Structured discriminative Gaussian graph learning for multimode process monitoring

Aiming at the actual industrial process background that different modes share the same system configurations and control structure, this article proposes a novel structured discriminant Gaussian graph learning for multimode process monitoring. The proposed method considers not only the sparsity of graph model but also the measurement of data variation based on a mismatched graph and the common node support between different graphical structures. The objective function involves two sets of regularization terms: the trace terms for mismatched measurements and the l2,1$$ {\ell}_{2,1} $$-norm imposed on the union of decomposed graph matrices. Due to the introduced mismatched trace terms, the cost of matching the data points and graph models that have inconsistent class labels can be expanded, which brings more discrimination for the graph-based mode identification. While the common structure extracted by the l2,1$$ {\ell}_{2,1} $$-norm forces the estimated graph models to have structural similarities, thus alleviating the negative influence caused by graph discrimination. Once a relatively accurate and discriminative reference graph model is obtained, the downstream test graph learning and analysis can be conducted online by employing the moving window techniques. By comparing the matched and mismatched graph-based measurements, the process mode can be identified correctly and stably. To grasp the abnormal process changes, the l2,1$$ {\ell}_{2,1} $$-norm for the row sparsity is again applied to the graph difference matrices, the sensitive monitoring statistics and the fault isolation results can be obtained effectively. All the optimization problems in this paper can be solved using the alternating direction multiplier (ADMM) algorithm. The effectiveness of our proposed approach is illustrated by the application to a real blast furnace iron-making production process. This article proposes a process monitoring method based on a structured sparse Gaussian graphical model, which is more suitable for real-world industrial processes with multiple modes. The proposed method considers not only the sparsity of graph model, but also the measurement of data variation based on a mismatched graph and the common node support between different graphical structures. And the accuracy of mode identification and the monitoring effectiveness is illustrated by a real blast furnace iron-making production process.