Structured sequential Gaussian graphical models for monitoring time-varying process

Abstract

This article introduces a structured and sequential Gaussian graphical approach for monitoring time-varying industrial systems. To address the presence of time-varying trends, the article utilizes a sequential update procedure for Gaussian graphical models that is based on a moving window approach. The implementation of this approach requires that the Gaussian graph models are constructed based on two additional regularization terms. For a time-varying graphical structure, the overall trend can be isolated by the first additional regularization term; while abnormal events can be timely captured using the second regularization term. Unlike conventional graphical networks that rely on other methods for fault detection, this article proposes a unified graphical framework for fault detection and isolation. In addition, the optimization problem of the Gaussian graphical model can be solved using the Alternative Direction Method of Multiplier (ADMM) algorithm, which has a linear convergence rate, making it easily applicable to large-scale systems. The performance of this graph-based technique is demonstrated by a simulation example and the application study to an industrial distillation process.