方向重点サンプリング・シミュレーションに基づく構造信頼性解析の効率化手法（設計点方向に重み付けられた方向重点サンプリング確率密度の決定）

概要

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This study describes an efficient directional importance sampling method for the simulation-based estimation of the structural failure probability. Samples are generated in the orthogonal coordinates from importance sampling p.d.f.s centered at the design points on the limit state surfaces of the respective failure modes and directional vector samples are determined by the directions from the origin to the respective sampled points. The probability content of the importance sampling p.d.f.s contained in a hyperconical domain subtended by an infinitesimal increment at the respective sampled direction is evaluated numerically and adopted as a directional importance sampling probability density at the sampled direction. When estimating the structural failure probability, the effect of the importance sampling in each simulation cycle is compensated by the ratio of the uniform density distributed over the unit hypersphere and the respective directional importance sampling probability density thus determined. Numerical examples to estimate the failure probability of structures with multiple failure modes show that the proposed method gives accurate estimations of structural failure probabilities efficiently.