Dynamic Variational Bayesian Student's T Mixture Regression With Hidden Variables Propagation for Industrial Inferential Sensor Development

Abstract

Data-driven inferential sensors have been increasingly applied to estimating important yet difficult-to-measure quality-relevant variables in industrial processes. However, complicated data characteristics (such as nonlinearities, non-Gaussianities, uncertainties, outlying data, etc.) existing in industrial datasets impose significant difficulties in developing inferential sensors with high accuracy. In particular, modeling process dynamics with sequential data is practically very important but quite challenging. In order to deal with such issues, this article proposes a dynamic variational Bayesian Student's t mixture regression (D-VBSMR) with hidden variables propagation. In D-VBSMR, the probabilistic mixture model structure can deal with nonlinearities, non-Gaussianities, and uncertainties; meanwhile, the Student's t-distribution with heavy tails enables D-VBSMR to be highly robust against outliers. Most importantly, the first-order Markov chain is used to connect hidden state variables, such that the process dynamic characteristic can be effectively modeled. In addition, parameter learning for D-VBSMR is also developed by adopting the variational inference framework and forward–backward algorithm. Experimental results on both a numerical example and a real industrial process validate the effectiveness and advantages of the proposed method.