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Evaluation of nonlinear scaling and transformation for nonlinear process fault detection

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Abstract

On-line fault detection of nonlinear processes involving dynamic dependencies and similar/overlapping fault signatures, is a fairly challenging and daunting task. Early detection and unambiguous diagnosis require that the monitoring approaches are able to deal with these daunting features. This paper compares two broad multivariate statistical approaches proposed in the literature for the detection task: (i) nonlinear transformations to generate linear maps and their dynamic variants in high dimensional feature space, as exemplified by kernel principal component analysis and dynamic kernel principal component analysis, and (ii) nonlinear scaling of the data to promote better self aggregation of data classes and hence improved discrimination, as exemplified by correspondence analysis. Using the Tennessee Eastman benchmark problem, we compare the performance of the above methods with respect to the known metrics such as detection delays, false alarm rates (Type I error) and missed detection rates (Type II error). As well, we compare the methods on the basis of computational cost and provide summarizing remarks on the ease of deployment and maintenance of such approaches for plant-wide fault detection of complex chemical processes.

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References

  1. Macgregor, J.F., Kourti, T.: Statistical process-control of multivariate processes. Control Eng. Pract. 3, 403–414 (1995)

    Article  Google Scholar 

  2. Wold, S., Trygg, J., Berglund, A., Antti, H.: Some recent developments in PLS modeling. Chemom. Intell. Lab. Syst. 58, 131–150 (2001)

    Article  Google Scholar 

  3. He, Q.P., Qin, S.J., Wang, J.: A new fault diagnosis method using fault directions in fisher discriminant analysis. AIChE J. 51, 555–571 (2005)

    Article  Google Scholar 

  4. Bakshi, B.R.: Multiscale PCA with application to multivariate statistical process monitoring. AIChE J. 44, 1596–1610 (1998)

    Article  Google Scholar 

  5. Rotem, Y., Wachs, A., Lewin, D.R.: Ethylene compressor monitoring using model-based PCA. AIChE J. 46, 1825–1836 (2000)

    Article  Google Scholar 

  6. Kramer, M.A.: Autoassociative neural networks. Comput. Chem. Eng. 16, 313–328 (1992)

    Article  Google Scholar 

  7. Kramer, M.A.: Nonlinear principal component analysis using autoassociative neural networks. AIChE J. 37, 233–243 (1991)

    Article  Google Scholar 

  8. Dong, D., McAvoy, T.J.: Nonlinear principal component analysis—based on principal curves and neural networks. Comput. Chem. Eng. 20, 65–78 (1996)

    Article  Google Scholar 

  9. Jia, F., Martin, E.B., Morris, A.J.: Non-linear principal components analysis for process fault detection. Comput. Chem. Eng. 22, S851–S854 (1998)

    Article  Google Scholar 

  10. Lin, W.L., Qian, Y., Li, X.X.: Nonlinear dynamic principal component analysis for on-line process monitoring and diagnosis. Comput. Chem. Eng. 24, 423–429 (2000)

    Article  Google Scholar 

  11. Fourie, S.H., de Vaal, P.: Advanced process monitoring using an on-line non-linear multiscale principal component analysis methodology. Comput. Chem. Eng. 24, 755–760 (2000)

    Article  Google Scholar 

  12. Jakubek, S.M., Strasser, T.I.: Artificial neural networks for fault detection in large-scale data acquisition systems. Eng. Appl. Artif. Intell. 17, 233–248 (2004)

    Article  Google Scholar 

  13. Kulkarni, S.G., Chaudhary, A.K., Nandi, S., Tambe, S.S., Kulkarni, B.D.: Modeling and monitoring of batch processes using principal component analysis (PCA) assisted generalized regression neural networks (GRNN). Biochem. Eng. J. 18, 193–210 (2004)

    Article  Google Scholar 

  14. Cheng, C., Chiu, M.S.: Nonlinear process monitoring using JITL-PCA. Chemometr. Intell. Lab. Syst. 76, 1–13 (2005)

    Article  Google Scholar 

  15. Maulud, A., Wang, D., Romagnoli, J.A.: A multi-scale orthogonal nonlinear strategy for multi-variate statistical process monitoring. J. Process Control 16, 671–683 (2006)

    Article  Google Scholar 

  16. Yoo, C.K., Vanrolleghem, P.A., Lee, I.B.: Nonlinear modeling and adaptive monitoring with fuzzy and multivariate statistical methods in biological wastewater treatment plants. J. Biotechnol. 105, 135–163 (2003)

    Article  Google Scholar 

  17. Mahadevan, S., Shah, S.L.: Fault detection and diagnosis in process data using one-class support vector machines. J. Process Control 19, 1627–1639 (2009)

    Article  Google Scholar 

  18. Zhang, Y.W., Li, Z.M., Zhou, H.: Statistical analysis and adaptive technique for dynamical process monitoring. Chem. Eng. Res. Des. 88, 1381–1392 (2010)

    Article  Google Scholar 

  19. Kim, K., Lee, J.M., Lee, I.B.: A novel multivariate regression approach based on kernel partial least squares with orthogonal signal correction. Chemometr. Intell. Lab. Syst. 79, 22–30 (2005)

    Article  Google Scholar 

  20. Xi, Z., Weiwu, Y., Xu, Z., Huihe, S.: Nonlinear biological batch process monitoring and fault identification based on kernel fisher discriminant analysis. Process Biochem. 42, 1200–1210 (2007)

    Article  Google Scholar 

  21. Scholkopf, B., Smola, A., Muller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10, 1299–1319 (1998)

    Article  Google Scholar 

  22. Choi, S.W., Lee, I.B.: Nonlinear dynamic process monitoring based on dynamic kernel PCA. Chem. Eng. Sci. 59, 5897–5908 (2004)

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. Ge, Z.Q., Yang, C.J., Song, Z.H.: Improved kernel PCA-based monitoring approach for nonlinear processes. Chem. Eng. Sci. 64, 2245–2255 (2009)

    Article  Google Scholar 

  25. Zhang, Y.W.: Enhanced statistical analysis of nonlinear processes using KPCA, KICA and SVM. Chem. Eng. Sci. 64, 801–811 (2009)

    Article  Google Scholar 

  26. Cheng, C.Y., Hsu, C.C., Chen, M.C.: Adaptive kernel principal component analysis (KPCA) for monitoring small disturbances of nonlinear processes. Ind. Eng. Chem. Res. 49, 2254–2262 (2010)

    Article  Google Scholar 

  27. Lee, J.M., Yoo, C., Lee, I.B.: Fault detection of batch processes using multiway kernel principal component analysis. Comput. Chem. Eng. 28, 1837–1847 (2004)

    Article  Google Scholar 

  28. Cui, P.L., Li, J.H., Wang, G.Z.: Improved kernel principal component analysis for fault detection. Expert Syst. Appl. 34, 1210–1219 (2008)

    Article  Google Scholar 

  29. Sumana, C., Bhushan, M., Venkateswarlu, C., Gudi, R.D.: Improved nonlinear process monitoring using KPCA with sample vector selection and combined index. Asia-Pac. J. Chem. Eng. 6, 460–469 (2011)

    Article  Google Scholar 

  30. Ding, C., He, X., Zha, H., Simon, H.: Unsupervised learning: self-aggregation in scaled principal component space. Paper presented at 6th European Conference on Principles of Data Mining and Knowledge Discovery, Berlin, Springer (2002)

  31. Khare, S.R., Bavdekar, V.A., Kadu, S.C., Detroja, K.P., Gudi, R.D.: Scaling and discrimination issues in monitoring, fault detection and diagnosis. Paper presented at: 8th International IFAC Symposium on Dynamics and Control of Process Systems, Cancún, Mexico (June 6–8, 2007,)

  32. Detroja, K.P., Gudi, R.D., Patwardhan, S.C., Roy, K.: Fault detection and isolation using correspondence analysis. Ind. Eng. Chem. Res. 45, 223–235 (2006)

    Article  Google Scholar 

  33. Greenacre, M.J.: Theory and application of correspondence analysis. Academic Press Inc, London (1984)

    Google Scholar 

  34. Choi, S.W., Lee, C., Lee, J.M., Park, J.H., Lee, I.B.: Fault detection and identification of nonlinear processes based on kernel PCA. Chemometr. Intell. Lab. Syst. 75, 55–67 (2005)

    Article  Google Scholar 

  35. Ku, W.F., Storer, R.H., Georgakis, C.: Disturbance detection and isolation by dynamic principal component analysis. Chemometr. Intell. Lab. Syst. 30, 179–196 (1995)

    Article  Google Scholar 

  36. Chiang, L.H., Russell, E.L., Braatz, R.D.: Fault detection and diagnosis in industrial systems. Springer-Verlag, London (2001)

    Book  MATH  Google Scholar 

  37. Hardle, W., Simar, L.: Applied multivariate statistical analysis, vol 13. MD Tech, Berlin (2003)

    Google Scholar 

  38. Detroja, K.P., Gudi, R.D., Patwardhan, S.C.: Plant-wide detection and diagnosis using correspondence analysis. Control Eng. Pract. 15, 1468–1483 (2007)

    Article  Google Scholar 

  39. Sumana, C., Mani, B., Venkateswarlu, C., Gudi, R.D.: Improved fault diagnosis using dynamic Kernel scatter-difference-based discriminant analysis. Ind. Eng. Chem. Res. 49, 8575–8586 (2010)

    Article  Google Scholar 

  40. Zhu, Z.B., Song, Z.H.: Fault diagnosis based on imbalance modified Kernel Fisher discriminant analysis. Chem. Eng. Res. Des. 88, 936–951 (2010)

    Article  Google Scholar 

  41. Russell, E.L., Chiang, L.H., Braatz, R.D.: Fault detection in industrial processes using canonical variate analysis and dynamic principal component analysis. Chemometr. Intell. Lab. Syst. 51, 81–93 (2000)

    Article  Google Scholar 

  42. Chiang, L.H., Russell, E.L., Braatz, R.D.: Fault diagnosis in chemical processes using Fisher discriminant analysis, discriminant partial least squares, and principal component analysis. Chemometr. Intell. Lab. Syst. 50, 243–252 (2000)

    Article  Google Scholar 

  43. Raich, A., Cinar, A.: Statistical process monitoring and disturbance diagnosis in multivariable continuous processes. AIChE J. 42, 995–1009 (1996)

    Article  Google Scholar 

  44. Botev, Z.I., Grotowski, J.F., Kroese, D.P.: Kernel density estimation via diffusion. Ann. Stat. 38, 2916–2957 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  45. Li, J.H., Cui, P.L.: Improved kernel fisher discriminant analysis for fault diagnosis. Expert Syst. Appl. 36, 1423–1432 (2009)

    Article  Google Scholar 

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Authors and Affiliations

  1. Indian Institute of Chemical Technology, Hyderabad, India

    C. Sumana

  2. Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India

    C. Sumana & Ravindra D. Gudi

  3. Department of Electrical Engineering, Indian Institute of Technology, Hyderabad, India

    Ketan Detroja

Authors
  1. C. Sumana
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  2. Ketan Detroja
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  3. Ravindra D. Gudi
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Correspondence to Ravindra D. Gudi.

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Sumana, C., Detroja, K. & Gudi, R.D. Evaluation of nonlinear scaling and transformation for nonlinear process fault detection. Int J Adv Eng Sci Appl Math 4, 52–66 (2012). https://doi.org/10.1007/s12572-012-0060-4

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