Nonlinear Variational Bayesian Factor Regression for Inferential Sensor Modeling

Abstract

Inferential sensors are mathematical methods to describe the dependence of quality-related variables called primary variables on those easy-to-measure variables called secondary variables. For majority complex cases in biological and chemical industrial processes with especially nonlinear characteristics, traditional VBFR-based inferential sensor method may not function well because of its linearity assumption on the process data. To tackle the issue that nonlinear relationships exist between input and output variables, an enhanced nonlinear variational Bayesian factor regression (NVBFR) approach is proposed for inferential sensing. On the basis of the probabilistic modeling method, with incorporation of nonlinear mapping, this paper aims to extend the linear probabilistic inferential sensor into the nonlinear form. To evaluate the feasibility and efficiency of the developed Inferential sensors, a real industrail process example is demonstrated.