Impact reduction of the uncertain geometrical parameters on magnetic material identification of an EI electromagnetic inductor using an adaptive inverse algorithm A. Abdallh n , G. Crevecoeur, L. Dupre ´ Department of Electrical Energy, Systems and Automation, Ghent University, Sint Pietersnieuwstraat 41, B-9000 Ghent, Belgium article info Article history: Received 15 March 2011 Received in revised form 26 October 2011 Available online 1 December 2011 Keywords: Inverse problem Magnetic material identification Uncertainty analysis abstract The magnetic characteristics of the electromagnetic devices’ core materials can be recovered by solving an inverse problem, where sets of measurements need to be properly interpreted using a forward numerical model of the device. However, the uncertainties of the geometrical parameter values in the forward model lead to appreciable recovery errors in the recovered values of the material parameters. In this paper, we propose an effective inverse approach technique, in which the influences of the uncertainties in the geometrical model parameters are minimized. In this proposed approach, the cost function that needs to be minimized is adapted with respect to the uncertain geometrical model parameters. The proposed methodology is applied onto the identification of the magnetizing B–H curve of the magnetic material of an EI core inductor. The numerical results show a significant reduction of the recovery errors in the identified magnetic material parameter values. Moreover, the proposed methodology is validated by solving an inverse problem starting from real magnetic measurements. & 2011 Elsevier B.V. All rights reserved. 1. Introduction Classically, standard techniques, such as an Epstein frame or a single sheet tester, are utilized for characterizing the magnetic properties of the magnetic material in electromagnetic devices (EMDs) [1]. However, this requires extra samples of the electrical steel sheet of which the EMD is manufactured, which are often unavailable. Moreover, the manufacturing processes of the EMD may deteriorate the magnetic material characteristic [2–6]. Therefore, in order to characterize the present magnetic properties, it is more accurate to identify the magnetic properties on the specific geometry of the EMD itself. Recently, a coupled experimental-numerical inverse approach is proposed for identifying the magnetic material properties in an EMD [7]. This inverse approach iteratively minimizes the difference between the numerical model responses and the measure- ment quantities. In fact, numerical model responses, and hence inverse problem resolution, are highly affected by the uncertainties in the geometrical model parameter values, especially the air gap thickness [8]. Therefore, a more robust inverse approach is needed. We present in this paper an effective inverse approach for estimating the magnetic material properties of an EMD, e.g. an EI core inductor, with minimum influence of the uncertainty in the geometrical model parameter values. 2. Studied geometry Fig. 1 shows the profile of the studied geometry. It is an EI core with one ‘middle’ air gap in the middle limb (g 1 ), and two ‘outer’ air gaps (g 2 ) between E and I yokes. The excitation coil is wound over the middle limb of the E-core with 356 number of excitation winding turns. In this paper, we assume that the dimensions of the EI core inductor are precisely known, except for the values of the two air gap thicknesses g 1 and g 2 , which are uncertain with the mean values of 0.85 mm and 0.25 mm, respectively. The mean value of the g 1 thickness is taken from the manufacturer data, however, the mean value of the g 2 thickness is the thickness of the plastic spacer inserted between the E and I yokes, the two yokes are fixed together by a mechanical clamp to prevent the movement of the I-yoke. 3. Magnetic material modeling The material under consideration is a high-quality, non-oriented electrical steel (M 700/50 A), with a low degree of material anisotropy. The single-valued non-linear constitutive characteristic (normal magnetizing characteristic), of the magnetic material of the Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jmmm Journal of Magnetism and Magnetic Materials 0304-8853/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2011.11.031 n Corresponding author. E-mail addresses: Ahmed.Abdallh@UGent.Be, amyazeed@yahoo.com (A. Abdallh). Journal of Magnetism and Magnetic Materials 324 (2012) 1353–1359