Meta-model-based importance sampling for reliability sensitivity analysis

Reliability sensitivity analysis aims at studying the influence of the parameters in the proba-bilistic model onto the probability of failure of a given system. Such an influence may either be quantified on a given range of values of the parameters of interest using a parametric analysis, or only locally by means of its partial derivatives. This paper is concerned with the latter approach when the limit-state function involves the output of an expensive-to-evaluate computational model. In order to reduce the computational cost it is proposed to compute the failure probability by means of the recently proposed meta-model-based importance sam-pling method. This method resorts to the adaptive construction of a Kriging meta-model which emulates the limit-state function. Then, instead of using this meta-model as a surro-gate for computing the probability of failure, its probabilistic nature is used in order to build an quasi-optimal instrumental density function for accurately computing the actual failure Improved probability through importance sampling. The proposed estimator of the failure probability recasts as a product of two terms. The augmented failure probability is estimated using the emulator only, while the correction factor is estimated using both the actual limit-state function and its emulator in order to quantify the substitution error. This estimator is then differentiated by means of the score function approach which enables the estimation of the gradient of the failure probability without any additional call to the limit-state function (nor its Kriging emulator). The approach is validated on three structural reliability examples