Abstract:

The directional importance sampling method is a structural reliability simulation method， which is suitable for evaluating nonlinear， multi-dimensional complex structural reliability problems. However， for multidimensional problems， it is relatively inefficient and poorly executable to obtain significant vector samples using the accept/reject method. Therefore， it is necessary to improve or reconstruct distribution functions that are easy to sample. By summarizing the existing distribution functions， the distribution function based on vector-angle geometric mapping is approximated by interpolation methods， and the important angles are sampled uniformly using the one-dimensional Latin hypercube method and then mapped to the important vector samples. The obtained vector samples have stratified uniformity， avoiding aggregation phenomena while covering the entire sample space. The method is effectively used in the analysis of reliability problems of multiple design points and multiple failure modes， and sample allocation scheme is further developed. The applicability and accuracy of the proposed method are verified by nonlinear numerical examples and body structure engineering.

Key words: reliability analysis, directional importance sampling, distribution function, interpolation, multiple failure modes, sample allocation