Multimode process monitoring with PCA mixture model

For multimode processes, Gaussian mixture model (GMM) has been applied to estimate the probability density function of the process data under normal-operational condition in last few years. However, learning GMM with the expectation maximization (EM) algorithm from process data can be difficult or even infeasible for high-dimensional and collinear process variables. To address this issue, a novel multimode process monitoring approach based on PCA mixture model is proposed. First, the PCA technique is directly applied to the covariance matrix of each Gaussian component to reduce the dimension of process variables and to obtain nonsingular covariance matrices. Then the Bayesian Ying-Yang incremental EM algorithm is adopted to automatically optimize the number of mixture components. With the obtained PCA mixture model, a novel process monitoring scheme is derived for fault detection of multimode processes. Three case studies are provided to evaluate the monitoring performance of the proposed method.