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• Traditional Gaussian Process Regression models typically assume independent identically distributed noises for all observations. However, applications with colored noises/disturbances frequently arise in modeling of complex processes. • We modeled the colored noise by an ARMA time series model and determined its covariance for subsequent Gaussian Process modeling. • A novel approach based on hybrid kernels is proposed, thereby avoiding parametric modeling of the colored noises. • A synthetic data, a simulated example and a polyester polymerization process were used to demonstrate the effectiveness of the proposed approach. Traditional Gaussian Process Regression (TGPR) models typically assume independent identically distributed (i.i.d.) noises for all observations. However, applications with colored noises/disturbances frequently arise in modeling of complex processes. In this work, first, we consider to model noise by an ARMA time series model and determine its covariance for subsequent Gaussian Process (GP) modeling. Then a novel approach based on hybrid kernels is proposed, thereby avoiding parametric modeling of the colored noises. Moreover, all hyper-parameters are estimated simultaneously by using a particle swarm optimization (PSO) algorithm. Finally, a synthetic data, a simulated example, as well as a polyester polymerization process are used to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

A composite multiple-model approach based on multivariate Gaussian process regression (MGPR) with correlated noises is proposed in this paper. In complex industrial processes, observation noises of multiple response variables can be correlated with each other and process is nonlinear. In order to model the multivariate nonlinear processes with correlated noises, a dependent multivariate Gaussian process regression (DMGPR) model is developed in this paper. The covariance functions of this DMGPR model are formulated by considering the “between-data” correlation, the “between-output” correlation, and the correlation between noise variables. Further, owing to the complexity of nonlinear systems as well as possible multiple-mode operation of the industrial processes, to improve the performance of the proposed DMGPR model, this paper proposes a composite multiple-model DMGPR approach based on the Gaussian Mixture Model algorithm (GMM-DMGPR). The proposed modelling approach utilizes the weights of all the samples belonging to each sub-DMGPR model which are evaluated by utilizing the GMM algorithm when estimating model parameters through expectation and maximization (EM) algorithm. The effectiveness of the proposed GMM-DMGPR approach is demonstrated by two numerical examples and a three-level drawing process of Carbon fiber production. [ABSTRACT FROM AUTHOR]