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An Improved High-Dimensional Kriging Surrogate Modeling Method through Principal Component Dimension Reduction

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  • Yaohui Li

    (College of Mechanical and Electrical Engineering, Xuchang University, Xuchang 461000, China
    College of Science, Huazhong Agricultural University, Wuhan 430070, China)

  • Junjun Shi

    (College of Mechanical and Electrical Engineering, Xuchang University, Xuchang 461000, China
    College of Science, Huazhong Agricultural University, Wuhan 430070, China)

  • Zhifeng Yin

    (College of Mechanical and Electrical Engineering, Xuchang University, Xuchang 461000, China)

  • Jingfang Shen

    (College of Science, Huazhong Agricultural University, Wuhan 430070, China)

  • Yizhong Wu

    (National CAD Supported Software Engineering Centre, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Shuting Wang

    (National CAD Supported Software Engineering Centre, Huazhong University of Science and Technology, Wuhan 430074, China)

Abstract

The Kriging surrogate model in complex simulation problems uses as few expensive objectives as possible to establish a global or local approximate interpolation. However, due to the inversion of the covariance correlation matrix and the solving of Kriging-related parameters, the Kriging approximation process for high-dimensional problems is time consuming and even impossible to construct. For this reason, a high-dimensional Kriging modeling method through principal component dimension reduction (HDKM-PCDR) is proposed by considering the correlation parameters and the design variables of a Kriging model. It uses PCDR to transform a high-dimensional correlation parameter vector in Kriging into low-dimensional one, which is used to reconstruct a new correlation function. In this way, time consumption of correlation parameter optimization and correlation function matrix construction in the Kriging modeling process is greatly reduced. Compared with the original Kriging method and the high-dimensional Kriging modeling method based on partial least squares, the proposed method can achieve faster modeling efficiency under the premise of meeting certain accuracy requirements.

Suggested Citation

  • Yaohui Li & Junjun Shi & Zhifeng Yin & Jingfang Shen & Yizhong Wu & Shuting Wang, 2021. "An Improved High-Dimensional Kriging Surrogate Modeling Method through Principal Component Dimension Reduction," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1985-:d:617735
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    References listed on IDEAS

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    1. Nobuo Namura & Koji Shimoyama & Shigeru Obayashi, 2017. "Kriging surrogate model with coordinate transformation based on likelihood and gradient," Journal of Global Optimization, Springer, vol. 68(4), pages 827-849, August.
    2. Mohamed Amine Bouhlel & Nathalie Bartoli & Abdelkader Otsmane & Joseph Morlier, 2016. "An Improved Approach for Estimating the Hyperparameters of the Kriging Model for High-Dimensional Problems through the Partial Least Squares Method," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-11, June.
    3. Keshtegar, Behrooz & Mert, Cihan & Kisi, Ozgur, 2018. "Comparison of four heuristic regression techniques in solar radiation modeling: Kriging method vs RSM, MARS and M5 model tree," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 330-341.
    4. Li, Yaohui & Shi, Junjun & Cen, Hui & Shen, Jingfang & Chao, Yanpu, 2021. "A kriging-based adaptive global optimization method with generalized expected improvement and its application in numerical simulation and crop evapotranspiration," Agricultural Water Management, Elsevier, vol. 245(C).
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    Cited by:

    1. Camelia Petrescu & Valeriu David, 2022. "Preface to the Special Issue on “Modelling and Simulation in Engineering”," Mathematics, MDPI, vol. 10(14), pages 1-3, July.

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