Robust Mixture Probabilistic Partial Least Squares Model for Soft Sensing With Multivariate Laplace Distribution

Data collected in modern industrial processes often exhibit complex non-Gaussian and multimodal characteristics. In order to address these problems, a robust mixture probabilistic partial least squares (RMPPLS) model-based soft sensor is developed in this article, where two different kinds of hidden variables are introduced in the formulated model structure. The multivariate Laplace distribution is employed for robust modeling, and mixture form of the probabilistic partial least squares model is adopted for multimodal description. The unknown parameters are estimated in the expectation-maximization (EM) scheme and the corresponding soft sensor is finally constructed. A numerical example and the Tennessee Eastman (TE) process case study are explored to verify the effectiveness of the proposed algorithm.