Estimation of Structural Failure Probability Based on Simulation within a Limited Sampling Region

Abstract

This paper outlines an estimation method of structural failure probabilities based on simulation within a limited sampling region. The basic random variables are assumed to be independent standard normal variables and the reliability index β to be known. To estimate such a small value of failure probability through the crude Monte Carlo simulation, a very large amount of samples as well as long computer processing time are usually required. To save computational efforts, a new sampling method is proposed to generate samples restricted outside the β-sphere, whose radius is the reliability index β, and within an effective distance range which is defined as a range to have effective probability values. In the proposed simulation method, a truncated chi-square distribution is introduced. Each sample within the limited sampling region is produced by combining a random radius generated from the truncated chi-square probability density function with a random directional vector generated from standard normal samples. Numerical examples are presented to show the validity of the proposed method.