Semi-Supervised Dynamic Latent Variable Regression for Prediction and Quality-Relevant Fault Monitoring

Supervised latent variable regression methods such as partial least squares (PLS) and dynamic PLS have found wide applications in data analytics, quality prediction, and fault monitoring in various industries. In this article, we tackle the unbalanced data problem of sparse quality measurement and abundant process data in process control systems to make use of all data samples for modeling. A novel semi-supervised dynamic latent variable regression (SemiDLVR) method is proposed for quality prediction and quality-relevant fault monitoring. The proposed SemiDLVR method integrates Laplacian manifold regularization with dynamic regularized latent variable regression (DrLVR) to form a semi-supervised framework to efficiently model unlabeled data. A unified objective that combines DrLVR and the Laplacian matrix is proposed and the solution is provided. Statistical monitoring indices are, thereafter, defined for quality-relevant fault monitoring in the semi-supervised framework. Results from experimental studies on a numerical simulation, an industrial sulfur recovery unit (SRU), and the Tennessee Eastman (TE) process benchmark are presented to demonstrate the effectiveness of the proposed method.