1
CE
Computational Errors in Hysteresis Preisach Modelling
Valentin Ionita and Lucian Petrescu
University “Politehnica” of Bucharest, Electrical Engineering Dept.
Spl. Independentei-313, Bucharest, 060042, Romania
[email protected]
Abstract— The paper analyses the influence of the
computational errors on the accuracy of magnetic material
modelling by scalar Preisach model. The numerical tests on
magnetic recording media allow the corect choosing of
numerical algorithms for model parameter identification.
Keywords— Hysteresis modelling,
computational errors, magnetic materials.
I.
Preisach
model,
INTRODUCTION
The magnetic excitation systems are very useful in
technical applications. Their design starts from the required
distribution (in time and space) of the magnetic field, in
order to produce the desired effects. But, this behaviour
depends on the magnetic properties of the target object and
requires a material model, including the hysteresis
phenomenon.
For technical applications, the Preisach hysteresis model
[1, 2] offers a good rate between the computational
efficiency and the result accuracy. The magnetic material
behavior is modeled by a statistical distribution function
(Preisach function) which may be identified in analytical or
numerical form [3], started from a reduced set of
experimental data. The modeling errors can be: intrinsic
model errors (according to the Preisach’ hysteresis theory),
experimental errors (e.g. measurement noise) and
computational errors.
The computational errors of the model parameter
identification influence the model accuracy in all the
electromagnetic field computation which uses it. One will
assume that the Preisach function is identified in a numerical
form, started from a set of experimental FORCs (first-order
reversal curves). The FORC number imposes the cells
number of the Preisach triangle mesh.
II.
Fig. 1. Preisach function for 80 FORCs of bank card sample.
III.
MODEL ACCURACY TESTING
The model accuracy was tested for different magnetic
field history. For example, in fig. 2 are presented the
experimental and the computed values of the sample
magnetic moment for an evolution on hysteresis minor
curves. The use of Everett functions minimizes the
numerical identification errors, implying a double
integration on the Preisach triangle.
NUMERICAL TESTS
The paper is focused on the computational errors of the
classical Preisach identification procedure, in order to
minimize it. The experimental FORC are obtained by a
vibrating sample magnetometer (VSM) for magnetic
recording materials: bank card, access card tape, floppy disk.
In these cases, the scalar Preisach model can be used, but the
conclusion are also valid for any generalized model. The
identification of Preisach function assumes that it is constant
in each cell of the meshed triangle. These values are
computed from a linear algebraic equation system by direct
substitution or Gauss method. Another way is using the
experimental Everett functions [1], direct in the magnetic
field computation.
Our tests show that the conditioning number of the
system matrix (cond) depends on the mesh refinement; e.g.
for a bank card, cond = 873 for (80 x 80) cells and cond =
301 for (40 x 40) cells. The obtained Preisach function (see
fig. 1) presents small differences (10-12 % in only 6 cells)
between the two methods of the system solving.
Fig. 2. Model accuracy for an arbitrary magnetization of bank card
sample
The conclusions of this study will allow the correct
choosing of numerical algorithms which are used for
Preisach model identification and offer some explanations
about the reported accuracy of the hysteretic magnetic
material modeling.
IV.
[1]
[2]
[3]
REFERENCES
I.D.Mayergoyz, Mathematical Models of Hysteresis, Springer Verlag,
New York, 1990.
E.Della Torre, Magnetic Hysteresis, IEEE Press, Piscataway, 1999.
O.Henze and W.Rucker, “Identification procedures of Preisach
model”, IEEE Trans. on Magnetics, vol. 38, pp. 833-836, 2002.