Local explicit interval fields for non-stationary uncertainty modelling in finite element models

Abstract

Interval fields have been introduced to model spatial uncertainty in Finite Element Models when the stochastic resolution of available data is too limited to build representative probabilistic models. However, current interval fields modelling techniques are according to the state-of-the-art limited in potential, as they homogenise the uncertain parameters to globally defined parameters. Hence, these techniques are inherently unable to represent local uncertainty. In practice, local variations in the uncertain parameters (non-stationary uncertainty) often occur, e.g., through local effects in manufacturing processes. This paper presents a novel method to model local explicit interval fields, that is furthermore less computationally demanding and less conservative than global explicit interval fields. The method presented in this paper is based on the concept of explicit interval fields and develops an alternative approach for the commonly applied inverse distance weighting approach for the generation of the basis functions. The paper includes three case studies to compare the introduced local explicit interval fields approach with the global explicit interval fields method. The obtained results are discussed from a numerical and application point of view to show the effectiveness and efficiency of the proposed methods.