On auto- and cross-interdependence in interval field finite element analysis

This paper discusses the concepts of auto- and cross-interdependence in interval field finite element analysis. In classic interval analysis, independent intervals are used to construct hyper-rectangular input spaces that correspond to the bounded uncertainty that is present on some model parameters. This is a direct result from the inability of modeling interdependence. Such assumption of complete independence might prove in some cases to be highly over-conservative. A first example is the modeling of spatial uncertainty, where the interdependence is governed by allowable spatial gradients of field realizations. Secondly, interdependence can also occur in case uncertainty in several structural quantities has the same root cause (eg, the manufacturing process). Recent work by the authors introduced concepts for modeling dependence between intervals in a spatial and multivariate context. However, it is unclear how an analyst has to deal with multiple quantities that have a spatial uncertainty component and are furthermore interdependent. This paper presents an approach to link multiple interval fields using recently introduced convex hull pair constructions and inverse distance weighting interpolation. Two case studies to illustrate the new methodology are included, proving the flexibility of the methodology in the modeling of auto- and cross-interdependence between multiple interval scalars and/or interval fields.