Articles & Issues
- Language
- English
- Conflict of Interest
- In relation to this article, we declare that there is no conflict of interest.
- Publication history
-
Received December 5, 2016
Accepted April 25, 2017
-
This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits
unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright © KIChE. All rights reserved.
All issues
Sparse probabilistic principal component analysis model for plant-wide process monitoring
State Key Lab of Industrial Control Technology, Institute of Industrial Control Technology, Zhejiang University, Hangzhou, 310027, P. R. China
jliang@iipc.zju.edu.cn
Korean Journal of Chemical Engineering, August 2017, 34(8), 2135-2146(12), 10.1007/s11814-017-0119-9
Download PDF
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.
Keywords
References
Chiang LH, Russell EL, Braatz RD, Meas. Sci. Technol., 12, 1745 (2001)
Qin SJ, J. Chemometr., 17, 4808 (2003)
Zhang YW, Qin SJ, AIChE J., 54(12), 3207 (2008)
Wang X, Kruger U, Irwin GW, McCullough G, McDowell N, IEEE Trans. Control Syst. Technol., 16, 122 (2008)
Zhang Y, Ma C, Chem. Eng. Sci., 6+6, 64 (2011)
Jiang Q, Yan X, Korean J. Chem. Eng., 31(11), 1935 (2014)
Tipping ME. Bishop CM, J. R. Stat. Soc. Ser. B Statistical Methodol, 61, 611 (1999)
Kim D, Lee IB, Chemom. Intell. Lab. Syst., 67, 109 (2003)
Choi SW, Park JH, Lee IB, Comput. Chem. Eng., 28(8), 1377 (2004)
Chen T, Sun Y, Control Eng. Practice, 17, 469 (2009)
Ge ZQ, Song ZH, AIChE J., 56(11), 2838 (2010)
Vines SK, J. R. Stat. Soc. Ser. C-Applied Stat., 49, 441 (2000)
Jolliffe IT, Trendafilov NT, Uddin M, J. Comput. Graph. Stat., 12, 531 (2003)
Zou H, Hastie T, Tibshirani R, J. Comput. Graph. Stat., 15, 265 (2006)
Xie L, Lin XZ, Zeng JS, Ind. Eng. Chem. Res., 52(49), 17475 (2013)
Tipping ME, J. Mach. Learn. Res., 1, 211 (2001)
Sigg CD, Buhmann JM, Proc. 25th Int. Conf. Mach. Learn. - ICML ’08., 960 (2008).
Cawley G, Talbot N, Girolami M, NIPS, 19, 209 (2007)
Archambeau C, Bach FR, NIPS, 1 (2008).
Guan Y, Dy JG, AISTATS, 5, 185 (2009)
Koyejo O, Ghosh J, Khanna R, Poldrack RA, NIPS, 676 (2014).
Khanna R, Ghosh J, Poldrack R, Koyejo OO, AISTATS, 38, 453 (2015)
Latouche P, Mattei PA, Bouveyron C, Chiquet J, J. Multivariate Anal., 146, 177 (2014)
Bouveyron C, Latouche P, Mattei PA, Bayesian variable selection for globally sparse probabilistic PCA, Technical Report, HAL- 01310409, Universite Paris Descartes (2016).
Qin SJ, Valle S, Piovoso MJ, J. Chemometr., 15, 715 (2001)
Choi SW, Lee IB, J. Process Control, 15(3), 295 (2005)
Zhang Y, Zhou H, Qin SJ, Chai T, IEEE T. Ind. Inform., 6, 3 (2010)
Wang B, Jiang Q, Yan X, Korean J. Chem. Eng., 31(6), 930 (2014)
Bishop CM, NIPS, 11, 382 (1998)
Bishop CM, Springer-Verlag, New York (2006).
Martin EB, Morris AJ, J. Process Control, 6(6), 349 (1996)
Chen Q, Wynne RJ, Goulding P, Sandoz D, Control Eng. Practice, 8, 531 (2000)
Chen Q, Kruger U, Leung ATY, Control Eng. Practice, 12, 267 (2004)
Downs JJ, Vogel EF, Comput. Chem. Eng., 17, 245 (1993)
Grbovic M, Li WC, Xu P, Usadi AK, Song LM, Vucetic S, J. Process Control, 22(4), 738 (2012)
Ge ZQ, Song ZH, Ind. Eng. Chem. Res., 52(5), 1947 (2013)
Qin SJ, J. Chemometr., 17, 4808 (2003)
Zhang YW, Qin SJ, AIChE J., 54(12), 3207 (2008)
Wang X, Kruger U, Irwin GW, McCullough G, McDowell N, IEEE Trans. Control Syst. Technol., 16, 122 (2008)
Zhang Y, Ma C, Chem. Eng. Sci., 6+6, 64 (2011)
Jiang Q, Yan X, Korean J. Chem. Eng., 31(11), 1935 (2014)
Tipping ME. Bishop CM, J. R. Stat. Soc. Ser. B Statistical Methodol, 61, 611 (1999)
Kim D, Lee IB, Chemom. Intell. Lab. Syst., 67, 109 (2003)
Choi SW, Park JH, Lee IB, Comput. Chem. Eng., 28(8), 1377 (2004)
Chen T, Sun Y, Control Eng. Practice, 17, 469 (2009)
Ge ZQ, Song ZH, AIChE J., 56(11), 2838 (2010)
Vines SK, J. R. Stat. Soc. Ser. C-Applied Stat., 49, 441 (2000)
Jolliffe IT, Trendafilov NT, Uddin M, J. Comput. Graph. Stat., 12, 531 (2003)
Zou H, Hastie T, Tibshirani R, J. Comput. Graph. Stat., 15, 265 (2006)
Xie L, Lin XZ, Zeng JS, Ind. Eng. Chem. Res., 52(49), 17475 (2013)
Tipping ME, J. Mach. Learn. Res., 1, 211 (2001)
Sigg CD, Buhmann JM, Proc. 25th Int. Conf. Mach. Learn. - ICML ’08., 960 (2008).
Cawley G, Talbot N, Girolami M, NIPS, 19, 209 (2007)
Archambeau C, Bach FR, NIPS, 1 (2008).
Guan Y, Dy JG, AISTATS, 5, 185 (2009)
Koyejo O, Ghosh J, Khanna R, Poldrack RA, NIPS, 676 (2014).
Khanna R, Ghosh J, Poldrack R, Koyejo OO, AISTATS, 38, 453 (2015)
Latouche P, Mattei PA, Bouveyron C, Chiquet J, J. Multivariate Anal., 146, 177 (2014)
Bouveyron C, Latouche P, Mattei PA, Bayesian variable selection for globally sparse probabilistic PCA, Technical Report, HAL- 01310409, Universite Paris Descartes (2016).
Qin SJ, Valle S, Piovoso MJ, J. Chemometr., 15, 715 (2001)
Choi SW, Lee IB, J. Process Control, 15(3), 295 (2005)
Zhang Y, Zhou H, Qin SJ, Chai T, IEEE T. Ind. Inform., 6, 3 (2010)
Wang B, Jiang Q, Yan X, Korean J. Chem. Eng., 31(6), 930 (2014)
Bishop CM, NIPS, 11, 382 (1998)
Bishop CM, Springer-Verlag, New York (2006).
Martin EB, Morris AJ, J. Process Control, 6(6), 349 (1996)
Chen Q, Wynne RJ, Goulding P, Sandoz D, Control Eng. Practice, 8, 531 (2000)
Chen Q, Kruger U, Leung ATY, Control Eng. Practice, 12, 267 (2004)
Downs JJ, Vogel EF, Comput. Chem. Eng., 17, 245 (1993)
Grbovic M, Li WC, Xu P, Usadi AK, Song LM, Vucetic S, J. Process Control, 22(4), 738 (2012)
Ge ZQ, Song ZH, Ind. Eng. Chem. Res., 52(5), 1947 (2013)
