High-Precision Kriging Modeling Method Based on Hybrid Sampling Criteria

Junjun Shi, Jingfang Shen and Yaohui Li
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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

Mathematics, 2021, vol. 9, issue 5, 1-25

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.

Keywords: surrogate model; Kriging; infill sampling criteria; multiplication and division (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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