Reliability sensitivity estimation with sequential importance sampling

In applications of reliability analysis, the sensitivity of the probability of failure to design parameters is often crucial for decision-making. A common sensitivity measure is the partial derivative of the probability of failure with respect to the design parameter. If the design parameter enters the definition of the reliability problem through the limit-state function, i.e. the function defining the failure event, then the partial derivative is given by a surface integral over the limit-state surface. Direct application of standard Monte Carlo methods for estimation of surface integrals is not possible. To circumvent this difficulty, an approximation of the surface integral in terms of a domain integral has been proposed by the authors. In this paper, we propose estimation of the domain integral through application of a method termed sequential importance sampling (SIS). The basic idea of SIS is to gradually translate samples from the distribution of the random variables to samples from an approximately optimal importance sampling density. The transition of the samples is defined through the construction of a sequence of intermediate distributions, which are sampled through application of a resample-move scheme. We demonstrate effectiveness of the proposed method in estimating reliability sensitivities to both distribution and limit-state parameters with numerical examples.