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High-Precision Kriging Modeling Method Based on Hybrid Sampling Criteria

Author

Listed:
  • Junjun Shi

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

  • Jingfang Shen

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

  • Yaohui Li

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

Abstract

Finding new valuable sampling points and making these points better distributed in the design space is the key to determining the approximate effect of Kriging. To this end, a high-precision Kriging modeling method based on hybrid sampling criteria (HKM-HS) is proposed to solve this problem. In the HKM-HS method, two infilling sampling strategies based on MSE (Mean Square Error) are optimized to obtain new candidate points. By maximizing MSE (MMSE) of Kriging model, it can generate the first candidate point that is likely to appear in a sparse area. To avoid the ill-conditioned correlation matrix caused by the too close distance between any two sampling points, the MC (MSE and Correlation function) criterion formed by combining the MSE and the correlation function through multiplication and division is minimized to generate the second candidate point. Furthermore, a new screening method is used to select the final expensive evaluation point from the two candidate points. Finally, the test results of sixteen benchmark functions and a house heating case show that the HKM-HS method can effectively enhance the modeling accuracy and stability of Kriging in contrast with other approximate modeling methods.

Suggested Citation

  • Junjun Shi & Jingfang Shen & Yaohui Li, 2021. "High-Precision Kriging Modeling Method Based on Hybrid Sampling Criteria," Mathematics, MDPI, vol. 9(5), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:536-:d:510143
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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. Xinyu An & Baowei Song & Zhaoyong Mao & Congcong Ma, 2018. "Layout Optimization Design of Two Vortex Induced Piezoelectric Energy Converters (VIPECs) Using the Combined Kriging Surrogate Model and Particle Swarm Optimization Method," Energies, MDPI, vol. 11(8), pages 1-22, August.
    3. Behrad Bezyan & Radu Zmeureanu, 2020. "Machine Learning for Benchmarking Models of Heating Energy Demand of Houses in Northern Canada," Energies, MDPI, vol. 13(5), pages 1-20, March.
    4. Fan, Yi & Zhao, Xudong & Li, Jing & Li, Guiqiang & Myers, Steve & Cheng, Yuanda & Badiei, Ali & Yu, Min & Golizadeh Akhlaghi, Yousef & Shittu, Samson & Ma, Xiaoli, 2020. "Economic and environmental analysis of a novel rural house heating and cooling system using a solar-assisted vapour injection heat pump," Applied Energy, Elsevier, vol. 275(C).
    5. 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.
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