Reliability sensitivity algorithm based on line sampling

In this paper, reliability sensitivity algorithm based on line sampling is presented. In the line sampling for structural reliability analysis, the failure probability P_f of structure is calculated by averaging the failure probability P_fj(j = 1, ⋯, N) corresponding to each simulated sample. From P_f in the line sampling, the reliability sensitivity of P_f with respect to the distribution parameter θ, i.e. ∂P_f/∂θ, can be calculated by averaging ∂P_fj/∂θ, and ∂P_fj/∂θ can be obtained by using the analytical relationship between P_fj and θ. The expressions of ∂P_fj/∂θ and ∂P_f/∂θ are derived in detail. With the use of the line sampling, reliability sensitivity algorithm enjoys the advantages of the line sampling, such as high precision, high efficiency and wide applicability in high dimensions and multiple failure modes. Examples are used to show the advantages of the presented reliability sensitivity algorithm.