2015 年 81 巻 831 号 p. 15-00265
This study describes an efficient estimation method of the structural failure probability based on a limited directional importance sampling simulation. The sampling space is limited to a predetermined directional domain effective to the structural failure probability. In the preliminary stage, executing specified sample numbers of directional simulations, and the conditional failure probabilities in the sampled directions are evaluated by calculating the respective radial distances from the origin to the failure surfaces and determine the minimum radial distance. The conditional failure probabilities in the sampled directions having the radial distances smaller than the minimum radial distance+3 are considered to be effective to the structural failure probability, while the conditional failure probabilities in the other sampled directions having the radial distances larger than the minimum radial distance+3 are considered to have ineffective contributions to the structural failure probability. Then the directional domain containing the conditional failure probabilities having these smaller radial distances is referred to as a limited directional sampling domain, where a directional importance sampling probability density is constructed on the basis of the respective upper probability of the chi-square distribution per unit hypersurface area. By using the directional vector samples generated from the directional importance sampling probability density constructed in the limited directional sampling domain, a directional importance sampling simulation is executed to estimate the structural failure probability. This is referred to as a limited directional importance sampling simulation. Numerical examples to estimate the failure probability of structures with multiple and nonlinear limit state functions are presented to illustrate that the proposed method gives accurate estimations effectively.