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A Transformation-Based Improved Kriging Method for the Black Box Problem in Reliability-Based Design Optimization

Author

Listed:
  • Li Lu

    (National Center of Technology Innovation for Intelligent Design and Numerical Control, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Yizhong Wu

    (National Center of Technology Innovation for Intelligent Design and Numerical Control, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Qi Zhang

    (National Center of Technology Innovation for Intelligent Design and Numerical Control, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Ping Qiao

    (School of Mechanical Engineering, Suzhou University of Science and Technology, Suzhou 215011, China)

Abstract

In order to overcome the drawbacks of expensive function evaluation in the practical reliability-based design optimization (RBDO) problem, researchers have proposed the black box-based RBDO method. The algorithm flow of the commonly employed RBDO method for the black box problem consists of the outer construction loop of the surrogate model of the constraint function and the inner surrogate model-based solving loop. To improve the solving ability of the black box RBDO problem, this paper proposes a transformation-based improved kriging method to increase the effectiveness of the two loops identified above. For the outer loop, a sample distribution-based learning function is suggested to improve the construction efficiency of the surrogate model of the constraint function. For the inner loop, a paired incremental sample-based limit reliability boundary construction approach is suggested to transform the RBDO problem into an equivalent deterministic design optimization problem that can be efficiently solved by classical optimization algorithms. The test results of five cases demonstrate that the proposed method can accurately construct the surrogate model of the constraint function and efficiently solve the black box RBDO problem.

Suggested Citation

  • Li Lu & Yizhong Wu & Qi Zhang & Ping Qiao, 2023. "A Transformation-Based Improved Kriging Method for the Black Box Problem in Reliability-Based Design Optimization," Mathematics, MDPI, vol. 11(1), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:1:p:218-:d:1022085
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    References listed on IDEAS

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    1. Jing, Zhao & Chen, Jianqiao & Li, Xu, 2019. "RBF-GA: An adaptive radial basis function metamodeling with genetic algorithm for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 42-57.
    2. 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).
    3. Ni, Pinghe & Li, Jun & Hao, Hong & Yan, Weimin & Du, Xiuli & Zhou, Hongyuan, 2020. "Reliability analysis and design optimization of nonlinear structures," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    4. Jinghong Liang & Zissimos P. Mourelatos & Jian Tu, 2008. "A single-loop method for reliability-based design optimisation," International Journal of Product Development, Inderscience Enterprises Ltd, vol. 5(1/2), pages 76-92.
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