Derivation of an input interval field decomposition based on expert knowledge using locally defined basis functions

In uncertainty calculation, the inability of interval parameters to take into account mutual dependence is a major shortcoming. When parameters with a geometric perspective are involved, the construction of a model using intervals at discrete locations not only increases the problem dimensionality unnecessarily, but it also assumes no dependency whatsoever, including unrealistic parameter combinations leading to possibly very conservative results. The concept of modelling uncertainty with a geometric aspect using interval fields eliminates this problem by defining basis functions and expressing the uncertain process as a weighted sum of these functions. The definition of the functions enables the model to take into account geometrically dependent parameters, whereas the coefficients in a non-interactive interval format represent the uncertainty. This paper introduces a new type of interval field specifically tailored for geometrically oriented uncertain parameters. The field has a non-interactive interval parameter in each node of the FE mesh to keep the true dimensionality of the uncertainty intact, but it obeys a bound on the gradient of the field to account for the dependency within the field.

Jaar van publicatie:2015

Toegankelijkheid:Open