New Approximations for SORM: Part 2

Abstract

In the second-order reliability method, the Hessian matrix is used to construct a paraboloid approximation of the limit state surface and compute a second-order estimate of the failure probability. In this paper, a practical point-fitting second-order reliability approximation is proposed, by which the explicit second-order approximation of the performance function is obtained directly in standard normal space with neither the computation of Hessian matrix nor the computation of gradients of the function. Once the point-fitted performance function is obtained, the failure probability is estimated by the empirical second-order reliability index, which is generally simple and works well compared to other second-order reliability method formulas. For accurate computation of the failure probability, an IFFT method is proposed, from which the failure probability is obtained conveniently using the Inverse Fast Fourier Transformation. The proposed methods are investigated and their accuracy and efficiency are demonstrated using numerical examples.