Reliability assessment of truss structures with natural frequency constraints using metaheuristic algorithms

The failure probability (reliability index) and evaluation of safety of structures is a subject of interest in structural engineering. In order to calculate the reliability index, moment methods require an explicit mathematical form of the limit state function and gradient of this function, and simulation methods are dependent on a large number of evaluations of this function. In this study, in order to reduce computational efforts, the optimization problem is formulated so it can calculate the reliability index for structural problems with an implicit limit-state function. For this purpose, the objective function is formulated based on the Hasofer and Lind method, and the limit state function is defined based the first mode frequency. The random variables consist of modulus of elasticity, material density, non-structural mass, and cross-sectional area. To evaluate accuracy of the proposed approach in estimating the reliability index, four truss structures are selected and their reliability index is calculated by using six meta-heuristic algorithms including WEO, AWEO, CBO, ECBO, VPS, and EVPS. Compared with the Monte Carlo simulation method, the proposed approach shows acceptable performance.