Abstract
A local discriminant regularized soft k-means (LDRSKM) method with Bayesian inference is proposed for multimode process monitoring. LDRSKM extends the regularized soft k-means algorithm by exploiting the local and non-local geometric information of the data and generalized linear discriminant analysis to provide a better and more meaningful data partition. LDRSKM can perform clustering and subspace selection simultaneously, enhancing the separability of data residing in different clusters. With the data partition obtained, kernel support vector data description (KSVDD) is used to establish the monitoring statistics and control limits. Two Bayesian inference based global fault detection indicators are then developed using the local monitoring results associated with principal and residual subspaces. Based on clustering analysis, Bayesian inference and manifold learning methods, the within and cross-mode correlations, and local geometric information can be exploited to enhance monitoring performances for nonlinear and non-Gaussian processes. The effectiveness and efficiency of the proposed method are evaluated using the Tennessee Eastman benchmark process.
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References
Cai, L.F., Tian, X.M., Zhang, N., 2014. A kernel time structure independent component analysis method for nonlinear process monitoring. Chin. J. Chem. Eng., 22(11-12): 1243–1253. [doi:10.1016/j.cjche.2014.09.021]
Chiang, L.H., Russell, E.L., Braatz, R.D., 2000. Fault diagnosis in chemical processes using Fisher discriminant analysis, discriminant partial least squares, and principal component analysis. Chemometr. Intell. Lab. Syst., 50(2):243–252. [doi:10.1016/S0169-7439(99)00061-1]
Deng, X.G., Tian, X.M., 2013. Sparse kernel locality preserving projection and its application in nonlinear process fault detection. Chin. J. Chem. Eng., 21(2):163–170. [doi:10.1016/S1004-9541(13)60454-1]
Deng, X.G., Tian, X.M., Chen, S., 2013) Modified kernel principal component analysis based on local structure analysis and its application to nonlinear process fault diagnosis. Chemometr. Intell. Lab. Syst., 127: 195–209. [doi:10.1016/j.chemolab.2013.07.001]
Dong, W.W., Yao, Y., Gao, F.R., 2012. Phase analysis and identification method for multiphase batch processes with partitioning multi-way principal component analysis (MPCA) model. Chin. J. Chem. Eng., 20(6):1121–1127. [doi:10.1016/S1004-9541(12)60596-5]
Downs, J.J., Vogel, E.F., 1993. A plant-wide industrial process control problem. Comput. Chem. Eng., 17(3):245–255. [doi:10.1016/0098-1354(93)80018-I]
Feital, T., Kruger, U., Dutra, J., et al., 2013. Modeling and performance monitoring of multivariate multimodal processes. AIChE J., 59(5):1557–1569. [doi:10.1002/aic.13953]
Ge, Z.Q., Song, Z.H., 2010. Maximum-likelihood mixture factor analysis model and its application for process monitoring. Chemometr. Intell. Lab. Syst., 102(1):53–61. [doi:10.1016/j.chemolab.2010.04.002]
Ge, Z.Q., Song, Z.H., 2012. A distribution-free method for process monitoring. Exp. Syst. Appl., 38(8):9812–9829. [doi:10.1016/j.eswa.2011.02.048]
Ge, Z.Q., Zhang, M.G., Song, Z.H., 2010. Nonlinear process monitoring based on linear subspace and Bayesian inference. J. Process Contr., 20(5):676–688. [doi:10.1016/j.jprocont.2010.03.003]
Ge, Z.Q., Song, Z.H., Gao, F.R., 2013. Review of recent research on data-based process monitoring. Ind. Eng. Chem. Res., 52(10):3543–3562. [doi:10.1021/ie302069q]
Ghosh, K., Ramteke, M., Srinivasan, R., 2014) Optimal variable selection for effective statistical process monitoring. Comput. Chem. Eng., 60: 260–276. [doi:10.1016/j.compchemeng.2013.09.014]
He, X.F., Cai, D., Shao, Y.L., et al., 2011. Laplacian regularized Gaussian mixture model for data clustering. IEEE Trans. Knowl. Data Eng., 23(9):1406–1418. [doi:10.1109/TKDE.2010.259]
Howland, P., Wang, J., Park, H., 2006. Solving the small sample size problem in face recognition using generalized discriminant analysis. Patt. Recog., 39(2):277–287. [doi:10.1016/j.patcog.2005.06.013]
Jing, L.P., Ng, M.K., Huang, J.Z., 2007. An entropy weighting k-means algorithm for subspace clustering of highdimensional sparse data. IEEE Trans. Knowl. Data Eng., 19(8):1026–1041. [doi:10.1109/TKDE.2007.1048]
Kano, M., Nagao, K., Hasebe, S., et al., 2002. Comparison of multivariate statistical process monitoring methods with applications to the Eastman challenge problem. Comput. Chem. Eng., 26(2):161–174. [doi:10.1016/S0098-1354(01)00738-4]
Kano, M., Fujioka, T., Tonomura, O., et al., 2007. Data-based and model-based blockage diagnosis for stacked microchemical processes. Chem. Eng. Sci., 62(4):1073–1080. [doi:10.1016/j.ces.2006.11.011]
Lee, D., Lee, J., 2007. Domain described support vector classifier for multi-classification problems. Patt. Recog., 40(1):41–51. [doi:10.1016/j.patcog.2006.06.008]
Lee, J., Kang, B., Kang, S., 2011. Integrating independent component analysis and local outlier factor for plant-wide process monitoring. J. Process Contr., 21(7):1011–1021. [doi:10.1016/j.jprocont.2011.06.004]
Liu, J.L., Cai, D., He, X.F., 2010. Gaussian mixture model with local consistency. Proc. 24th AAAI Conf. on Artificial Intelligence, p.512–517.
Miao, A.M., Ge, Z.Q., Song, Z.H., et al., 2015) Nonlocal structure constrained neighborhood preserving embedding model and its application for fault detection. Chemometr. Intell. Lab. Syst., 142: 184–196. [doi:10.1016/j.chemolab.2015.01.010]
Miyamoto, S., Mukaidono, M., 1997. Fuzzy C-means as a regularization and maximum entropy approach. Proc. IFSA, p.86–92.
Molina, G.D., Zumoffen, D.A.R., Basualdo, M.S., 2011. Plant-wide control strategy applied to the Tennessee Eastman process at two operating points. Comput. Chem. Eng., 35(10):2081–2097. [doi:10.1016/j.compchemeng.2010.11.006]
Ng, Y.S., Srinivasan, R., 2009. An adjoined multi-model approach for monitoring batch and transient operations. Comput. Chem. Eng., 33(4):887–902. [doi:10.1016/j.compchemeng.2008.11.014]
Perez, C.F.A., 2011. Fault Diagnosis with Reconstruction- Based Contributions for Statistical Process Monitoring. PhD Thesis, University of Southern California USA.
Serradilla, J., Shi, J.Q., Morris, A.J., 2011. Fault detection based on Gaussian process latent variable models. Chemometr. Intell. Lab. Syst., 109(1):9–21. [doi:10.1016/j.chemolab.2011.07.003]
Shen, J.F., Bu, J.J., Ju, B., et al., 2012) Refining Gaussian mixture model based on enhanced manifold learning. Neurocomputing, 87: 19–25. [doi:10.1016/j.neucom.2012.01.029]
Song, B., Ma, Y.X., Shi, H.B., 2014) Multimode process monitoring using improved dynamic neighborhood preserving embedding. Chemometr. Intell. Lab. Syst., 135: 17–30. [doi:10.1016/j.chemolab.2014.03.013]
Tan, S.C., Lim, C.P., Rao, M.V.C., 2007. A hybrid neural network model for rule generation and its application to process fault detection and diagnosis. Eng. Appl. Artif. Intell., 20(2):203–213. [doi:10.1016/j.engappai.2006.06.007]
Teppola, P., Mujunen, S.P., Minkkinen, P., 1999. Adaptive fuzzy C-means clustering in process monitoring. Chemometr. Intell. Lab. Syst., 45(1-2):23–38. [doi:10.1016/S0169-7439(98)00087-2]
Tong, C.D., Palazoglu, A., Yan, X.F., 2013. An adaptive multimode process monitoring strategy based on mode clustering and mode unfolding. J. Process Contr., 23(10):1497–1507. [doi:10.1016/j.jprocont.2013.09.017]
Venkatasubramanian, V., Rengaswamy, R., Yin, K., et al., 2003. A review of process fault detection and diagnosis: Part I: quantitative model-based methods. Comput. Chem. Eng., 27(3):293–311. [doi:10.1016/S0098-1354(02)00160-6]
Xie, L., Liu, X.Q., Zhang, J.M., et al., 2009. Non-Gaussian process monitoring based on NGPP-SVDD. Acta Autom. Sin., 35(1):107–112 (in Chinese).
Xie, X., Shi, H.B., 2012. Multimode process monitoring based on fuzzy C-means in locality preserving projection subspace. Chin. J. Chem. Eng., 20(6):1174–1179. [doi:10.1016/S1004-9541(12)60604-1]
Xu, X., Xie, L., Wang, S., 2011. Multi-mode process monitoring method based on PCA mixture model. CIESC J., 62(3):743–752 (in Chinese).
Yang, Y.H., Li, X., Liu, X.Z., et al., 2015) Wavelet kernel entropy component analysis with application to industrial process monitoring. Neurocomputing, 147: 395–402. [doi:10.1016/j.neucom.2014.06.045]
Yin, X.S., Chen, S.C., Hu, E.L., 2013) Regularized soft K-means for discriminant analysis. Neurocomputing, 103: 29–42. [doi:10.1016/j.neucom.2012.08.021]
Yu, J., 2012. A nonlinear kernel Gaussian mixture model based inferential monitoring approach for fault detection and diagnosis of chemical processes. Chem. Eng. Sci., 68(1):506–519. [doi:10.1016/j.ces.2011.10.011]
Zang, X., Vista Iv, F.P., Chong, K.T., 2014. Fast global kernel fuzzy c-means clustering algorithm for consonant/vowel segmentation of speech signal. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 15(7):551–563. [doi:10.1631/jzus.C1300320]
Zhang, M., Ge, Z.Q., Song, Z.H., et al., 2011. Global-local structure analysis model and its application for fault detection and identification. Ind. Eng. Chem. Res., 50(11): 6837–6848. [doi:10.1021/ie102564d]
Zhang, S.J., Wang, Z.L., Qian, F., 2010. FS-SVDD based on LTSA and its application to chemical process monitoring. CIESC J., 61(8):1894–1900 (in Chinese).
Zhang, Y.W., 2009. Enhanced statistical analysis of nonlinear processes using KPCA, KICA and SVM. Chem. Eng. Sci., 64(5):801–811. [doi:10.1016/j.ces.2008.10.012]
Zhang, Y.W., Li, S., 2014. Modeling and monitoring of nonlinear multi-mode processes. Contr. Eng. Pract., 22: 194–204. [doi:10.1016/j.conengprac.2013.04.007]
Zhang, Y.W., An, J.Y., Li, Z.M., et al., 2013) Modeling and monitoring for handling nonlinear dynamic processes. Inform. Sci., 235: 97–105. [doi:10.1016/j.ins.2012.04.023]
Zhu, Z.B., Wang, P.L., Song, Z.H., 2010. PCA-SVDD based fault detection and self-learning identification. J. Zhejiang Univ. (Eng. Sci.), 44(4):652–658 (in Chinese).
Zhu, Z.B., Song, Z.H., Palazoglu, A., 2012. Process pattern construction and multi-mode monitoring. J. Process Contr., 22(1):247–262. [doi:10.1016/j.jprocont.2011.08. 002]
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Project supported by the National Natural Science Foundation of China (No. 61272297)
ORCID: Shi-jin REN, http://orcid.org/0000-0002-8321-1879
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Ren, Sj., Liang, Y., Zhao, Xj. et al. A novel multimode process monitoring method integrating LDRSKM with Bayesian inference. Frontiers Inf Technol Electronic Eng 16, 617–633 (2015). https://doi.org/10.1631/FITEE.1400263
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DOI: https://doi.org/10.1631/FITEE.1400263
Keywords
- Multimode process monitoring
- Local discriminant regularized soft k-means clustering
- Kernel support vector data description
- Bayesian inference
- Tennessee Eastman process