Soft Sensor Development Based on the Hierarchical Ensemble of Gaussian Process Regression Models for Nonlinear and Non-Gaussian Chemical Processes

Chemical processes are often characterized by nonlinearity, non-Gaussianity, shifting modes, and inherent uncertainty that pose significant challenges for accurate quality prediction. Therefore, a novel soft sensor based on the hierarchical ensemble of Gaussian process regression models (HEGPR) is developed for the quality variable predication of nonlinear and non-Gaussian chemical processes. The method first creates a set of diverse input variable sets based on multiple random resampling data sets and a partial mutual information criterion. Then, a set of the sample partition based ensemble Gaussian process regression model (SP-EGPR) is built from different input variable sets and the corresponding subspace training data sets by the Gaussian mixture model. Next, those influential local SP-EGPR models obtained after partial least-squares (PLS) pruning are used for the first level of ensemble learning. Finally, the second level of ensemble learning is achieved by integrating the high-performance predictions from local SP-EGPR models into the overall prediction mean and variance by the Bayesian inference and finite mixture mechanism. The usefulness and superiority of the proposed HEGPR soft sensor is verified with the Tennessee Eastman chemical process and industrial rubber-mixing process.