A critical evaluation of asymptotic sampling method for highly safe structures

Abstract

Asymptotic sampling is an efficient simulation-based technique for estimating small failure probabilities of structures. The concept of asymptotic sampling utilizes the asymptotic behavior of the reliability index with respect to the standard deviations of the random variables. In this method, the standard deviations of the 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 square regression is performed using these support points to establish a relationship between the scale parameter and scaled reliability indices. Finally, an extrapolation is performed to estimate the actual reliability index. The accuracy and performance of the asymptotic sampling method are affected by various factors including the sampling method used, the values of the scale parameters, the number of support points, and the formulation of extrapolation models. The purpose of this study is to make a critical evaluation of the performance of the asymptotic sampling method for highly safe structures, and to provide some guidelines to improve the performance of asymptotic sampling method. A comprehensive numerical procedure is developed, and structural mechanics example problems with varying number of random variables and probability distribution types are used in assessment of the performance of asymptotic sampling method. It is found that generating the random variables by Sobol sequences and using the 6-model mean extrapolation formulation give slightly more accurate results. Besides, the optimum initial scale parameter is approximately around 0.3 and 0.4, and the optimum number of support points is typically four for all problems. As the reliability level increases, the optimum initial scale parameter value decreases, and the optimum number of support points increases.