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

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.