Reliability Sensitivity Algorithm Based on Stratified Importance Sampling Method for Multiple Failure Modes Systems

Combining the advantages of the stratified sampling and the importance sampling,a stratified importance sampling metho(SISM) is presented to analyze the reliability sensitivity for structure with multiple failure modes.In the presented method,th variable space is divided into several disjoint subspace by n-dimensional coordinate planes at the mean point of the random vec tor,and the importance sampling functions in the subspaces are constructed by keeping the sampling center at the mean poin and augmenting the standard deviation by a factor of λ.The sample size generated from the importance sampling function i each subspace is determined by the contribution of the subspace to the reliability sensitivity,which can be estimated by iterativ simulation in the sampling process.The formulae of the reliability sensitivity estimation,the variance and the coefficient o variation are derived for the presented SISM.Comparing with the Monte Carlo method,the stratified sampling method and th importance sampling method,the presented SISM has wider applicability and higher calculation efficiency,which i demonstrated by numerical examples.Finally,the reliability sensitivity analysis of flap structure is illustrated that the SISM ca be applied to engineering structure.