Nonparametric identification of batch process using two-dimensional kernel-based Gaussian process regression

•A two-dimensional (2D) kernel-based Gaussian process regression identification method for batch process is proposed.•The 2D kernel is designed by means of addition / multiplication operation based on coordinate decomposition, and the properties of the proposed 2D kernel are analyzed.•The developed GPR-based identification method considers the time-varying noise, which is modeled as another zero-mean Gaussian process. In this work, a two-dimensional (2D) kernel-based Gaussian process regression (GPR) method for the identification of batch process is proposed. Under the GPR framework, the estimate of the time-varying impulse response is a realization from a zero-mean Gaussian process (GP), wherein the kernel function encodes the possible structural dependencies. However, the existing kernels designed for system identification are one-dimensional (1D) kernels and underutilize the 2D data information of batch process. Utilizing the 2D correlation property of batch process impulse response, we propose the amplitude modulated 2D locally stationary kernel by means of addition / multiplication operation based on coordinate decomposition. Then, a nonparametric identification method using 2D kernel-based GPR for batch process is developed. Furthermore, the properties of the proposed 2D kernel are analyzed. Finally, we demonstrate the effectiveness of the proposed identification method in two examples.