  In modern engineering, physical processes are modelled and analysed using
advanced computer simulations, such as finite element models. Furthermore,
concepts of reliability analysis and robust design are becoming popular, hence,
making efficient quantification and propagation of uncertainties an important
aspect. In this context, a typical workflow includes the characterization of
the uncertainty in the input variables. In this paper, input variables are
modelled by probability-boxes (p-boxes), accounting for both aleatory and
epistemic uncertainty. The propagation of p-boxes leads to p-boxes of the
output of the computational model. A two-level meta-modelling approach is
proposed using non-intrusive sparse polynomial chaos expansions to surrogate
the exact computational model and, hence, to facilitate the uncertainty
quantification analysis. The capabilities of the proposed approach are
illustrated through applications using a benchmark analytical function and two
realistic engineering problem settings. They show that the proposed two-level
approach allows for an accurate estimation of the statistics of the response
quantity of interest using a small number of evaluations of the exact
computational model. This is crucial in cases where the computational costs are
dominated by the runs of high-fidelity computational models.
