Mixture Principal Component Analysis Models for Process Monitoring

Abstract

A mixture principal component analysis (MixPCA) model detector is proposed. The detector creates each cluster by aggregating input exemplars. The number of clusters in the data set is automatically determined by a Gaussian filter technique called heuristic smoothing clustering. The structure building contains two stages: (1) sizing each cluster on the basis of the clustering analysis and (2) setting up the multivariable statistic confidence levels for each cluster. After the clusters are identified, MixPCA, which is a group of PCA models, will then be created. If any input pattern is under normal operation, it would fall into the accepted region whose criteria are set on the basis of the principal component analysis (PCA), T2 and Q charts. In addition, the techniques of similarity measuring and merging between clusters are also developed for the new correlation structure of the process variables when new data sets are included. The proposed model development procedure is favorable because of its simplicity of construction, intuitive modeling based on data distribution, and flexibility of updating procedures. Extensive testing on three problems demonstrates the effectiveness and excellence of the proposed methodology.