Advanced solution framework for time-dependent reliability-based design optimization under fuzzy and interval uncertainties

The problem which is actually being addressed in this study includes two parts: One is on establishing time-dependent reliability-based design optimization (tRBDO) formulation under fuzzy and interval uncertainties to obtain the optimal design parameter solution for the time-dependent structure. The other is on presenting a serial single-loop optimization (SSLO) strategy to estimate the optimal design parameter. For addressing the optimal design parameter of the time-dependent structure involving fuzzy and interval uncertainties, a novel tRBDO model with the constraint of time-dependent failure possibility (TDFP) based on the possibility theory of the safety measure is proposed. For evaluating the optimal design parameter, the established SSLO method converts the original triple-loop optimization which is TDFP-index-based approach into a sequence of deterministic optimization, interval value corresponding to the worst case scenario, the estimation of time instant, and the minimum most probable point. Iterative searching step is not needed to find the minimum most probable point at each iteration step in the proposed SSLO strategy; therefore, the computational time is extremely reduced. Several examples are given to demonstrate the efficiency of the proposed approach.