Robust inferential sensor development based on variational Bayesian Student’s-t mixture regression

Abstract

Owing to the requirements of various product grades or operation conditions, most of industrial processes work with multiple modes. Gaussian mixture regression (GMR) is one of the most widely adopted methods to develop inferential sensors for these processes. However, outliers exist widely due to data points that are incorrectly observed, recorded, or imported and are very hard to be completely recognized and removed. These outliers render the predictive performance of the GMR-based inferential sensors quite disappointing. Aiming at resolving this problem, we propose a robust inferential sensing method based on variational Bayesian Student’s-t mixture regression (VBSMR). In the VBSMR, we first explicitly consider the dependency of quality variables on process variables, where the Bayesian regularization is enabled to find the regression coefficients, and the Student’s-t distributions are introduced for handling outliers. Subsequently, a computationally efficient parameter learning procedure for the VBSMR using the variational Bayesian expectation maximization (VBEM) technique is developed, where the optimal number of mixing components can be automatically determined. Experiments conducted on both numerical and practical industrial examples are provided to demonstrate the availability and flexibility of the developed inferential sensor.