領域分割シミュレーション法に基づく構造システムの信頼性解析

概要

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This paper is concerned with an estimation method of structural failure probabilities based on the simulation with partition of the region technique. The defining domain of k basic variables of the structural system is divided into two parts, one is a domain inside the k-dimensional β-sphere and the other is one outside of it. The β is a radius of the k-dimensional hypersphere which has its center at the origin of standardized coordinates and is tangent to the limit state function in the safety region. The actual sampling region is made small by excluding the domain inside the β-sphere. As the basic variables are assumed to be stochastically independent and standard normal variates, a square of the magnitude of their vector follows a chi-square distribution with k degrees of freedom, which is proposed to use as a basis of a truncated probability density function defined for the domain outside the β-sphere. The structural failure probabilities for several types of limit state functions are estimated by the proposed simulation method. It is shown that the proposed method is more effective, from the points of the accuracy and efficiency of the simulation for the estimation, than the crude Monte Carlo simulation and the importance sampling method.
1993-12-15