Analytical modelling of a magnetization curve obtained by the measurements of magnetic materials’ properties using evolutionary algorithms

Abstract

Magnetization curves are obtained with measurements and used for the description of magnetic material properties. In the case where the curve is rough problems can appear during the Finite Element Method (FEM) calculations. One of the solutions is the use of an analytically written curve, which fits the measured curve. In this paper different analytical expressions are tested on different measured magnetization curves and compared with each other. Different evolutionary methods are used and tested for the determination of the analytical expressions’ parameters: The Genetic Algorithm, Differential Evolution with three different strategies, Teaching-Learning Based Optimization and Artificial Bee Colony. To obtain credible and optimal results, we made a statistic evaluation of the results using Cross-validation, CRS4EAs (Chess rating system for evolutionary algorithms), and the Holm test. Based on the test’s results we improved the more appropriate evolutionary method, which was Artificial Bee Colony, using the Levenberg-Marquardt algorithm. As a result, two different methods: are presented and tested which combine Artificial Bee Colony and the Levenberg-Marquardt algorithm. An analytical expression is presented which can be used for a wide range of different materials’ curves and also a stable and efficient method for the determination of the analytical expression’s parameters. The presented solution is appropriate to be used together with, or as a part of, FEM calculation software. For preparation of magnetic material data the presented solution can be used as an independent programme for the transformation of the H-B table of values presenting not-smooth measured magnetic material curves (or measured with too few points) into the H-B table of values presenting smooth magnetic material curve which can be used as input data for any FEM software.