An adaptive directional importance sampling method for structural reliability analysis

The importance sampling is merged with directional simulation in this paper. A sampling function is defined on the unit hyper sphere which samples random directions. The directions are sampled around a direction that aims to the design point. The sampling function uses spherical coordinates to generate random directions. The method is made adaptive by a closed form updating rule to renew the sampling parameters. To reduce the number of calls on the limit state function, a root finding procedure is put forward. The proposed method is tested with well-known test problems and its performance is compared with the conventional directional simulation. The results demonstrate the accuracy and efficiency of the proposed method for rare event estimation. (C) 2017 Elsevier Ltd. All rights reserved.