A bootstrapping-based weighted average asymptotic sampling formulation for reliability estimation of highly safe structures

Asymptotic sampling (AS) is an efficient simulation-based technique for estimating the small failure probabilities of structures. AS utilizes the asymptotic behavior of the reliability index with respect to the standard deviations of random variables. In this method, the standard deviations of random variables are progressively inflated using a scale parameter to obtain a set of scaled reliability indices. The collection of the standard deviation scale parameters and corresponding scaled reliability indices are called support points. Then, least squares regression is performed using these support points to establish a relationship between the scale parameter and scaled reliability indices. Finally, extrapolation is performed to estimate the actual reliability index. Various extrapolation models have been used in AS to improve accuracy. Moreover, a mean extrapolation formulation using the average value of different extrapolation models was proposed to further improve its accuracy. Although the mean extrapolation formulation protects against using the wrong extrapolation model, it did not guarantee a reliability estimation better than that of the best available extrapolation model. In this paper, we propose a weighted average AS formulation in which the weight factors are optimized to minimize the variance of the reliability index estimation through the bootstrapping method. In the weight factor determination, both convex and affine formulations are considered and the results are compared. The performance of the proposed method is evaluated using six benchmark example problems and a complicated engineering problem. It is found that the proposed weighted average formulation has higher accuracy than the mean extrapolation formulation. For weight factor optimization, the affine formulation yields more accurate results than the convex formulation in most cases.