Adaptation of fast Fourier transformations to estimate structural failure probability

Structural reliability analysis by univariate decomposition and numerical integration

“…exceeds 0.374 73 [16]. If random variables X 1 = α m , X 2 = S u , X 3 = ω, X 4 = ρ, X 5 = R o , and X 6 = R i have their statistical properties defined in Table 3, the performance function becomes Table 4 presents the predicted failure probability of the disk and the associated computational effort using new and existing MPP-based univariate methods, FORM, Hohenbichler's SORM [5], and direct Monte Carlo simulation (10 6 samples).…”

A univariate approximation at most probable point for higher-order reliability analysis

“…exceeds a critical threshold of 0.37473 (Penmetsa and Grandhi, 2003). If random variables X 1 = a m , X 2 = S u , X 3 = x, X 4 = q, X 5 = R o , and X 6 = R i , and have their statistical properties defined in Table 3, the performance function becomes Table 4 presents predicted failure probability of the disk and associated computational effort using MPPbased univariate method, mean-point-based univariate and bivariate methods (Xu and Rahman, accepted for publication), FORM, HohenbichlerÕs SORM (Hohenbichler et al, 1987), and direct Monte Carlo simulation (10 6 samples).…”

Bounds on structural system reliability in the presence of interval variables

“…(9). Only the part of the PDF of X i over which the approximate model e G j is accurate is taken into consideration to obtain the PDF of the intervening variable…”

“…The use of fast Fourier transforms (FFT) for solving the convolution integral has been explored previously [8,9] using surrogate models for representing the failure surface. This surrogate model has to be a separable function that can be linearized in order to be able to apply the method.…”