Random field expansion with interval correlation length using interval fields
Wim Verhaeghe, Wim Desmet, Dirk Vandepitte, David Moens · Lirias (KU Leuven) · 2011
In recent years many methods, both probabilistic and non-probabilistic, were developped to deal with scalar parameter uncertainties in Finite Element (FE) analysis. These approaches cover a large part of the uncertainty problems in engineering, but a blind-spot remains for uncertainties that give rise to a spatially distributed influence. In the probabilistic setting random fields are commonly used to describe spatially correlated uncertain input data of an FE problem. The autocorrelation structure of such a field is crucial for its discretization into a set of uncorrelated random variables. Very often the autocorrelation structure of such a random field has an unknown correlation length. The correlation length itself is an uncertain parameter, that affects the uncertainty on the final FE results. The paper presents an interval field method that attempts to capture the influence of an interval correlation length on a random field representation of an uncertain FE input. First, the concept of interval fields is briefly reviewed. Next, random fields are presented, with a focus on the influence of an uncertain correlation length on its discretization. The methods for applying the interval field framework to represent the uncertain correlation length are explained in the next section. Finally, the application of interval fields for representing a random field expansion in the uncertain correlation length space is illustrated using a numerical example.