A Generalized Probabilistic Monitoring Model with Both Random and Sequential Data

TL;DR

This paper introduces a comprehensive probabilistic monitoring model that integrates random and sequential data, analyzes connections between various methods, and provides rigorous statistical tools for process anomaly detection and fault analysis.

Contribution

It develops a generalized probabilistic monitoring model (GPMM) that unifies different process monitoring approaches and derives statistical properties for effective fault detection.

Findings

The GPMM can be reduced to various existing models under restrictions.

Monitoring statistics follow their theoretical distributions, enabling accurate control limits.

The model's effectiveness is validated on the Tennessee Eastman process example.

Abstract

Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insightful 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.