Global reliability sensitivity analysis by Sobol-based dynamic adaptive kriging importance sampling

The stochastic uncertainties affecting the models used to describe the behavior of structural/mechanical systems may give rise to unfavorable scenarios leading to failures. In this framework, the quantification of the failure probability is a recognized fundamental task for structural safety and reliability analyses. Unfortunately, the estimation of the failure probability of structural/mechanical systems is a computationally demanding task, especially when the failure is a rare event and the computer codes used to model the system response require large computational efforts. One major issue further complicates the estimation process, i.e., the parameters of the probability distributions of the random variables used to describe the uncertainties involved can, in turn, be imprecise, since they are typically estimated by means of statistical inference based on observations and engineering judgment. In this context, reliability sensitivity analysis aims at estimating the influence of this additional source of uncertainty on the system failure probability in order to assess the robustness of the system to the modeling of uncertainties. Intuitively, reliability sensitivity analyses may easily become prohibitive by standard sampling-based methods (e.g., Monte Carlo method), since a nested, second level of uncertainties is involved. To overcome this issue, in this work we embed the efficient AK-IS algorithm for estimating small failure probabilities within an original computational framework that allows to perform a Sobol-based, global sensitivity analysis of the failure probability at an affordable number of computer model evaluations. The algorithm is demonstrated with reference to two case studies of literature of structural/mechanical reliability, often used in the literature as benchmark tests.