Robust Variational Bayesian-Based Soft Sensor Model for LPV Processes With Delayed and Integrated Output Measurements

To satisfy the objectives of industrial process control and automation, accurate real-time measurements of quality variables are desired. While most of the process variables are measured frequently, some quality variables cannot be recorded regularly due to economical considerations or technical limitations. To measure the quality variables of some processes, samples are usually collected over a considerable time interval (integration interval) and sent to the laboratory. Due to the time-consuming offline analysis in the laboratory, the measurements would be available only after a significant delay. The lack of frequent measurements for such variables may hamper the performance of control and optimization techniques. Furthermore, the processes often show time-varying properties due to operating over different conditions, aging, and so on. This article proposes a soft sensor model for the quality variables in linear parameter-varying (LPV) processes subject to unknown varying integration intervals, unknown varying delays, and outliers. The unknown parameters of the soft sensor model and noise variance along with their uncertainties are estimated using a robust variational Bayesian (VB) algorithm. Also, the proposed algorithm estimates various statistics based on a nonparametric distribution technique. Finally, a numerical example and an experimental study on a hybrid three-tank (HTT) system demonstrate the advantages of the developed model.