Nonparametric identification based on Gaussian process regression for distributed parameter systems

This paper proposes a nonparametric identification method based on Gaussian process regression (GPR) for completely unknown nonlinear distributed parameter systems (DPSs). Inspired by linear parameter-varying (LPV) modelling approach, an interpolated spatio-temporal Volterra model is developed to represent the DPSs in nonparametric form, in which local Volterra models are interpreted as Gaussian processes. According to the empirical Bayesian approach, we design the third-order stable kernel structure used for embedding prior knowledge and derive the estimation of hyperparameters. The hyperparameters included in local weighting functions and kernel functions are determined by the maximum likelihood method. By utilising the nonparametric identification approach to avoid model structure selection, the proposed method can improve identification result for completely unknown distributed parameter systems. Finally, two case studies validate the effectiveness of the proposed identification method.