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

Abstract

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 4×4 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.