@article{fae-moe-19-aa-intfld,
  author = {Faes, Matthias and Moens, David},
  title = {Multivariate Dependent Interval Finite Element Analysis via Convex Hull Pair Constructions and the {Extended} {Transformation} {Method}},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume = {347},
  pages = {85-102},
  year = 2019,
  month = apr,
  doi = {10.1016/j.cma.2018.12.021},
  comment = {Defines an ``interval field'' as a field $f$ defined by a linear combination of $n$ basis functions with interval coefficients.  This makes the value of the field $f(z)$ at a point $z$ of space into an nth-order affine form. The affine forms of $f(z')$ and $f(z'')$ then capture the correlation between the field values at those two points.},
  abstract = {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.}
}