Mixture semisupervised probabilistic principal component regression model with missing inputs

Abstract Principal component regression (PCR) has been widely used as a multivariate method for data-based soft sensor design. In order to take advantage of probabilistic features, it has been extended to probabilistic PCR (PPCR). Commonly, industrial processes operate in multiple operating modes. Moreover, in most cases, outputs are measured at a slower rate than inputs, and for each sample of input variable, its corresponding output may not always exist. These two issues have been solved by developing the mixture semi-supervised PPCR (MSPPCR) method. In this paper, we extend this developed model to the case of simultaneous missing data in both input and output. Missing data in multidimensional input space constitutes a significantly more challenging problem. Missing input data occurs frequently in industrial plants because of sensor failure and other problems. We develop and solve the MSPPCR model by using the expectation-maximization (EM) algorithm to deal with missing inputs, in addition to missing outputs and multi-mode conditions. Finally, we present two case studies to demonstrate its performance.

[1]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[2]  Sten Bay Jørgensen,et al.  A systematic approach for soft sensor development , 2007, Comput. Chem. Eng..

[3]  Paul Geladi,et al.  Principal Component Analysis , 1987, Comprehensive Chemometrics.

[4]  Furong Gao,et al.  Mixture probabilistic PCR model for soft sensing of multimode processes , 2011 .

[5]  E. F. Vogel,et al.  A plant-wide industrial process control problem , 1993 .

[6]  Tao Chen,et al.  Probabilistic contribution analysis for statistical process monitoring: A missing variable approach , 2009 .

[7]  Xiao Fan Wang,et al.  Soft sensing modeling based on support vector machine and Bayesian model selection , 2004, Comput. Chem. Eng..

[8]  Julian Morris,et al.  Artificial neural networks in process estimation and control , 1992, Autom..

[9]  Luigi Fortuna,et al.  Soft Sensors for Monitoring and Control of Industrial Processes (Advances in Industrial Control) , 2006 .

[10]  N. Lawrence Ricker,et al.  Decentralized control of the Tennessee Eastman Challenge Process , 1996 .

[11]  Biao Huang,et al.  Design of inferential sensors in the process industry: A review of Bayesian methods , 2013 .

[12]  Jar-Ferr Yang,et al.  Improved Principal Component Regression for Face Recognition Under Illumination Variations , 2012, IEEE Signal Processing Letters.

[13]  D. Massart,et al.  Dealing with missing data: Part II , 2001 .

[14]  Bogdan Gabrys,et al.  Data-driven Soft Sensors in the process industry , 2009, Comput. Chem. Eng..

[15]  Michael E. Tipping,et al.  Probabilistic Principal Component Analysis , 1999 .

[16]  Christopher M. Bishop,et al.  Mixtures of Probabilistic Principal Component Analyzers , 1999, Neural Computation.

[17]  Biao Huang,et al.  Dealing with Irregular Data in Soft Sensors: Bayesian Method and Comparative Study , 2008 .

[18]  Zhiqiang Ge,et al.  Soft sensor model development in multiphase/multimode processes based on Gaussian mixture regression , 2014 .

[19]  Zhi-huan Song,et al.  Mixture Bayesian regularization method of PPCA for multimode process monitoring , 2010 .

[20]  B. Kowalski,et al.  Partial least-squares regression: a tutorial , 1986 .

[21]  Jin Wang,et al.  Comparison of the performance of a reduced-order dynamic PLS soft sensor with different updating schemes for digester control , 2012 .

[22]  K. Esbensen,et al.  Regression on multivariate images: Principal component regression for modeling, prediction and visual diagnostic tools , 1991 .

[23]  Luiz Augusto da Cruz Meleiro,et al.  ANN-based soft-sensor for real-time process monitoring and control of an industrial polymerization process , 2009, Comput. Chem. Eng..

[24]  Zhiqiang Ge,et al.  Mixture semisupervised principal component regression model and soft sensor application , 2014 .

[25]  Hans-Peter Kriegel,et al.  Supervised probabilistic principal component analysis , 2006, KDD '06.