Bayesian Regularized Gaussian Mixture Regression with Application to Soft Sensor Modeling for Multi-Mode Industrial Processes

Abstract

The Gaussian mixture regression (GMR) is an effective approach to predict those difficult-to-measure quality variables for industrial processes with multiple operating modes. However, the GMR easily gets stuck into overfitting in the scenario of insufficient labeled samples, particularly when the dimensionality of the secondary variables is high. To alleviate this issue, this paper proposes the Bayesian regularized GMR (BGMR), and applies it to soft sensor modeling. In the BGMR, an alternative model structure, which explicitly considers the functional dependency between the primary and secondary variables, is presented to facilitate the Bayesian regularization that is widely used for anti-overfitting. In addition, an efficient learning procedure is developed for the BGMR based on the expectation-maximization algorithm. The performance of the BGMR is evaluated through two case studies including a numerical example and a real-life industrial process, which demonstrates the effectiveness of the proposed approach.