Nonlinear variational Bayesian Student’s-t mixture regression and inferential sensor application with semisupervised data

Abstract

Gaussian mixture models have been widely applied to predict those significant but hard-to-measure quality variables in industrial processes. However, outliers that result from disturbances of noise, and incorrect instrument readings, will deteriorate the prediction accuracy of Gaussian mixture models. Student’s-t mixture regression and its variants have been proposed for robust inferential sensor development. Nevertheless, for those Student’s-t mixture regression-based inferential sensors, the functional dependency between the quality and process variables in each component is assumed to be linear. Such configuration in practice might be incapable of adequately modeling the complicated nonlinearity between the quality and process variables. In addition, large amounts of unlabeled samples are easily to be obtained and informative for model performance improvement, however, the computations are significantly increased as well. To get over these issues, this paper proposes a novel semisupervised nonlinear variational Bayesian Student’s-t mixture regression model, in which the nonlinear component model can effectively capture the non-linearity between the quality and process variables. For tackling the low training efficiency issue caused by large number of training samples, the parallel computing strategy is introduced to complete model training. A numerical example and two real industrial processes are supplied to validate the effectiveness of the proposed method.