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

Li Lu, Yizhong Wu (), Qi Zhang and Ping Qiao
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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

Mathematics, 2023, vol. 11, issue 1, 1-19

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.

Keywords: RBDO; learning function; limit reliability boundary; paired incremental sample (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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