Process monitoring using a Gaussian mixture model via principal component analysis and discriminant analysis

Conventional process monitoring based on principal component analysis (PCA) has been applied to many industrial chemical processes. However, such PCA-based approaches assume that the process is operating in a steady state and consequently that the process data are normally distributed and contain no time correlations. These assumptions significantly limit the applicability of PCA-based approaches to the monitoring of real processes. In this paper, we propose a more exact and realistic process monitoring method that does not require that the process data be normally distributed. Specifically, the concept of conventional PCA is expanded such that a Gaussian mixture model (GMM) is used to approximate the data pattern in the model subspace obtained by PCA. The use of a mixture of local Gaussian models means that the proposed approach can be applied to arbitrary datasets, not just those showing a normal distribution. To use the GMM for monitoring, the overall T-2 and Q statistics were used as the monitoring guidelines for fault detection. The proposed approach significantly relaxes the restrictions inherent in conventional PCA-based approaches in regard to the raw data pattern, and can be expanded to dynamic process monitoring without developing a complicated dynamic model. In addition, a GMM via discriminant analysis is proposed to isolate faults. The proposed monitoring method was successfully applied to three case studies: (1) simple two-dimensional toy problems, (2) a simulated 4 x 4 dynamic process, and (3) a simulated non-isothermal continuous stirred tank reactor (CSTR) process. These application studies demonstrated that, in comparison to conventional PCA-based monitoring, the proposed fault detection and isolation (FDI) scheme is more accurate and efficient. (C) 2003 Elsevier Ltd. All rights reserved.