G0310307 限定方向重点サンプリング・シミュレーションに基づく構造システムの信頼性解析(材料力学部門一般セッション:解析・シミュレーション)

Abstract

This study describes an efficient directional importance sampling method for the simulation-based estimation of the structural failure probability. The proposed method is composed of two-stage procedures. In the first stage, executing specified numbers of directional simulations, the conditional failure probabilities on various random directions are determined by calculating the radial distances from the origin to the failure surfaces. When the basic random variables are subject to the normal distributions, the conditional failure probabilities on the respective random directions are evaluated by using the upper probabilities of the chi-square distribution. Random directional vectors with the radial distances smaller than the minimum radial distance+3 are considered to have effective contributions to the structural failure probability, while random directions with the radial distances larger than minimum radial distance+3 are considered to be ineffective to the structural failure probability. It is proposed that by using random directions with the effective radial distances only, a directional importance sampling probability density is constructed on the basis of the respective upper probability of the chi-square distribution per unit hypersurrace area. In the second stage, a directional importance sampling simulation is executed to estimate the structural failure probability by using the directional vector samples generated from the directional importance sampling probability density constructed in the first stage. Numerical emples to estimate the failure probability of structure with multiple failure surfaces and structure with nonlinear limit state function are presented to illustrate that the proposed method gives accurate estimations effectively.