Equilibrium reliability measure for structural design under twofold uncertainty

In structural reliability engineering, designer may encounter twofold uncertainty that arises from the existence of the insufficient statistical data and the incorporated experts’ information. For this case, the randomness and fuzziness coexist in each uncertain element. This paper aims to develop a new approach to evaluating structural reliability and obtain the optimal structural design under twofold uncertainty. Specifically, we first introduce a metric termed equilibrium chance to formulate equilibrium reliability index (ERI) for modeling structural reliability under linear limit-state function and nonlinear limit-state function. Second, a new class of equilibrium reliability-based structural design (ERSD) optimization problem with equilibrium reliability constraint is developed. Under mild conditions, we provide the equivalent reformulation of the equilibrium reliability constraint and demonstrate its convexity. Finally, we introduce the fuzzy simulation (FS) scheme to obtain the feasible solution generated by equilibrium reliability constraint, and a hybrid heuristic algorithm by integrating the FS, genetic algorithm (GA) and local search (LS) is designed to solve the proposed ERSD optimization problem. Several numerical examples are carried out to illustrate the applicability and effectiveness of our proposed reliability modeling method.