Extended Gaussian Kriging for computer experiments in engineering design

Metamodeling or surrogate modeling is becoming increasingly popular for product design optimization in manufacture industries. In this paper, an extended Gaussian Kriging method is proposed to improve the prediction performance of widely used ordinary Kriging in engineering design. Unlike the forgoing approaches, the proposed method places a variance-varying Gaussian prior on the unknown regression coefficients in the mean model of Kriging and makes prediction at untried design points based on the principle of Bayesian maximum a posterior. The achieved regression mean model is adaptive, therefore capable of capturing more effectively the overall trend of computer responses and leading to a more accurate metamodel. Particularly, the regression coefficients in the mean model are estimated by a fast numerical algorithm, making extended Gaussian Kriging implemented roughly as efficient as ordinary Kriging. Experiment results on several examples are presented, showing remarkable improvement in prediction using extended Gaussian Kriging over ordinary Kriging and several other metamodeling methods.