Nonlinear Gaussian Mixture Regression for Multimode Quality Prediction with Partially Labeled Data

An enhanced nonlinear Gaussian mixture regression (NLGMR) algorithm is proposed for quality prediction of a nonlinear multimode process. The traditional Gaussian mixture regression (GMR) model has been utilized for quality prediction with a linear model in each local mode, which will not suit for many cases that nonlinear relationships exist between input and output variables. Besides, large scales of process data that can be used for modeling are partially labeled on account of the low sampling rate of quality variables. Most of the unlabeled samples are discarded while building the GMR model, which leads to the loss of information and limits the improvement of prediction accuracy. To tackle these two problems, a locally weighted semisupervised factor analysis model is developed in each mode of GMR. The locally weighted model divides the nonlinear process into pieces of linear model and the semisupervised factor analysis model can effectively take advantage of the massive unlabeled data. Moreover, the variational inference (VI) algorithm is conducted on the GMR model to determine the amount of process modes automatically. The proposed method is first verified by a numerical example and then applied in a multimode primary reformer to predict the oxygen content, where prominent improvements are obtained, compared with traditional methods.