Robust Soft Sensing for Multi-mode Processes Based on Bayesian Regularized Student’s-t Mixture Regression

Gaussian mixture regression (GMR) is one widely adopted approach to construct soft sensors for industrial processes that work with multiple operating modes. However, outliers which usually result from inappropriately observed, recorded or stored measurements into database exist widely in industrial datasets and are very difficult to be completely recognized and removed. The presence of outliers renders the predictive performance of the GMR-based soft sensors quite unsatisfactory. Besides, labeled samples in industrial process are usually limited, which easily leads to overfitted soft sensors. To resolve these problems, a Bayesian regularized Student's-t mixture regression (BSMR) is proposed in this paper. In the BSMR, the outliers are dealt with by the Student's-t distribution that has heavier tail than the Gaussian distribution; in addition, the overfitting issue is tackled by an explicit model structure that facilitates Bayesian regularizations on the regression coefficients. An efficient parameter learning algorithm based on variational Bayesian expectation maximization is also designed for the BSMR. Two case studies including a numerical example and a real-world industrial process are supplied to assess the performance of the BSMR, which demonstrate the effectiveness and feasibility of the proposed approach.