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.

Multivariate statistical process control charts: an overview

“…Furthermore, a graphical technique which can be applied in these limiting situations was also provided. Choi et al 192 have developed a fault-detection method based on a maximum likelihood-PCA mixture.…”

A branch and bound method for isolation of faulty variables through missing variable analysis

“…If needed, the PPCA can be extended to a mixture model to suit non-Gaussian distributed process data [20].…”

Reconstruction-based multivariate contribution analysis for fault isolation: A branch and bound approach

“…In the community of MSPM, PPCA mixture model was introduced to monitor processes with multiple modes or non-Gaussian distributions [14,15]. The use of a fully probabilistic model provided a unified likelihood-based statistic (8) This integral can be calculated using numerical methods such as Mote Carlo simulation [14].…”

“…When data are not Gaussian distributed, notable solutions to MSPM include kernel density estimation [8], Gaussian mixture model (GMM) [9,10,11], independent component analysis [12], one-class SVM model [13], among others. The probabilistic PCA (PPCA) mixture model is an extension of GMM by incorporating a probabilistic version of PCA, and it has been shown to be effective for MSPM [14,15]. The probabilistic formulation used by the PPCA mixture model provides a unified likelihood-based statistic that offers clearer monitoring result.…”