No-Delay Multimodal Process Monitoring Using Kullback-Leibler Divergence-Based Statistics in Probabilistic Mixture Models

Abstract

The primary goal of multimodal process monitoring is to detect abnormalities or occurrence of faults. However, the profound challenge in the multimodal monitoring problem is that it is difficult to quickly distinguish the fault occurrence on a process mode from other operating modes. In this work, a Gaussian mixture model based variational Bayesian principal component analysis (GMM-VBPCA) is proposed. GMM is used to capture the global multimodal information where each Gaussian component of GMM represents a corresponding normal operating mode. VBPCA is employed to construct a probabilistic model for each operating mode. Using the weights of posterior probabilities from global GMM, local VBPCA models can then be fused to characterize the normal multimodal processes. In order to detect the occurrence of faults, Kullback-Leibler (KL) divergence of latents and model residuals of the multimodal process are used as the monitoring statistics that measure the deviation from the normal multimodal distribution. Owing to the variational local model, the posterior distribution of latents and model residuals of the GMM-VBPCA can characterize the process behavior for every test sample. Finally, GMM-VBPCA based monitoring statistics are compared with existing process monitoring methods through a simulated numerical example and an industrial hydrocracking process. Note to Practitioners—In this paper, a novel process monitoring statistics has been proposed that can aid the practitioners in accurately identifying the process faults in near real-time with minimal false alarm. Also, the sensitivity to small bias faults is higher that the traditional methods, thus enabling higher fault detection rate. Based on the proposed statistics, an online monitoring scheme has been proposed. Hence, it is useful for practitioners in quickly taking preventive measures to avoid catastrophe, and also taking corrective measures to bring the plant to normal operating range or scheduling maintenance in case of early detection of sensor or equipment failures.