Abstract
In the industrial monitoring process, probabilistic principal component analysis (PPCA) is a popular algorithm for reducing the dimension. However, the principal components (PCs) are not easy to interpret and its preserved number cannot be determined automatically. In this paper, we propose a sparse PPCA (SPPCA) to improve the interpretability by adding a prior and introducing sparsification to the loading matrix of PPCA. An expectation-maximization (EM) algorithm is used to obtain the parameters of the probabilistic formulation, and the dimensionality of the latent variable space can be automatically determined during the iterative process. With the sparse representation, a process monitoring strategy is then developed with the construction of several partial PPCA models. Case studies of SPPCA to a numerical case and Tennessee Eastman (TE) benchmark process demonstrate its feasibility and efficiency.
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L. H. Chiang, E. L. Russell and R. D. Braatz, Meas. Sci. Technol., 12, 1745 (2001).
S. J Qin, J. Chemom., 17, 480 (2003).
Y. Zhan and S. J. Qin, AIChE. J., 54, 3207 (2008).
X. Wang, U. Kruger, G. W. Irwin, G. McCullough and N. McDowell, IEEE Trans. Control Syst. Technol., 16, 122 (2008).
Y. Zhang and C. Ma, Chem. Eng. Sci., 66, 64 (2011).
Q. C. Jiang and X. F. Korean J. Chem. Eng., 31, 1935 (2014).
M. E. Tipping and C. M. Bishop, J. R. Stat. Soc. Ser. B Statistical Methodol., 61, 611 (1999).
D. Kim and I.-B. Lee, Chemom. Intell. Lab. Syst., 67, 109 (2003).
S. W. Choi, J. H. Park and I.-B. Lee, Comput. Chem. Eng., 28, 1377 (2004).
T. Chen and Y. Sun, Control Eng. Pract., 17, 469 (2009).
Z. Q. Ge and Z. H. Song, AIChE J., 56, 2838 (2010).
S. K. Vines, J. R. Stat. Soc. Ser. C-Applied Stat., 49, 441 (2000).
I. T. Jolliffe, N. T. Trendafilov and M. Uddin, J. Comput. Graph. Stat., 12, 531 (2003).
H. Zou, T. Hastie and R. Tibshirani, J. Comput. Graph. Stat., 15, 265 (2006).
L. Xie, X. Lin and J. Zeng, Ind. Eng. Chem. Res., 52, 17475 (2013).
M. E. Tipping, J. Mach. Learn. Res., 1, 211 (2001).
C. D. Sigg and J. M. Buhmann, Proc. 25th Int. Conf. Mach. Learn. - ICML’ 08., 960 (2008).
G. Cawley, N. Talbot and M. Girolami, NIPS, 19, 209 (2007).
C. Archambeau and F. R. Bach, NIPS, 1 (2008).
Y. Guan and J. G. Dy, AISTATS, 5 185 (2009).
O. Koyejo, J. Ghosh, R. Khanna and R. A. Poldrack, NIPS, 676 (2014).
R. Khanna, J. Ghosh, R. Poldrack and O. O. Koyejo, AISTATS, 38, 453 (2015).
P. Latouche, P. A. Mattei, C. Bouveyron and J. Chiquet, J. Multivariate Anal., 146, 177 (2014).
C. Bouveyron, P. Latouche and P. A. Mattei, Bayesian variable selection for globally sparse probabilistic PCA, Technical Report, HAL-01310409, Universite Paris Descartes (2016).
S. J. Qin, S. Valle and M. J. Piovoso, J. Chemometr., 15, 715 (2001).
S. W. Choi and I. B. Lee, J. Process Contr., 15, 295 (2005).
Y. Zhang, H. Zhou, S. J. Qin and T. Chai, IEEE T. Ind. Inform., 6, 3 (2010).
B. Wang, Q. C. Jiang and X. F. Yan, Korean J. Chem. Eng., 31, 930 (2014).
C. M. Bishop, NIPS, 11, 382 (1998).
C. M. Bishop, Springer-Verlag, New York (2006).
E. B. Martin and A. J. Morris, J. Process Contr., 6, 349 (1996).
Q. Chen, R. J. Wynne, P. Goulding and D. Sandoz, Control Eng. Pract., 8, 531 (2000).
Q. Chen and U. Kruger and A. T. Y. Leung, Control Eng. Pract., 12, 267 (2004).
J. J. Downs and E. F. Vogel, Comput. Chem. Eng., 17, 245 (1993).
M. Grbovic, W. C. Li, P. Xu, A. K. Usadi, L. M. Song and S. Vucetic, J. Process Contr., 22, 738 (2012).
Z. Ge and Z. Song, Ind. Eng. Chem. Res., 52, 1947 (2013).
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Zeng, J., Liu, K., Huang, W. et al. Sparse probabilistic principal component analysis model for plant-wide process monitoring. Korean J. Chem. Eng. 34, 2135–2146 (2017). https://doi.org/10.1007/s11814-017-0119-9
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DOI: https://doi.org/10.1007/s11814-017-0119-9