Multivariate Gaussian process regression for nonlinear modelling with colored noise

Abstract

Nonlinearity of process systems along with colored noises is common in chemical processes. A multivariate (multiple inputs and multiple outputs) Gaussian process regression (MGPR) modelling approach, which can model multivariate nonlinear processes, is developed in this paper. The developed GPR model considers the Gaussian colored noise, rather than the traditional Gaussian white noise. The colored noise is described by the moving average (MA) model and the autoregressive (AR) model, respectively, with unknown parameters so that a MA-GPR model and an AR-GPR model are developed. These two colored noise based models are further extended to the MGPR model to generate the MA-MGPR model and the AR-MGPR model. The covariance functions of the MA-MGPR model or the AR-MGPR model are formulated with consideration of the autocorrelation of noises. Moreover, all parameters are estimated by using a unidimensional updated particle swarm optimization (PSO) algorithm, simultaneously. Numerical examples as well as a three-level drawing model of Carbon fiber production process are used to demonstrate the effectiveness of the proposed modelling approaches.