Identification of a hysteresis model parameters with genetic algorithms

doi:10.1016/j.matcom.2006.01.002

Mathematics and Computers in Simulation

Volume 71, Issue 3, 11 May 2006, Pages 206-211

https://doi.org/10.1016/j.matcom.2006.01.002 Get rights and content

Abstract

The paper is concerned about the application of genetic algorithms to the estimation of magnetic hysteresis model parameters, based on the description of magnetization process proposed by Jiles and Atherton. The genetic algorithm approach has been applied to estimation of model parameters for two magnetic materials – a conventional non-oriented steel and a modern amorphous material. The errors between the modelled and experimental data points on $M - H$ plane have been determined. The results have been compared with the results obtained with the previously proposed approach, based on direct search method. It has been proved that the genetic algorithm approach results in lower percentage errors.

Introduction

Hysteresis phenomena are widespread in various branches of technology. Recent progress in magnetic technology and its application in mechatronics and telecommunication result in growing interest in the development of descriptions of magnetization processes.

The description of magnetization process in soft magnetic materials proposed by Jiles and Atherton [8] is attractive from engineering point of view, because of simplicity of its computer implementation and physical interpretation of its parameters. However, as already noticed [11], the iterative procedure of estimation of J–A model parameters [9], [10], might pose convergence problems. The classic procedure is very sensitive to initial values of parameters and to the order of their evaluation. Therefore, other estimation techniques have been proposed recently. They are usually based either on implementations of global optimization techniques, e.g. simulated annealing method [6] or on exhaustive search in the trusted solution space [4], [13], [16]. Much attention has also been paid recently to heuristic methods such as genetic algorithms [1], [12], [15], [19].

In the paper, the results of estimation of J–A model parameters using an implementation of genetic algorithm toolbox for MatLab environment [7] for selected soft magnetic materials are given. The core materials were non-oriented electrical steel V3250-50A and amorphous material VITROVAC 6025 F [17].

It has been proved that the genetic algorithm approach resulted in smaller errors in comparison to the direct search method, examined in [4].

Section snippets

Implementation

The following form of Jiles–Atherton equation was considered [3], [18]: $\frac{d M}{d H} = \frac{δ_{M} (M_{an} - M) + c k δ (d M_{an} / d H_{eff})}{k δ - α (δ_{M} (M_{an} - M) + c k δ (d M_{an} / d H_{eff}))},$ where $M_{an}$ is anhysteretic magnetization, $H_{eff} = H + α M$ is effective field, $α, c, k$ are model parameters, $δ$ is the sign of $d H / d t$ , whereas $δ_{M}$ is defined as $δ_{M} = \{\begin{matrix} 0 : \dot{H} < 0 and M_{an} (H_{eff}) - M (H) > 0 \\ 0 : \dot{H} > 0 and M_{an} (H_{eff}) - M (H) < 0 \\ 1 : in other cases . \end{matrix}$ Introduction of $δ_{M}$ keeps unphysical negative susceptibility away from numerical solutions of Eq. (1) ([5], [18]) and makes the problem

Results

Fig. 1 presents the measured and the modelled major hysteresis loop for the non-oriented steel. The model parameters are given in Table 1.

The genetic algorithm was run for 30 times for different initial states of random number generator to assure the repetitiveness of convergence. It has been stated, that the obtained final solutions do not differ much. The results in Tables 1 and 2 are averaged.

Fig. 2 depicts the evolution of error during an exemplary action of genetic algorithm. It can be

Conclusions

It can be stated that the genetic algorithms estimate the J–A model parameters with an accuracy sufficient for technical applications, in spite of the fact, that their use generally does not guarantee reaching the global minimum [14].

The measurement data are inevitably affected with noise, whereas the model equations tend to give an averaged description of some macroscopic properties of magnetic material, expressed by major hysteresis loop. This explains obtainment of relatively high values of

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Identification of a hysteresis model parameters with genetic algorithms

Abstract

Introduction

Section snippets

Implementation

Results

Conclusions

J. Magn. Magn. Mater.

J. Magn. Magn. Mater.

Physica B

J. Magn. Magn. Mater.

J. Magn. Magn. Mater.

Komputerowy system do pomiaru dynamicznych wlasciwosci magnetycznych materialow magnetycznie miekkich (Computer-aided system for measurement of dynamic magnetic properties of soft magnetic materials) (in Polish)

Zesz. Nauk. PSwietokrz. Elekt.

Modeling the dynamics of nonlinear inductor circuits

IEEE Trans. Magn.