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A constraint-based optimization technique for estimating physical parameters of Jiles – Atherton hysteresis model

Brijesh Upadhaya (Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland)
Paavo Rasilo (Unit of Electrical Engineering, Tampere University, Tampere, Finland)
Lauri Perkkiö (Department of Mathematics and Systems Analysis, Aalto University, Espoo, Finland)
Paul Handgruber (Institute of Fundamentals and Theory in Electrical Engineering (IGTE), Graz University of Technology, Graz, Austria)
Anouar Belahcen (Department of Electrical Engineering, Aalto University, Espoo, Finland, Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland)
Antero Arkkio (Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland)

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering

ISSN: 0332-1649

Article publication date: 24 August 2020

Issue publication date: 15 December 2020

203

Abstract

Purpose

Improperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops.

Design/methodology/approach

A physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process.

Findings

The implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops.

Originality/value

The physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.

Keywords

Acknowledgements

The authors would like to thank the computational resources provided by the Aalto Science-IT Project. This work was supported by the Foundation for Aalto University Science and Technology and the European Research Council (ERC) under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement n^o 339380.

Citation

Upadhaya, B., Rasilo, P., Perkkiö, L., Handgruber, P., Belahcen, A. and Arkkio, A. (2020), "A constraint-based optimization technique for estimating physical parameters of Jiles – Atherton hysteresis model", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 39 No. 6, pp. 1281-1298. https://doi.org/10.1108/COMPEL-08-2019-0332

Publisher

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Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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