A Novel Semi-Supervised Probabilistic Model of Fisher Discriminant Analysis for Data-Driven Fault Classification and Detection

Fault classification and detection is an important and challenging work to ensure the efficiency and safety of modern industrial processes. Data are being generated rapidly, but most of them are fetched in normal condition, and labeling abnormal data is a time consuming and costly job; therefore, semi-supervised learning is attracting more attention. Fisher discriminant analysis (FDA) is a prevalent supervised classification method, and there is an inherent connection between FDA and the well-known Gaussian mixture model. Motivated by such a connection, we proposed a new semi-supervised classification method based on FDA. In virtue of the expectation maximization algorithm, one can obtain projection directions, means and covariance matrices of all classes, and the predicted labels of unlabeled data simultaneously. Then these information can be utilized for fault analysis, classification and online detection. The method is guaranteed to converge with an acceptable computational cost. A numerical example and Tennessee Eastman case studies are carried out to demonstrate potential advantages of the proposed method.