Title: A general framework for data-driven uncertainty quantification under complex input dependencies using vine copulas,
Abstract: Systems subject to uncertain inputs produce uncertain responses. Uncertainty
quantification (UQ) deals with the estimation of statistics of the system
response, given a computational model of the system and a probabilistic model
of its inputs. In engineering applications it is common to assume that the
inputs are mutually independent or coupled by a Gaussian or elliptical
dependence structure (copula). In this paper we overcome such limitations by
modelling the dependence structure of multivariate inputs as vine copulas. Vine
copulas are models of multivariate dependence built from simpler pair-copulas.
The vine representation is flexible enough to capture complex dependencies.
This paper formalises the framework needed to build vine copula models of
multivariate inputs and to combine them with virtually any UQ method. The
framework allows for a fully automated, data-driven inference of the
probabilistic input model on available input data. The procedure is exemplified
on two finite element models of truss structures, both subject to inputs with
non-Gaussian dependence structures. For each case, we analyse the moments of
the model response (using polynomial chaos expansions), and perform a
structural reliability analysis to calculate the probability of failure of the
system (using the first order reliability method and importance sampling).
Reference solutions are obtained by Monte Carlo simulation. The results show
that, while the Gaussian assumption yields biased statistics, the vine copula
representation achieves significantly more precise estimates, even when its
structure needs to be fully inferred from a limited amount of observations.