Asymptotic Sampling Regression with Machine Learning and Surrogate Modeling Techniques

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 increased 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, a 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. In the previous studies, the relationship between reliability indices and support points has been established using nonlinear regression. In this study, we explored the use of more advanced machine learning (e.g., Gaussian process, support vector regression) and surrogate modeling (e.g., Kriging, linear Shepard) techniques, and compared the accuracies of these techniques to that of the nonlinear regression on six benchmark problems. It is found that using nonlinear regression yields more accurate results than machine learning and surrogate modeling techniques evaluated within the scope of this study.