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.

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In uncertainty calculation, the inability of interval parameters to take into account mutual dependency 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 results that probably overestimate the true uncertainty. 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, based on a maximum gradient condition to model the dependency. This field definition is then applied to a model of a clamped plate with uncertain clamping stiffness with the purpose of identifying the effects of spatial variability and mean value separately.

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This paper presents an objective comparison of random fields and interval fields to propagate spatial uncertainty, based on a finite element model of a lunar lander. The impulse based substructuring method is used to improve the analysis efficiency. The spatially uncertain input parameters are modeled by both random fields and interval fields. The objective of this work is to compare the applicability of both approaches in an early design stage under scarce information regarding the occurring spatial parameter variability. Focus is on the definition of the input side of the problem under this scarce knowledge, as well as the interpretation of the analysis outcome.To obtain an objective comparison between both approaches, the gradients in the interval field are tuned towards the gradients present in the random field. The result shows a very similar dependence and correlation structure between the local properties for both approaches. Furthermore, through the transient dynamic estimation, it is shown that the response ranges that are predicted by the interval field and random field are very close to each 1 other.