Estimation of Structural System Reliability Using Fast Fourier Transforms

In probabilistic analysis, the failure probability of a structural component is estimated based on a particular performance criterion. However, 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. In a multidisciplinary environment, where all the failure criteria are equally important, there is no methodology to convert the system reliability problem into a component reliability problem. These failure criteria are often correlated and the accuracy of the estimated structural failure probability is highly dependent on the ability to model the joint failure surface. The evaluation of limit states often requires expensive Finite Element Analysis (FEA) or Computational Fluid Dynamics (CFD) simulation. Therefore, to efficiently predict the failure probability of the structural system, the use of 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 approximated as a closed-form expression, the convolution integral can be solved efficiently using a Fast Fourier Transform (FFT) technique to estimate the structural failure probability. Due to the high non-linearity of the joint failure region, a methodology is presented to solve this convolution integral based on multiple function approximations over several disjointed regions over the design space. Numerical examples are presented to show the applicability, efficiency, and accuracy of the proposed method.