Structural optimization under dynamic reliability constraints utilizing probability density evolution method and metamodels in augmented input space

An effective method for solving a class of dynamic-reliability-based design optimization (DRBDO) problems is proposed in the present paper. Failure probability functions and their sensitivities with respect to the design variables are estimated in the framework of the probability density evolution method (PDEM). In particular, a PDEM-based metamodel-refined approach is defined in an augmented input space to improve the efficiency of failure probability estimations and sensitivity analyses. Moving trust regions are imposed on the augmented input space to ensure the accuracy of the metamodel. To solve the optimization problems, the PDEM-based metamodel-refined approach is embedded into a feasible direction interior point scheme. In this scheme, a feasible search direction is first obtained by solving the perturbed Karush–Kuhn–Tucker (KKT) conditions. Then, a line search technique, which is consistent with the PDEM-based metamodel-refined approach, is employed to speed up the convergence of the optimization process. The results of the numerical examples indicate that the proposed method is a competitive choice for solving a class of DRBDO problems with a small number of reliability and structural analyses.