Mixture robust semi-supervised probabilistic principal component regression with missing input data

Abstract Industrial processes often operate in multiple operating modes. In most cases, the outputs are measured at a slower rate than the inputs due to various reasons, such as the unavailability of real-time sensors. In some cases, measurements of inputs are also not available and/or there are outliers in the measurements due to sensor failures. Furthermore, there can exist different properties of outliers in different variables. Not all of the aforementioned challenges have been considered or considered simultaneously while modeling a probabilistic principal component regression model in the existing literature. In the current paper, a mixture robust semi-supervised probabilistic principal component regression model with missing input data is developed, which can handle all the aforementioned challenges effectively when utilized for online predictions of process variables. The proposed approach is solved using the Expectation-Maximization algorithm, and the performance is demonstrated by a numerical example. An experimental case study of the hybrid tanks system is also utilized to demonstrate the practical applicability of the proposed method.

[1]  Leo H. Chiang,et al.  Dimensionality reduction for visualizing industrial chemical process data , 2019 .

[2]  Michel Verleysen,et al.  Mixtures of robust probabilistic principal component analyzers , 2008, ESANN.

[3]  Zhiqiang Ge,et al.  Robust semi-supervised mixture probabilistic principal component regression model development and application to soft sensors , 2015 .

[4]  Biao Huang,et al.  Simultaneous estimation of sub-model number and parameters for mixture probability principal component regression , 2017, 2017 11th Asian Control Conference (ASCC).

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

[6]  Young-Don Ko,et al.  A neural network-based soft sensor for particle size distribution using image analysis , 2011 .

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

[8]  Jose A. Romagnoli,et al.  Chapter B4 – Process design and operation: Incorporating environmental, profitability, heat integration and controllability considerations , 2004 .

[10]  Biao Huang,et al.  Real-Time Mode Diagnosis for Processes With Multiple Operating Conditions Using Switching Conditional Random Fields , 2020, IEEE Transactions on Industrial Electronics.

[11]  Zhiqiang Ge,et al.  Robust modeling of mixture probabilistic principal component analysis and process monitoring application , 2014 .

[12]  Biao Huang,et al.  Robust probabilistic principal component analysis for process modeling subject to scaled mixture Gaussian noise , 2016, Comput. Chem. Eng..

[13]  Hyun Myung,et al.  Outlier-Robust Student's-$t$-Based IMM-VB Localization for Manned Aircraft Using TDOA Measurements , 2020, IEEE/ASME Transactions on Mechatronics.

[14]  Weixin Yao,et al.  Robust mixture regression model fitting by Laplace distribution , 2014, Comput. Stat. Data Anal..

[15]  Zhiqiang Ge,et al.  Dynamic Bayesian network for robust latent variable modeling and fault classification , 2020, Eng. Appl. Artif. Intell..

[16]  Biao Huang,et al.  Robust probabilistic principal component analysis based process modeling: Dealing with simultaneous contamination of both input and output data , 2017, Journal of Process Control.

[17]  Jianlin WANG,et al.  On-line Estimation of Biomass in Fermentation Process Using Support Vector Machine , 2006 .

[18]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

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

[20]  Weiming Shao,et al.  Semi-supervised variational Bayesian Student’s t mixture regression and robust inferential sensor application , 2019, Control Engineering Practice.

[21]  Xiao Wang,et al.  Soft sensor based on stacked auto-encoder deep neural network for air preheater rotor deformation prediction , 2018, Adv. Eng. Informatics.

[22]  Reza Langari,et al.  Nonlinear sensor fault diagnosis using mixture of probabilistic PCA models , 2017 .

[23]  Biao Huang,et al.  Identification of robust Gaussian Process Regression with noisy input using EM algorithm , 2019 .

[24]  Nima Sammaknejad,et al.  Approaches to robust process identification: A review and tutorial of probabilistic methods , 2018, Journal of Process Control.

[25]  Xianqiang Yang,et al.  Mixture robust L1 probabilistic principal component regression and soft sensor application , 2020 .

[26]  Jeremy F. P. Ullmann,et al.  Laplace mixture autoregressive models , 2016 .

[27]  Biao Huang,et al.  Mixture semisupervised probabilistic principal component regression model with missing inputs , 2017, Comput. Chem. Eng..

[28]  Biao Huang,et al.  A Bayesian approach to robust process identification with ARX models , 2013 .

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

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

[31]  Zhiqiang Ge,et al.  Process Data Analytics via Probabilistic Latent Variable Models: A Tutorial Review , 2018, Industrial & Engineering Chemistry Research.