Fault detection based on a maximum-likelihood principal component analysis (PCA) mixture

Abstract

Multivariate statistical process control (MSPC) that is based on principal component analysis (PCA) has been applied to many industrial processes. Such an approach assumes that the process signals are normally distributed and exhibit stationary behavior. These assumptions significantly limit the range of applicability of the methodology. In this paper, a monitoring scheme based on a maximum-likelihood PCA (MLPCA) mixture is proposed. The main idea behind the approach is that complex data patterns obtained from a process can be described by several local models. A learning algorithm that helps determine model structure, i.e., the number of local PCA models to be constructed and the number of principal components to be included in each local model, is proposed, resulting in the efficient determination of a MLPCA mixture model. Two monitoring statistics used in the MLPCA-based monitoring scheme are then derived and a two-step fault detection method is proposed. Several mathematical models that describe different process features, including multiple steady states, nonlinearity, and process dynamics, are used to demonstrate the potential of the proposed method. The approach is compared with previous approaches, including nonlinear PCA and dynamic PCA, and it is confirmed that the developed methodology is a good alternative. Finally, the method is applied for fault detection on a continuously stirred tank reactor process, and its performance for detecting six types of faults, in terms of false alarm rate, missed alarm rate, and detection delay, is shown to outperform current approaches.