Hybrid FORM-Sampling simulation method for finding design point and importance vector in structural reliability

Abstract

It is still a big challenge to calculate the structural reliability index. Although first order reliability method (FORM) is effective in calculating the reliability index, it encounters many obstacles due to the need for differentiation of the limit state function (LSF) and using an optimization method, particularly when the LSF is nonlinear and non-differentiable. On the other hand, although simulation methods do not suffer from none of these problems, they require a large number of random samples. Moreover, simulation methods can only calculate the failure probability (ρf) directly, and they are not capable of calculating the design point. In the present paper, a new hybrid FORM-sampling simulation algorithm has been proposed to calculate the reliability index, design point, and importance vector. The proposed algorithm is viable to analysis the structural reliability with few random samples by using superior capabilities of importance sampling and step-by-step correction of the standard deviation (SD) of variables associated with the sampling density function. Furthermore, the LSF has been well approximated using the artificial neural network (ANN), leading to a significant reduction in the computation time. The efficiency of the present algorithm is illustrated through some examples in comparison to conventional methods. © 2020 Elsevier B.V.