Fast Fourier transform based system reliability analysis

In probabilistic analysis, the failure of a structural system is governed by multiple failure criteria, all of which are to be taken into consideration for the reliability estimation. The accuracy of the estimated structural failure probability highly depends on the joint failure surface and its representation. Moreover, the evaluation of limit-states often requires computationally expensive simulations. To improve the efficiency of reliability analysis methods high quality function approximations for each of the limit-states and the joint failure surface are considered in this paper. Once the joint failure surface is represented using a surrogate model, the convolution integral can be solved efficiently using a Fast Fourier Transform (FFT) technique. Due to the high non-linearity of the joint failure region, a methodology is developed to evaluate the convolution integral based on multiple approximations over several disjoint regions spanning the entire design space. Numerical examples are presented to show the applicability, efficiency and accuracy of the proposed method.