Deep Probabilistic Principal Component Analysis for Process Monitoring

Probabilistic latent variable models (PLVMs), such as probabilistic principal component analysis (PPCA), are widely employed in process monitoring and fault detection of industrial processes. This article proposes a novel deep PPCA (DePPCA) model, which has the advantages of both probabilistic modeling and deep learning. The construction of DePPCA includes a greedy layer-wise pretraining phase and a unified end-to-end fine-tuning phase. The former establishes a hierarchical deep structure based on cascading multiple layers of the PPCA module to extract high-level features. The latter builds an end-to-end connection between the raw inputs and the final outputs to further improve the representation of the model to high-level features. After constructing the model structure of DePPCA, we first present the detailed training processes of the pretraining and fine-tuning stages, then clarify the theoretical merits of the proposed model from the perspective of variational inference. For process monitoring purposes, we develop two statistics based on the established DePPCA. The monitoring performance of these two statistics can remain superior even if the features extracted by DePPCA are significantly compressed to univariate. This makes the feature extraction process and online monitoring procedure of DePPCA quite fast. In other words, the proposed DePPCA can achieve accurate and efficient process monitoring by only extracting one feature for each sample. Finally, the effectiveness of DePPCA is evaluated on the Tennessee Eastman (TE) process and the multiphase flow (MPF) facility.