Deep Learning of Latent Variable Models for Industrial Process Monitoring

Data-driven process monitoring based on latent variable models are widely employed in industry. This article proposes a novel monitoring framework for latent variable models using hierarchical feature extraction, Bayesian inference, and weighting strategy. We first establish a deep structure to implement hierarchical latent variables extraction, the extracted features are used to construct diverse monitoring statistics. Then, we utilize Bayesian inference and proper weighting strategy to fuse various useful information. In line with the different characteristics of principal component analysis (PCA) and independent component analysis (ICA), we construct a deep PCA-ICA model for process monitoring according to the proposed framework. The deep PCA-ICA model performs hierarchical feature extraction, which can simultaneously extract deep Gaussian information and deep non-Gaussian information. The features extracted by different layers are then transformed to posterior probabilities through Bayesian inference. After that, different posterior probabilities are combined through appropriate weighting strategy to build new probabilistic statistic, which can give more synthetic monitoring results. Moreover, the Bayesian inference and weighting strategy are further used to integrate the advantages of different models by transforming various probabilistic statistics into an overall monitoring index, which can comprehensively indicate the process status. The Tennessee Eastman process is used to validate the superiority of the proposed model over the existing methods. Besides, the extracted features are further analyzed to show the effectiveness and benefits of the deep hierarchical feature extraction structure.