Two layered mixture Bayesian probabilistic PCA for dynamic process monitoring

In this article, two layer mixture Bayesian probabilistic principal component analyser model is developed and proposed for fault detection. It is suitable for the data driven process monitoring applications where data with non-Gaussian distribution and temporal correlations are encountered. Model development involves modifying the original observation matrix to make it suitable for building dynamic models and followed by two stages of estimation. In the first stage, the data is divided into a manageable number of clusters and in the second stage, a mixture model is built over each cluster. This strategy provides a scalable mixture model that can have multiple local models. It has the potential to provide a parsimonious model and be less susceptible to local optima compared to the existing approaches that build mixture models in a single stage. Dimension reduction during the estimation is automated using the Bayesian regularization approach. The proposed model essentially provides a probability density function for the training data. It is deployed for fault detection and the performance highlights are demonstrated in two real datasets, one is from the oil sands industry and the other is a publicly available experimental dataset.