A penalized blind likelihood Kriging method

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雨下的叶2021年10月26日
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Surrogate modeling is commonly used to replace expensive simulations of engineering problems. Kriging is a popularsurrogate for deterministic approximation due to its good nonlinear fitting ability. Previous researches demonstrate thatconstructing an appropriate trend function or a better stochastic process can improve the prediction accuracy of Kriging.However, they are not improved simultaneously to estimate the model parameters, thus limiting the further improvementon the prediction capability. In this paper, a novel penalized blind likelihood Kriging (PBLK) method is proposed to obtainbetter model parameters and improve the prediction accuracy. It improves the trend function and stochastic process withregularization techniques simultaneously. First, the formulation of the penalized blind likelihood function is introduced,which penalizes the regression coefficients and correlation parameters at the same time. It is a general expression andtherefore can incorporate any type of penalty functions easily. To maximize the penalized blind likelihood functioneffectively and efficiently, a nested optimization algorithm is proposed to estimate the model parameters sequentially withgradient and Hessian information. As different regularization parameters can lead to different optimal model parametersand influence the prediction accuracy, a cross-validation-based grid search method is proposed to select good regularizationparameters. The proposed PBLK method is tested on several analytical functions and two engineering examples, and theexperimental results confirm the effectiveness of the proposed method.
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