Fully decoupling approach based on weighted subset simulation and combination for reliability-based design optimization

An efficient fully decoupling approach is proposed to solve the reliability-based design optimization (RBDO) for structures including nonlinear systems in high dimensions, which is a challenging task. In the proposed approach, instead of repeated reliability analyses, the failure probability function (FPF) contained in the probabilistic constraint is estimated as an explicit function of the design parameters through a single implementation of weighted subset simulation. Then the obtained FPF estimate is substituted into the original target RBDO problem for decoupling. The sequential approximate optimization framework is integrated with the decoupling step to perform the RBDO iteratively, ensuring the convergence of the optimization. Furthermore, an optimal combination algorithm is proposed to reuse the information in the optimization iterations to improve the convergence and robustness of the approach. The proposed approach is highly efficient and applicable to nonlinear dynamic systems with moderate dimensional design parameters and high dimensional uncertainties. Three illustrative examples dealing with static and dynamic, linear and nonlinear systems, are used to demonstrate the effectiveness and feasibility of the proposed approach.