Variational Bayesian Student’s-t Mixture Model With Closed-Form Missing Value Imputation for Robust Process Monitoring of Low-Quality Data

Due to record errors, transmission interruptions, etc., low-quality process data, including outliers and missing data, commonly exist in real industrial processes, challenging the accurate modeling and reliable monitoring of the operating statuses. In this study, a novel variational Bayesian Student's-t mixture model (VBSMM) with a closed-form missing value imputation method is proposed to develop a robust process monitoring scheme for low-quality data. First, a new paradigm for the variational inference of Student's-t mixture model is proposed to develop a robust VBSMM model, which optimizes the variational posteriors in an extended feasible region. Second, conditioned on the complete and partially missing data information, a closed-form missing value imputation method is derived to address the challenges of outliers and multimodality in accurate data recovery. Then, a robust online monitoring scheme that can maintain its fault detection performance in the presence of poor data quality is developed, where a novel monitoring statistic called the expected variational distance (EVD) is first proposed to quantify the changes in operating conditions and can be easily extended to other variational mixture models. Case studies on a numerical simulation and a real-world three-phase flow facility illustrate the superiority of the proposed method in missing value imputation and fault detection of low-quality data.