Uncertainty assessment in random field representations: An interval approach

Abstract

This paper discusses the application of interval fields for the analysis of uncertain mechanical structures. More specifically, this work focuses on representing uncertainties with a spatially distributed influence in the context of finite element analysis. 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.

Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty

“…As an example, when applying the inverse distance weighting interpolation technique, subjectivity is present in the selection of the control points and the exponent of the distance weighting. Moreover, the application of interval fields to practical problems is still very scarce in literature (see e.g., [130,202,204,100]). This is however also partially explained by the relatively recent introduction of these techniques as compared to the well-established framework of random fields.…”

“…However, interval methods are by definition not capable of defining dependence between different model responses, which might make them severely over-conservative with respect to the actual uncertainty in the model responses. As concerns non-deterministic quantities that are time or space-dependent, the concept of interval fields has been introduced only very recently as non-probabilistic counterpart to random fields [130,204,202,203,180,181]. These concepts alleviate the dependency problem to a large extent.…”