Reliability sensitivity algorithm based on line sampling

In this paper, reliability sensitivity algorithm based online sampling is presented. In the line sampling for structural reliabilityanalysis, the failure probability Pf of structure is calculated byaveraging the failure probability Pfj (j=1,...,N) corresponding toeach simulated sample. From Pf in the linesampling, the reliability sensitivity of Pf with respect to thedistribution parameter \theta , i.e. \partial Pf / \partial \theta , canbe calculated by averaging \partial Pfj / \partial \theta , and\partial Pfj / \partial \theta can be obtained by using the analyticalrelationship between Pfj and \theta . The expressions of \partialPfj / \partial \theta and \partial Pf / \partial \theta are derivedin detail. With the use of the line sampling, reliability sensitivity algorithmenjoys the advantages of the line sampling, such as high precision,high efficiency and wide applicability in high dimensions and multiplefailure modes. Examples are used to show the advantages of thepresented reliability sensitivity algorithm.