Mixtures of Probabilistic PCA With Common Structure Latent Bases for Process Monitoring

Abstract

In this brief, we propose the mixtures of probabilistic principal component analyzers with latent bases having a common structure for modeling and monitoring multimodal processes. The proposed modeling framework attributes a joint distribution to each element of the latent bases across all the analyzers for bringing a consistent structure for the local models that correspond to various operating modes. Hierarchical prior distributions are attributed to regularize the parameters for obtaining sparse model structures. We employ the variational Bayesian expectation-maximization algorithm to train the model from the observed data. Faults are detected online if nonconformity of a data point to the developed model is identified. Furthermore, we identify faulty latent variables, and the process variables, which are significantly contributing to the faulty latent variables, are isolated by exploiting the unique structure of the model. We illustrate our proposed approach based on the simulations conducted on the Tennessee Eastman benchmark process.