Local Interval Fields for Spatial Inhomogeneous Uncertainty Modelling

Abstract

In an engineering context, design optimization is usually performed virtually using numerical models to approximate the underlying partial differential equations. However, valid criticism exists concerning such an approach, as more often than not, only partial or uninformative data are available to estimate the corresponding model parameters. As a result hereof, the results that are obtained by such numerical approximation can diverge significantly from the real structural behaviour of the design. Under such scarce data, especially interval analysis has been proven to provide robust bounds on the structure’s performance, often at a small-to-moderate cost. Furthermore, to model spatial dependence throughout the model domain, interval fields were recently introduced by the authors as an interval counterpart to the established random fields framework. However, currently available interval field methods cannot model local inhomogeneous uncertainty. This paper presents a local interval field approach to model the local inhomogeneous uncertainty under scarce data. The method is based on the use of explicit interval fields [1] and the recently used inverse distance weighting function [2]. This paper presents the approach for one dimension of spatial uncertainty. Nonetheless, the approach can be extended to an n-dimensional context. In the first part of the paper, a detailed theoretical background of interval fields is covered, and then the local interval fields approach is introduced. Furthermore, an academic case study is performed to compare the local interval field approach with inverse distance weighting.