An Efficient Method of Structural Reliability Analysis Based on a Directional Importance Sampling Simulation (A Determination of Equivalent Directional Importance Sampling Probability Densities Weighted in the Direction of the Design Points)

2013 Transactions of the Japan Society of Mechanical Engineers Series A  
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
more » ... ampling 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.
doi:10.1299/kikaia.79.609 fatcat:z55so54cfjbm7eoqywamhx2xbm