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Multivariate dependent interval finite element analysis via convex hull pair constructions and the Extended Transformation Method

Journal Contribution - Journal Article

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 a serious 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 modelled using a series expansion over a set of basis functions that interpolate a set of globally defined intervals to local (coupled) uncertainty. However, the application of basis functions is not always appropriate to model dependence, especially when such dependence does not have a spatial nature but is rather scalar. This paper therefore presents a flexible approach for the modelling of dependent intervals that is also applicable to multivariate problems. Specifically, it is proposed to construct the dependence structure in a similar approach to copula pair constructions, yielding a limited set of 2-dimensional dependence functions. Furthermore, the well-known Transformation Method is extended to the case of dependent interval analysis. The applied case studies indicate the flexibility and performance of the method.
Journal: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Volume: 347
Pages: 85 - 102
Publication year:2019