Directional simulation for sensitivity analysis of structural reliability

Directional simulation reduces the dimension of the limit state probability integral by identifying a set of directions for integration, integrating either in closed-form or by approximation in those directions, and estimating the failure probability as the average of the directional integrals. But when the limit state is an approximately plane, a majority of directions may be inefficient. In order to improve the simulation efficiency, reliability sensitivity analysis methods are proposed on the basis of the directional (importance) simulation. The idea of reliability sensitivity analysis based on directional (importance) simulation is that according to the χ² distribution characteristics of basic variables in the standard normal space and the relation between radius vector and distribution parameters, the formulae of reliability sensitivity are derived in detail by using the chain derivative rule in this paper. The results of these given numerical examples show that these proposed methods are both efficiency and precision.