An adaptive directional importance sampling method for structural reliability

In this paper, an adaptive directional importance sampling (ADIS) method is presented. The algorithm is based on a directional simulation scheme in which the most important directions are sampled exact and the others by means of a response surface approach. These most important directions are determined by a beta-sphere enclosing the most important part(s) of the limit state. The beta-sphere and response surface are constantly updated during sampling with information that becomes available from the exact evaluations making the scheme adaptive. Various widely used test problems, representing a broad range of complex limit states that can occur in practice, of which several that pose potential problems to stochastic methods in general, demonstrate the high efficiency, accuracy and robustness of the method. As such, the ADIS method is of particular interest in applications with a low probability of failure and medium number (up to about 40) of stochastic variables, for instance in aircraft and nuclear industry. (C) 2010 Elsevier Ltd. All rights reserved.