Sequential Graphical Lasso for Fault Detection and Isolation

Abstract

This article proposes a sequential graphical Lasso based approach for monitoring of complex industrial systems. The graphical Lasso is a widely used algorithm to estimate the precision matrix (inverse covariance matrix), which encodes the conditional relationship between pairs of variables given other entities. Based on the estimated precision matrix, a graphical model can be constructed to represent the structured correlation information between process variables. The proposed approach utilizes the graphical model to localize anomalous variables. Different from the conventional graphical Lasso approach, the proposed method considers an additional fusseed lasso term and a similarity term in the objective function and the optimization problem can be solved by the alternative direction method of multiplier (ADMM). Using a moving window approach, the proposed method generates a sequence of sparse Gaussian graphs and a new monitoring statistic based on penalized likelihood ratio and matrix norm is constructed. Once a fault is detected, the problem of fault isolation becomes a graph matching problem and a fault score index is calculated for each variable. The validity of proposed method in fault detection and isolation is illustrated by a typical fault observed in the Tennessee Eastman (TE) process.