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A new fault detection index based on Mahalanobis distance and kernel method

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Abstract

This paper suggests an extension of the PCMD index proposed for sensor fault diagnosis in linear systems to the nonlinear case. The proposed index is entitled KPCMD, and it is based on Mahalanobis distance and moving window kernel principal component analysis (MWKPCA) technique. The principle of this index is to detect dissimilarity between a reference KPCA model that represents normal operation of the system and a current KPCA model that represents current system behavior. The proposed KPCMD index compute Mahalanobis distance between principal components corresponding to the reference KPCA model and those corresponding to the current KPCA model which are obtained online using MWKPCA. The proposed KPCMD indices have been applied successfully for monitoring of numerical example as well a continuous stirred tank reactor (CSTR).

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References

  1. Qin SJ (2003) Statistical process monitoring: basics and beyond. J Chemom 17(8):480–502

    Article  Google Scholar 

  2. McAvoy TJ (2002) Intelligent "control" applications in the process industries. Annu Rev Control 26(1):75–86

    Article  Google Scholar 

  3. Frank PM (1990) Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy—a survey and some new results. Automatica 26(3):459–474

    Article  MathSciNet  MATH  Google Scholar 

  4. Tharraut Y, Mourot G, Ragot J, Maquin D (2008) Fault detection and isolation with robust principal component analysis. Int J Appl Math Comput Sci 18(4):429–442

    MATH  Google Scholar 

  5. Jaffel I, Taouali O, Elaissi I, Messaoud H (2014) A new online fault detection method based on PCA technique. IMAJ Math Control Inf 31(4):487–499

    Article  MathSciNet  MATH  Google Scholar 

  6. Li G, Qin SJ, Zhou D (2010) Geometric properties of partial least squares for process monitoring. Automatica 46(1):204–210

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang Y, Ma C (2011) Fault diagnosis of nonlinear processes using multiscale KPCA and multiscale KPLS. ChemEngSci 66:66–72

    Google Scholar 

  8. Lee J, Yoo C, Lee I (2004a) Statistical process monitoring with independent component analysis. J Process Control 14(5):467–485

    Article  Google Scholar 

  9. Zhao C, Wang F, Mao Z, Lu N, Jia M (2008) Adaptive monitoring based on independent component analysis for multiphase batch processes with limited modeling data. Am ChemSoc 47:3104–3113

    Google Scholar 

  10. Dunia R, Qin J, Edgar TF, McAvoy TJ 1996 Identification of faulty sensors using principal component analysis, AIChE Journal

  11. Harkat MF, Mourot G, Ragot J 2001 “Sensor failure detection and Isolation of air quality monitoring network”. 4th International Conference on Acoustical and Vibratory Surveillance Methods and Diagnostic Techniques, Compiègne, France

  12. Wang X, Kruger U, Irwin GW (2005) Process monitoring approach using fast moving window PCA. Ind Eng Chem Res 44:5691–5702

    Article  Google Scholar 

  13. Jeng JC (2010) Adaptive process monitoring using efficient recursive PCA and moving window PCA algorithms. J Taiwan Inst Chem Eng 41:475–481

    Article  Google Scholar 

  14. Krzanowski W (1979) Between-groups comparison of principal components. J Am Stat Assoc 74:703–707

    Article  MathSciNet  MATH  Google Scholar 

  15. Jaffel I, Taouali O, Harkat MF, Messaoud H (2015) Online process monitoring using a new PCMD index. Int J Adv Manuf Technol 80(5):947–957

    Article  Google Scholar 

  16. Schölkopf B, Smola A, Muller K-R (2012) Nonlinear component analysis as kernel eigenvalue problem. Neural Comput 10:1299–1319

    Article  Google Scholar 

  17. Lee JM, Yoo C, Choi SK, Vanrolleghemb PA, Lee I (2004b) Nonlinear process monitoring using kernel principal component analysis. ChemEngSci 59:223–234

    Google Scholar 

  18. Taouali O, Elaissi I, Messaoud H (2012) Online identification of non-linear system using reduced kernel principal component analysis. Neural Comput 21:161–169

    Article  Google Scholar 

  19. Fazai R, Taouali O, Harkat MF, Bouguila NA 2016 new fault detection method for nonlinear process monitoring. Int J Adv Manuf Technol

  20. Aronszajn N (1950) Theory of reproducing kernels. Trans Am Math Soc 68(3):337–404

    Article  MathSciNet  MATH  Google Scholar 

  21. Mika S, Schölkopf B, Smola AJ, Muller, KJ; Scholz M.; Ratsh G, “Kernel PCA and de-nosing in feature spaces”. Proc AdV Neural Inform Process Syst. II 1999, pp. 536–542.

  22. Liu X, Xie L, Kruger U, Littler T, Wang S (2009) Moving window kernel PCA for adaptive monitoring of nonlinear processes. ChemomIntell Lab Syst 96:132–143

    Article  Google Scholar 

  23. Dong D, McAvoy TJ (1996) Nonlinear principal component analysis-based on principal curves and neural networks. Comput Chem Eng 20:65–78

    Article  Google Scholar 

  24. Cho JH, Lee JM, Choi SW, Lee DW, Lee IB (2005) Fault identification for process monitoring using kernel principal component analysis. Chem Eng Sci 60:279–288

    Article  Google Scholar 

  25. Vapnik VN (1998) Statistical learning theory. Wiley, New York

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Research Laboratory of Automatic, Signal and Image Processing (LARATSI), National School of Engineering Monastir, University of Monastir, Rue IbnELJazzar, 5019, Monastir, Tunisia

    Hajer Lahdhiri, Okba Taouali, Ilyes Elaissi, Ines Jaffel & Hassani Messaoud

  2. Department of Electronics, Faculty of Engineering Annaba Badji Mokhtar BP. 12, 23000, Annaba, Algeria

    Mohamed Faouzi Harakat

Authors
  1. Hajer Lahdhiri
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  2. Okba Taouali
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  3. Ilyes Elaissi
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  4. Ines Jaffel
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  5. Mohamed Faouzi Harakat
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  6. Hassani Messaoud
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Correspondence to Okba Taouali.

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Lahdhiri, H., Taouali, O., Elaissi, I. et al. A new fault detection index based on Mahalanobis distance and kernel method. Int J Adv Manuf Technol 91, 2799–2809 (2017). https://doi.org/10.1007/s00170-016-9887-3

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  • DOI: https://doi.org/10.1007/s00170-016-9887-3

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