Computation of failure probabilities via local approximations

Abstract For failure probability estimates of large structural systems, the numerical expensive evaluations of the limit state function have to be replaced by suitable approximations. Most of the methods proposed in the literature so far construct global approximations of the failure hypersurface. The global approximation of the failure hypersurface does not correspond to the local character of the most likely failure, which is often concentrated in one or several regions in the design space, and may therefore introduce a high approximation error for the probability of failure. Moreover, it is noted that global approximations are often constructed for parameter spaces that ignore constraints imposed by the physical nature of the problem. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)