Estimation of failure probabilities by local approximation of the limit state function

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. Rather than concentrating on the construction of the failure hypersurface, an adaptive local approximation scheme for the limit state function that is based on the moving least squares method is proposed in this study. It integrates well with existing importance sampling schemes and yields both efficient and robust estimates of the failure probability.