Augmented Reliability-Based Design Optimization Model Under Double-Layer Uncertainty and Its Efficient Solution

Research on reliability-based design optimization (RBDO) that considers solely input variable uncertainty is well-established. However, studies on RBDO problems that involve both random input variables and their uncertain distribution parameters remain notably scarce. This study constructs an augmented-RBDO (A-RBDO) framework governed by target augmented failure probability (AFP) constraints under double-layer uncertainty. To enable its efficient solution, this study proposes an efficient sequential decoupling method for solving the A-RBDO model, utilizing augmented quantiles of the performance function. The proposed method first equivalently transforms the AFP constraint into an augmented quantile constraint. This transformation converts the A-RBDO problem into a sequential process involving augmented quantile estimation and deterministic optimization. Subsequently, for critical augmented quantile estimation, this study introduces an efficient strategy combining dimension-reduction integration based on a mixed-degree cubature formula with the bisection method, significantly reducing the expense associated with augmented quantile evaluation. The synergistic integration of this sequential decoupling strategy, the mixed-degree cubature formula, and the bisection method dramatically enhances efficiency in solving the A-RBDO model. The efficiency and robustness of the proposed method are comprehensively demonstrated through three examples.