Gaussian Process Regression Modelling With Complicated Noises

The Gaussian process regression(GPR)algorithm is a recently developed data-driven modelling method in the field of machine learning.The popularity of GPR is partly due to its solid theoretical basis in Bayesian Statistics,and partly because its hyper-parameters can be adaptively acquired.In addition,it has a strong generalization ability and convenience of implementation.Owing to these advantages,the GPR algorithm has been widely used in system identification,soft sensors,dynamic process modelling,ensemble learning,and other application fields.In real industrial processes,all the collected data are accompanied by various significant noises,As a result,process noise is one of the important problems in the Gaussian process modelling.Most of the traditional GPR models assume that observation noises follow a Gaussian white noise.Although this pragmatic and straightforward assumption makes GPR inference to be more computationally tractable,it also reduces the prediction accuracy and reliability of the model.This thesis consides GPR modelling approaches with various complicated noises,and proposes the improved GPR models which are adapted to the environments of the real industry process.The main contributions of the thesis lie in:(1)Considering the GPR modelling with the independent Gaussian heteroscedastic noises.Three weighted GPR models are proposed: the clustered GPR(C-GPR)model,the partial weighted GPR(PW-GPR)model and the weighted GPR(W-GPR)model.Further,the particle swarm optimization(PSO)algorithm is utilized to estimate the parameters of the proposed weighted GPR models to increase prediction accuracy of the proposed models.Two numerical examples and a wet spinning coagulation process example are used to illustrate the superiority of the proposed modelling approaches.(2)Considering the multivariate GPR(MGPR)modelling with the independent heteroscedastic noises.The weighting strategies are extended to the multivariate modelling problem,and the weighted models,the clustered multivariate GPR(C-MGPR)model,the partial weighted multivariate GPR(PW-MGPR)model,and the weighted multivariate GPR(W-MGPR)model,are proposed.Numerical examples as well as a six-level drawing of a Carbon fiber example are used to demonstrate the advantage of the proposed weighted MGPR modelling approaches.(3)Modelling the multivariate Gaussian process with the correlated Gaussian noises.A dependent multivariate Gaussian process regression(DMGPR)model is developed.Further,to improve the prediction performance of the DMGPR model,the composite multiple-model DMGPR approach based on the Gaussian Mixture Model(GMM-DMGPR)is proposed,which employs the Gaussian Mixture Model(GMM)algorithm to cluster data and evaluate their probabilities.Under a maximum likehood framework,the hyper-parameters of the proposed GMM-DMGPR model are estimated by utilizing the EM algorithm.The superiority of the proposed GMM-DMGPR approaches is demonstrated by utilizing two numerical examples and a drawing process of Carbon fiber.(4)Considering the GPR modelling with colored noises.The moving average(MA)process and the auto regressive(AR)process are utilized to model colored noise with unknown process parameters,respectively,and the MA-GPR model and the AR-GPR model are proposed.Further,the MA noise model and the AR noise model are extended to the MGPR modelling problem,and the MA-MGPR model and the AR-MGPR model are developed.Moreover,a unidimensional updated PSO algorithm is proposed to optimize the hyper-parameters of the proposed GPR models.Two numerical examples and a three-level drawing modelling example of Carbon fiber are used to demonstrate the superiority of the proposed GPR modelling approaches.Finally a conclusion is made for this thesis,together with the perspectives of this research field for the next step.