Dynamic Nonlinear Partial Least Squares Modeling Using Gaussian Process Regression

A dynamic Gaussian process regression based partial least-squares (D-GPR-PLS) model is proposed to improve estimation ability and compared to the conventional nonlinear PLS. Considering the strong ability of GPR in nonlinear process modeling, this method is used to build a nonlinear regression between each pair of latent variables in the partial least-squares. In addition, augmented matrices are embedded into the D-GPR-PLS model to obtain better prediction accuracy in nonlinear dynamic processes. To evaluate the modeling performance of the proposed method, two simulated cases and a real industrial process based on wastewater treatment processes (WWTPs) are considered. The simulated cases use data from two high fidelity simulators: benchmark simulation model no. 1 and its long-term version. The second study uses data from a real biological wastewater treatment process. The results show the superiority of D-GPR-PLS in modeling performance for both data sets. More specifically, in terms of the prediction for effluent chemical oxygen demand of the real WWTP data, the value of the root-mean-square error is decreased by 31%, 16%, and 52%, respectively, in comparison with that for linear PLS, quadratic PLS, and least-squares support vector machine based PLS.