A generalized probabilistic monitoring model with both random and sequential data

Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insight-ful connections between them have rarely been studied. In this study, a generalized probabilistic monitoring model (GPMM) is developed with both random and sequential data. Since GPMM can be reduced to various probabilistic linear models under specific restrictions, it is adopted to analyze the connections between different monitoring methods. Using expectation maximization (EM) algorithm, the parameters of GPMM are estimated for both random and sequential cases. Based on the obtained model parameters, statistics are designed for monitoring different aspects of the process system. Besides, the distributions of these statistics are rigorously derived and proved, so that the control limits can be calculated accordingly. After that, contribution analysis methods are presented for identifying faulty variables once the process anomalies are detected. Finally, the equivalence between monitoring models based on classical multivariate methods and their corresponding probabilistic graphic models is further investigated. The conclusions of this study are verified using a numerical example and the Tennessee Eastman (TE) process. Experimental results illustrate that the proposed monitoring statistics are subject to their corresponding distributions, and they are equivalent to statistics in classical deterministic models under specific restrictions. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This study develops a generalized probabilistic monitoring model (GPMM) to analyze the connections between different monitoring methods. The model parameters are estimated using the expectation maximization (EM) algorithm, and the distributions of monitoring statistics are rigorously derived and proved for calculating control limits. Contribution analysis methods are presented for identifying faulty variables and the equivalence between classical multivariate monitoring models and their corresponding probabilistic graphic models is investigated.