SAVU: A Statistical Approach for Uncertain Data in Dynamics of Axially Moving Materials

J. Jeronen ()
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J. Jeronen: University of Jyväskylä, Department of Mathematical Information Technology

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 831-839 from Springer

Abstract: Abstract In physics and engineering problems, model input is never exact. The effect of small uncertainties on the solution is thus an important question. In this study, a direct statistical-visual approach to approximate the solution set is investigated in the context of axially moving materials. The multidimensional probability distribution for the input uncertainties is assumed known. It is considered as a deterministic object, which is then mapped through the model. The resulting probability density of the model output is visualized. The proposed system consists of three non-trivial parts, which are briefly discussed: a multidimensional sampler, a density estimator, and a high dynamic range (HDR) plotter. Dynamic range compression is achieved via tone mapping techniques from HDR photography. This allows a contrast-preserving representation of the HDR data on a regular computer display or on paper. The model itself is treated as a black box; hence, the same approach can be used for investigating e.g. floating-point rounding errors or approximation error instead of uncertain data.

Keywords: High Dynamic Range; Uncertain Data; Latin Hypercube Sampler; Tone Mapping; Input Uncertainty (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_86

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DOI: 10.1007/978-3-642-33134-3_86

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