Multimode Process Monitoring Based on Modified Probabilistic Linear Discriminant Analysis

This paper focus on developing an effective method to monitor the industrial process with multiple operation conditions. By utilizing the technique of probabilistic linear discriminant analysis (PLDA), the between- and within-class latent variables can extract more useful information. The proposed method, the modified PLDA (MPLDA), transforms the centralized samples into a new type of between-class latent variables. The current mode operation condition can be identified by comparing a series of cosine similarities deduced by the original and the new between-class latent variables. The online monitoring procedures are built on the basis of this mode identification. Unlike the conventional $T^{2}$ and $Q$ statistics designed for within-class latent variable, the proposed monitoring statistics take both between- and within-class latent variables into consideration. For the model training, the joint updating expectation-maximization (EM) algorithm is developed. The enhanced performance of the MPLDA based method is illustrated by the application of Tennessee Eastman (TE) process.