Mixture Semisupervised Bayesian Principal Component Regression for Soft Sensor Modeling

In this paper, a mixture semisupervised Bayesian principal component regression-based soft sensor modeling method for nonlinear industrial process with multiple operating modes is presented. In many chemistry processes, part of output data samples may be unavailable due to the difficulties in measurement or recording. The semisupervised method is introduced to efficiently deal with the unlabeled data set. Moreover, the Bayesian regularization method is proposed to determine the unknown dimensionality of latent variables space in each submode by introducing three different formulations of two hyperparameters to construct the Gaussian prior distributions over the loading and regression matrices. The formulation of this method is derived in expectation maximization algorithm scheme, and the formulas to update unknown parameters are derived. The effectiveness of the proposed method is verified through a numerical example, the Tennessee Eastman benchmark process, and the comparisons with the existing method.