Streaming variational probabilistic principal component analysis for monitoring of nonstationary process

Abstract

Modern industrial processes are characteristic of nonstationary and uncertainty. To address these issues, this paper proposes a probabilistic principal component analysis based model that utilizes streaming variational inference for online monitoring of nonstationary process. The model parameters are updated in a streaming/batch-wise manner to track the nonstationary behavior in the process. In the updating procedures, the posterior distributions obtained from the previous data batch are used as priors for the current model, whose parameters can be estimated using the variational Bayesian inference. The streaming variational inference enables recursive parameter estimation over time. Additionally, in order to improve computational efficiency, a distributed update strategy is also applied to the proposed model. For online process monitoring, the noncentral chi-square distributions are derived to estimate the statistical control limits for each data batch, resulting in better adaptation to the nonstationary characteristics. The effectiveness and superiority of the proposed method are validated through simulation example and real-world industrial application.