Multimodal process monitoring based on variational Bayesian PCA and Kullback-Leibler divergence between mixture models

In modern industrial processes, multimodality is a common characteristic and process monitoring tools should be capable of detecting the occurrence of abnormalities in the presence of process mode changes. Although Gaussian mixture model (GMM) is often used to depict the multimodal characteristics of processes, the conventional monitoring schemes rely on identifying the process mode and applying the unimodal statistical methods to each Gaussian component. However, the process mode of any given observation is typically unknown and it may belong to any process mode. Thus, multimodal process cannot be well modeled by unimodal models. In this paper, a multimodal process monitoring method using variational Bayesian principal component analysis (VBPCA) and Kullback-Leibler (KL) divergence between mixture models is proposed. GMM-VBPCA is used to capture multimodal process information. KL divergence between mixture Gaussians is used as statistics of both latent and noise variables to measure the dissimilarity between the reference mixture model and the monitored mixture model with respect to each process mode. Then, Bayesian inference is employed to fuse the statistics and control limits, and the final monitoring result is obtained by considering both latent and noise statistics. Finally, the proposed method and three other representative methods are evaluated through a simulated Continuous Stirred Tank Reactor (CSTR) and an industrial hydrocracking process.