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• W3100267498 abstract "This paper introduces a novel method to model non-deterministic quantities based on experimental measurement data. The focus of this work is on quantities that vary over a continuous domain, e.g., material properties, time-dependent strain rate effects, or stress–strain curves. These quantities are modelled by means of the recently introduced concept of interval fields. An interval field defines intervals that are defined throughout the continuous domain and have dependence in this domain by expanding them over a set of basis functions, describing the spatial nature of the non-determinism of the modelled quantities. One of the more intuitive concepts of defining basis functions in an interval field is through inverse distance weighting interpolation (IDW), which starts from known intervals at specific control points within the domain. For each of these control points, a corresponding basis function is defined, the relative weight of which is decreasing inversely with the distance. Through this definition, all intervals have non-vanishing basis functions throughout the model domain. This makes the application of standard IDW extremely challenging when the interval uncertainty varies inhomogeneously over the domain, i.e., when local effects are present in the model. Therefore, in this paper standard IDW is adapted by changing the distance measure. More specifically, the weight of intervals is increased locally, while diminishing the weight in other regions. For this purpose, a function is introduced that maps the domain to a higher dimension feature space, in which the distances that determine the weight are measured. This mapping function is based on either the size of the intervals at the control points or experimental data, which both yield additional control resulting in increased agreement with experimental data. This paper demonstrates that this method outperforms standard IDW in controllability, while limiting the number of control points. This is illustrated in three case studies: a first case concerning modelling local non-determinism; a second case where a mix of global and local effects is modelled; and the third case, where the interval field is based on experimental stress strain curves. In all these cases, multiple configurations demonstrate the effects of the parameters, and how the new technique is applied. The proposed technique outperforms standard IDW in all three case studies, with an increased coefficient of determination, R2, between 22% and 56%, in comparison to standard IDW." @default.
• W3100267498 created "2020-11-23" @default.
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• W3100267498 date "2021-01-01" @default.
• W3100267498 modified "2023-10-16" @default.
• W3100267498 title "Inhomogeneous interval fields based on scaled inverse distance weighting interpolation" @default.
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• W3100267498 doi "https://doi.org/10.1016/j.cma.2020.113542" @default.
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