Sampling-Based Reliability Sensitivity Analysis Using Direct Differentiation

Abstract

This paper presents the derivation, verification, and application of sampling-based reliability sensitivities. The direct differentiation method is employed to develop the analytical derivatives of the failure probability, and thus the reliability index, with respect to the distribution parameters of the underlying random variables in a sampling analysis. Particular attention is devoted to deriving the formulation for correlated random variables with arbitrary probability distributions. This entails analytical differentiation of the Nataf transformation. The resulting formulation is verified through a linear example with a closed-form solution and a nonlinear example. Thereafter, the proposed approach is utilized in two real-world applications. First, it is used to identify the random variables that are most influential on the seismic reliability of a reinforced concrete structure. Second, the proposed approach is employed to prioritize a building portfolio for retrofit based on the amount of reduction of the risk to the entire portfolio per dollar spent on retrofitting each building. The proposed approach is robust and works for highly nonlinear or nondifferentiable limit-state functions. It also only slightly increases the computational cost of sampling because it does not need the gradient of the limit-state function with respect to the underlying random variables.