Reliability-based design optimization method with correlated variables using adaptive conjugate gradient analysis and Copula

Reliability-based design optimization (RBDO) with correlated input variables is an important issue in the field of RBDO. However, there has been no substantial progress in this direction, and existing RBDO methods that handle variables independently may result in optimization results with lower computational accuracy for such problems. To this gap, this study proposes an efficient RBDO method integrating with the Copula function to solve the problems with correlated input variables, which provides optimization results with sufficient confidence. The strategy is that an adaptive conjugate gradient analysis (ACGA) method composed of a parameterized search direction criterion and an adaptive step size adjustment strategy is firstly proposed to efficiently handle convex or highly nonlinear performance measure functions. On this basis, a Copula-based first-order inverse reliability method using ACGA is developed to search for the minimum performance target point in correlated input variable scenarios, where the maximum likelihood estimation method and the Akaike information criterion are employed to calculate the correlation parameters between variables and screen the optimal Copula function. Finally, the computational performance of the proposed method is demonstrated by several inverse reliability analysis examples and four RBDO problems with correlated input variables, and the effects of different Copula functions on the optimization results are analyzed.