Multivariate dependent interval finite element analysis via convex hull pair constructions and the Extended Transformation Method

Classical (independent) interval analysis considers a hyper-cubic input space consisting of independent intervals. This stems from the inability of intervals to model dependence and results in a serious over-conservatism when no physical guarantee of independence of these parameters exists. In a spatial context, dependence of one model parameter over the model domain is usually modelled using a series expansion over a set of basis functions that interpolate a set of globally defined intervals to local (coupled) uncertainty. However, the application of basis functions is not always appropriate to model dependence, especially when such dependence does not have a spatial nature but is rather scalar. This paper therefore presents a flexible approach for the modelling of dependent intervals that is also applicable to multivariate problems. Specifically, it is proposed to construct the dependence structure in a similar approach to copula pair constructions, yielding a limited set of 2-dimensional dependence functions. Furthermore, the well-known Transformation Method is extended to the case of dependent interval analysis. The applied case studies indicate the flexibility and performance of the method. (C) 2018 Elsevier B.V. All rights reserved.