applied Mathematics