IEEE TRANSACTIONS ON MAGNETICS, VOL. 39, NO. 3, MAY2003 1397 The Inverse Jiles–Atherton Model Parameters Identification J. V. Leite, N. Sadowski, P. Kuo-Peng, N. J. Batistela, and J. P. A. Bastos, Member, IEEE Abstract—An optimization procedure to obtain the parameters of both the original Jiles–Atherton and the inverse Jiles–Atherton hysteresis models is presented in this paper. Doing so, minor loops can be conveniently simulated without inserting scaling methods. The comparison between experimental and calculation results val- idates the procedure. Index Terms—Magnetic hysteresis modeling, magnetic mate- rials, parameters identification. I. INTRODUCTION I N THE original Jiles–Atherton (JA) model, the magnetiza- tion is decomposed into its reversible and irreversible components. This commonly employed model is formulated in terms of a set of equations having five parameters, which must be obtained from experimental data. The original JA model al- lows the computation of the magnetic induction from the known magnetic field history. However, in some calculation procedures the induction is known before the field as, for instance, when the magnetic vector potential formulation is em- ployed with the finite-element method (FEM). To perform such simulations, a modified JA model presenting the magnetic induction as independent variable was proposed in [1]. The main equation of this model is (1) with the following complementary relationships: (2a) (2b) (2c) (2d) (2e) (2f) (2g) Manuscript received June 18, 2002. The authors are with the GRUCAD/EEL/CTC/UFSC, Florianópolis SC 88040-900, Brazil (e-mail: jean@grucad.ufsc.br). Digital Object Identifier 10.1109/TMAG.2003.810216 Fig. 1. Proposed optimization procedure. As in the original JA model, the magnetization is decom- posed into its reversible component and its irreversible component ; represents the anhysteretic magnetiza- tion; is a directional parameter and takes the value 1 for and 1 for ; , , , , and the sat- uration magnetization are the same five original JA model parameters, which have to be determined from a measured hys- teresis loop which has achieved saturation [2], [4]. The main contribution of this paper is to present an optimiza- tion procedure using the inverse JA model, which allows good representations of inner loops. II. PARAMETERS IDENTIFICATION A methodology to calculate the set of parameters of the orig- inal JA model is presented in [2]. Nevertheless, the simulated inner hysteresis loops obtained using these data do not fit, in some cases, with the measured ones. To overcome this problem, some authors use scaling methods, as for instance in [3] and [4]. Other works are based on optimization methods to find the model parameters [5], [6]. The methodology presented here is also based on an opti- mization procedure and consists in varying the parameters and controlling their influence on the mean square error ( ) be- tween experimental and calculated data as shown in Fig. 1. First, , , , , and are obtained with the methodology presented in [2]. The method employed to optimize these pa- rameters is based on decision choices of type “yes” or “no” in a sequential algorithm. Let us call a generic parameter to be obtained. It will be individually submitted to the procedure shown in Fig. 2. The input data to this algorithm are (the initial varia- tion of ), the maximal iteration number , the MSE 0018-9464/03$17.00 © 2003 IEEE