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

Yaohui Li, Junjun Shi, Zhifeng Yin, Jingfang Shen, Yizhong Wu and Shuting Wang
Additional contact information
Yaohui Li: College of Mechanical and Electrical Engineering, Xuchang University, Xuchang 461000, China
Junjun Shi: College of Mechanical and Electrical Engineering, Xuchang University, Xuchang 461000, 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

Mathematics, 2021, vol. 9, issue 16, 1-18

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.

Keywords: surrogate model; Kriging; high-dimensional problems; principal component dimension reduction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/16/1985/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/16/1985/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:16:p:1985-:d:617735

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().