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<doi>0110-cd</doi>
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<article-title>Cross-dependence Between Interval Fields in Finite Element models: Definition and Analysis</article-title>
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<author>Matthias Faes<sup>a</sup> and David Moens<sup>b</sup></author>

<aff>KU Leuven, Department of Mechanical Engineering.</aff>
<email><a href="mailto:matthias.faes@kuleuven.be"><sup>a</sup>matthias.faes@kuleuven.be</a></email>
<email><a href="mailto:david.@kuleuven.be"><sup>b</sup>david.@kuleuven.be</a></email>
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<title>ABSTRACT</title>
<p>Classical (independent) interval analysis considers a hyper-cubic input space consisting of independent intervals. This stems from the inability of intervals to model dependence and results in over-conservatism when no physical guarantee of independence of these parameters exists. In a spatial context, dependence of one model parameter over the model domain is usually modeled using a series expansion over a set of base functions that interpolate a set of globally defined intervals to local (coupled) uncertainty, which yields an Interval Field. Dependence in this case can be referred to as auto-dependence. However, when multiple dependent parameters with spatial uncertainty co-exist in a Finite Element model, it is yet unclear how dependence between such parameters (cross-dependence) should be modeled in an interval context. This paper presents an approach to quantify cross-dependent interval fields on multiple model parameters. As a first step, cross-dependence between interval fields is accounted for by extending the explicit interval field formulation towards the definition of multiple, dependent interval field valued parameters. This is obtained via recently introduced convex hull pair constructions and the enriched transformation method, which is an extension of the well-known Transformation Method for the analysis of dependent intervals. A simple case study is included to illustrate the performance of the methodology.</p>
<p><italic>Keywords: </italic>Interval analysis, Interval Fields, Admissible Set Decomposition, Copula Pair Constructions, Crossdependent fields.</p>
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