Variational Bayesian Gaussian Mixture Regression for Soft Sensing Key Variables in Non-Gaussian Industrial Processes

In this brief, a variational Bayesian Gaussian mixture regression (VBGMR) method is developed for soft sensing key quality-related variables in a non-Gaussian industrial process. Traditional Gaussian mixture regression (GMR) is based on Gaussian mixture model (GMM) and can be easily stuck into the issue of model selection since the GMM model generally requires a large amount of local components so as to achieve desirable predicting performances. However, such assignation can be computationally extensive and may also result in some numerical issues since only a few components are positively adopted. In this brief, a fully Bayesian modeling method is proposed for GMR-based soft sensor development. Conjugate Bayesian prior is defined for each empirical parameter, while a Dirichlet process prior is further defined on the mixture component. The full Bayesian GMR is first validated on a numerical case study and then applied to the industrial hydrogen manufacturing units, both compared with GMR. The results demonstrate feasibility and reliability of the new soft sensor and show that VBGMR generally outperforms GMR with the requirement of only a few activated components.