Multiway Gaussian Mixture Model Based Adaptive Kernel Partial Least Squares Regression Method for Soft Sensor Estimation and Reliable Quality Prediction of Nonlinear Multiphase Batch Processes

The predictive model based soft sensor technique has become increasingly important to provide reliable online measurements, facilitate advanced process control and optimization, and improve product quality in process industries. The conventional soft sensors are normally single-model based and thus may not be appropriate for processes with shifting operating phases or conditions and the underlying changing dynamics. In this study, a multiway Gaussian mixture model (MGMM) based adaptive kernel partial least-squares (AKPLS) method is proposed to handle online quality prediction of batch or semibatch processes with multiple operating phases. The three-dimensional measurement data are first preprocessed and unfolded into two-dimensional matrix. Then, the multiway Gaussian mixture model is estimated in order to identify and isolate different operating phases. Further, the process and quality measurements are separated into multiple segments corresponding to those identified phases, and the various localized kernel PLS models are built in the high-dimensional nonlinear feature space to characterize the shifting dynamics across different operating phases. Using Bayesian inference strategy, each process measurement sample of a new batch is classified into a particular phase with the maximal posterior probability, and thus, the local kernel PLS model representing the identical phase can be adaptively chosen for online quality variable prediction. The presented soft sensor modeling method is applied to a simulated multiphase penicillin fermentation process, and the computational results demonstrate that the proposed MGMM-AKPLS approach is superior to the conventional kernel PLS model in terms of prediction accuracy and model reliability.