Efficient Process Monitoring via the Integrated Use of Markov Random Fields Learning and the Graphical Lasso

Process monitoring is an important aspect of safe operation of process plants. Various methods exist that monitor the process using data-driven methods, but they all have certain limitations. For instance, most of the fault detection methods are not able to detect the fault propagation path, and some methods require a priori knowledge on the faults, or the relationships between the monitored variables. In this study, a monitoring method for accurately detecting the faults and analyzing the fault propagation path is proposed. Named the Glasso-MRF monitoring framework, this method integrates the use of the graphical lasso algorithm (G-lasso) and the Markov random field (MRF) modeling framework to divide the monitored variables into relevant groups and then detect the faults separately for each of the groups. Graphical lasso uses the lasso constraint on the inverse covariance matrix of variables within the maximum likelihood estimation problem, driving it to be of sparse form. The use of graphical lasso downsizes the process into groups that are highly correlated, relieving the computational complexity of the MRF-based monitoring so that the process can be efficiently monitored, and enabling the fault propagation path to be identified. MRF modeling can extensively model the variable relationships including cyclic structures, and can be obtained without a priori knowledge of the relationships between variables, using the iterative graphical lasso algorithm proposed in this study. The inference of MRFs are usually complex due to the existence of partition functions, but by down-sizing the system using iterative G-lasso, this problem is resolved as well. The proposed method was applied to the well-known Tennessee Eastman process to evaluate its performance. The detection accuracy of the Glasso-MRF monitoring framework was higher than any other state-of-the-art monitoring methods, including autoencoders and Bayesian networks, showing more than 95% fault detection accuracy for all of the 28 faults programmed within the Tennessee Eastman process. Also, the fault propagation path could be detected according to the difference in fault detection time of the divided groups, providing enhanced analysis of the initiated fault. These results prove that the proposed methodology can effectively detect the fault as well as show its propagation throughout the process, without any a priori knowledge of the process variables.