Log Likelihood Monitoring for Multimode Process Using Variational Bayesian Mixture Factor Analysis Model

When a traditional mixture factor analysis (MFA) model is used for multimode process monitoring, the determination of parameter is complex, and the construction of monitoring statistics only considers the expectation in probability distributions of factor space and residual space. In this paper, a novel fault detection method based on a variational Bayesian MFA model for multimode process is introduced. The parameters of the MFA model structure, namely the number of local factor analyzer and the reduced dimensionality inside each factor analyzer, can be easily obtained through the birth-and-death Markov chain Monte Carlo algorithm and the variational inference technique. After parameter estimation for the Bayesian MFA model is done, a new monitoring index called negative variational log likelihood is developed by utilizing the whole information in probability distribution functions of all parameters. At last, two case studies, including a numerical example and the Tennessee Eastman (TE) process, verify the effectiveness and feasibility of the proposed monitoring scheme.