Robust supervised probabilistic principal component analysis model for soft sensing of key process variables

In this paper, a robust and mixture form of supervised probabilistic principal component analysis model is proposed to deal with the soft sensing problem, particularly for those processes with multiple operating conditions and the collected datasets may contain outliers. Under the framework of latent variable models, the commonly adopted multivariate Gaussian distribution assumption is replaced by the multivariate student t-distribution so as to tolerate the notorious outliers by using the adjusted heavy tail. After the construction of robust probabilistic model, the iterative expectation-maximization algorithm is derived to perform the parameter estimation for both single and mixture models. For online soft sensing application, the Bayes rule is introduced for soft alignment of local prediction results. Two case studies are provided for performance evaluation of the proposed method, both in comparison with the conventional supervised model. Results indicate that the new model is much more reliable under outlier contaminated and multimode conditions.