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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019025638
pages 85-102

STOCHASTIC MODELING OF MAGNETIC HYSTERETIC PROPERTIES BY USING MULTIVARIATE RANDOM FIELDS

Radoslav Jankoski
Graduate School for Computational Engineering, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany
Ulrich Römer
Institute of Dynamics and Vibrations, Technische Universität Braunschweig, Schleinitzstraße 20, 38106 Braunschweig, Germany
Sebastian Schöps
Graduate School for Computational Engineering, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany

ABSTRACT

In this paper a methodology is presented to model uncertainties in the hysteresis law of ferromagnetic materials. The uncertainties may arise, for example, from manufacturing imperfections. A phenomenological type of model, known as the Duhem model, is introduced to model the hysteretic properties. The Duhem model is described via two material functions and one scalar parameter. Random fields are used to incorporate uncertainties into the material law. The random field is discretized with a minimal number of random variables by the truncated Karhunen-Loève expansion. Subsequently, the presented stochastic Duhem model is used to compute the statistics of the hysteresis loss in a simple toroidal single-phase transformer for illustration purposes.