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Extended Gaussian Kriging for computer experiments in engineering design

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Abstract

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.

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Acknowledgments

Many thanks are given to the two anonymous reviewers for their pertinent and helpful suggestions. The research of Ma was supported by the Natural Science Foundation of China under Grant 70931002, and the work of Wei was supported by the National High Technology Research and Development Plan of China under Grant 2007AA12E100.

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Authors and Affiliations

  1. Department of Management Science and Engineering, Nanjing University of Science and Technology, 200 Xiaolingwei, Nanjing, 210094, China

    Wenze Shao

  2. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 211815, China

    Haisong Deng

  3. Department of Management Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Yizhong Ma

  4. School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, 210094, China

    Zhuihui Wei

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  1. Wenze Shao
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  2. Haisong Deng
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  3. Yizhong Ma
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  4. Zhuihui Wei
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Correspondence to Wenze Shao.

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Shao, W., Deng, H., Ma, Y. et al. Extended Gaussian Kriging for computer experiments in engineering design. Engineering with Computers 28, 161–178 (2012). https://doi.org/10.1007/s00366-011-0229-7

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