Maximized Mutual Information Analysis Based on Stochastic Representation for Process Monitoring

Abstract

This paper proposes a stochastic representation of maximized mutual information analysis (MIA) method for quality monitoring in which a manner of imposing prior probability distributions over projection parameters is employed and subsequently, a Bayesian estimation algorithm is put forward for projection learning. The proposed stochastic MIA (SMIA) based approach allows the enhanced performance of fault detection due to the following advantages over classic monitoring methods. First, the SMIA approach utilizes the mechanism of hierarchical priors and an individual prior over each projection direction, as a key feature of the proposed method, which enables SMIA to build a sparse model that can discard irrelevant components in the process data with respect to the prediction of quality variables. Second, the proposed SMIA method incorporates the advantage of maximizing mutual information on the minimum achievable error of model prediction as well as the advantage of describing the serial dynamics. Additionally, the optimal dimensionality of the latent space in an SMIA can be automatically determined during the procedure of Bayesian estimation by the utilization of these adaptive priors over projections. The effectiveness of the proposed approach for quality monitoring is demonstrated on the benchmark of Tennessee Eastman process.