A Multiway Gaussian Mixture Model based Adaptive Kernel Partial Least Squares Regression Approach for Inferential Quality Predictions of Batch Processes

Soft sensor technique has become increasingly important to provide reliable on-line measurements, facilitate advanced process control 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 conditions or phases. In this study, a multiway Gaussian mixture model (MGMM) based kernel partial least squares (PLS) method is proposed to handle multiple operating phases in batch or semibatch processes. The measurement data are first projected onto high-dimensional kernel feature space to account for the process nonlinearity. Then the multiway Gaussian mixture model is estimated with multiple Gaussian clusters in the kernel space. Thus various localized PLS models can be built within each Gaussian cluster to characterize the dynamics in the particular operating phase. Using Bayesian inference strategy, the soft sensor models for all the test samples are adaptively selected from the multiple localized kernel PLS models representing different phases and further used for online quality predictions. The presented soft sensor method is applied to the multiphase penicillin fermentation process and the computational results demonstrate that its performance is superior to the conventional multiway kernel PLS model.