Adaptive directional simulation for structural reliability estimation

This study describes a structural failure probability estimation based on an adaptive directional simulation, where directional samples are generated from the sampling density uniformly distributed over the surface of the unit hypersphere, whose center is transferred to the mean value point of the failure domain. The conditional failure probability is formulated as a piecewise integration with respect to the radial distance from the transferred center and the failure probability element is evaluated according to the distance from the origin. By a preliminary simulation procedure, the dominant failure modes effective for structural failure probability are selected and the mean value point of the failure domain is estimated simultaneously. Numerical examples are presented to illustrate that the proposed method can improve the computational efficiency of the structural failure probability estimation.