Parameters Identification for Jiles-Atherton Model using Genetic Algorithms

Parameters Identification for Jiles-Atherton Model using Genetic Algorithms

M. Zergoug, M. Amir, Y. Bennedjoue

Research Center in Industrial Technologies (CRTI), Algiers, Algeria Email: m.zergoug@csc.dz

Abstract— The aims of this work is the modeling of the hysteresis loop in ferromagnetic materials, and allowed to highlight of the difficulty that exists in the choice of an model, both accurate and fast, for implantation in a calculation code field. Through this work, we tried to implement the means to incorporate the hysteresis phenomenon; we proposed a procedure for the identification and optimization of the hysteresis loop by genetic algorithms (GA). The obtained results by this method permit to get the hysteresis loop using numerical simulation techniques. Experimental cycles on different samples allowed to us to identify the different optimized parameters and determine the GA approach on the calculation of various parameters of the hysteresis loop.

Index Terms—

I. INTRODUCTION

The Jiles-Atherton model was originally designed for use in static regime. It is based on different assumptions.

It is based on energy considerations on the Bloch walls displacements within the material. Overall, the model is described by a differential equation in which five parameters must be determined.

The Jiles-Atherton model is a model that describes the origin of the hysteresis phenomenon in ferromagnetic materials from a physical approach [1]. This description is mainly based on energy considerations related to the walls of travel within the magnet system [2, 3]. Found in the bibliography two categories of physical approaches to the description of the hysteresis phenomenon:

First, Jiles-Atherton magnetization defined as the sum of reversible and irreversible components such as:

rev irr

M M M (Eq. 1)

After a few energetic considerations on the deformation of a wall [4] and for small movements, Jiles Atherton shows that reversible magnetization is given by:

( )

rev an irr

M c M M (Eq. 2)

an sat coth

H M a

M M

a H M





  

     (Eq. 3)

 

 

m an irr

irr

an irr

M M

M dH

k M M



 

 

 



When δm and δ are given by:

1 si 0 et 1 si 0 et 0 ailleurs

an irr

m an irr

dH M M

dt

dH M M a

 dt

  



   





1 si 0 1 si 0

dH dt dH

dt



 

 

 



II. FLOWCHART OF OPTIMIZATION TECHNIQUE USING GENETIC ALGORITHMS

Genetic algorithms (GA) are robust methods that can afford to treat the general characteristics of electromagnetic optimization problems that are difficult to handled by other traditional optimization techniques.

The first stage of evolution calculations is the creation of the initial population.

The general principle of the functioning of a genetic algorithm is shown in the following Chart (figure 1.)

I. RESULTS AND DISCUSSION

In this section we study the ability of the proposed approach using genetic algorithms; for identification of the model parameters. we used the experimental results which were performed on different types of samples. This is carried out on the hysteresis loop performed on thin layers [A] and on cycles generated on heat treatment [A, C].

Figure 1. Flowchart of the parameters identification for JA model using AG’s

A. The generation of the hysteresis loop

In this section, we assume the knowledge of the different parameters ‘Ms’, ‘k’, ‘α’, ‘c’ and ‘a’ for the generation of the hysteresis loop, taken on various parameters of an article:

M 1.67e6 (A/m) magnetization saturation

k ^{82 (A/m)} Linked to hysteresis losses

α 49.07e-6 (A/m) Linked to the interaction between domains

c ^0.1 Coefficient of reversibility

a ^{50 (A/m)} form factor for magnetization anhysteretically

-600 -400 -200 0 200 400 600

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

H(A/m)

B(T)

Figure 2. The hysteresis loop by the JA model

B. Influence of Different Settings Influence of parameter ‘c’

For this study, we keep constant parameter values (Ms, K, α, a) and consider two values for the parameter c: 0.1 and 0.9.

Figure 3. Hysteresis loop for (a) c = 0.1 and (b) c = 0.9

Figures (Fig.3 (a) and (b)) show that the increase of the parameter (c) produces a restriction of the hysteresis loop (a decrease in the coercive field).

Influence of the parameter ‘k’

For this parametric study, we keep constant parameter values (Ms, c, α, a) and consider two values for the parameter K: 70et 82.

Figure 4. Hysteresis loop for (a) k=82 and (b) k=70

Figures (Fig.4 (a) and (b)) show that the increase of the parameter (k) produces a widening of the hysteresis loop.

Influence of the parameter ‘a’

To study the influence of the parameter (a), we consider two values: 50 and 200. The values of the other parameters are kept constant (Ms, k, α, c).

Figure 5. Hysteresis loop for (a) a=50 and (b) a=200

(a) (b)

(a) (b)

(b) (a)

Input parameters

Initial population

Genetics operator Selection, crossing,

Mutation, elitist

New generation

Stop criterion MSE≤ ɛ

end Yes

No

Evaluation of Cost function

Evaluation of Cost function

Jiles-Atherton model

Figures (Fig.5 (a) and (b)) show that the increase of the parameter (a) has:

• A decrease in the slope of the hysteresis loop.

• A reduction in the saturation magnetization.

-800 -600 -400 -200 0 200 400 600 800

-0.015 -0.01 -0.005 0 0.005 0.01 0.015

Figure 6. Comparison of the experimental loop and simulated loop for sample (B)

-300 -200 -100 0 100 200 300

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

B/Bmax

H(T) cycle expéré

cycle simulé

Figure 7. Comparison of the experimental loop and simulated loop for sample (C)

TABLE I. THE OBTAINED RESULTS AFTER THE OPTIMIZATION

C. Comparison between Jiles-Atherton and Preisach model’s

If we proceed to a comparison between the two models, the results are similar.

Figure 8 show that for this sample both models have given a good approximation of the cycle simulated to him for experimental.

-1.5 -1 -0.5 0 0.5 1 1.5

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

B/Bmax

H/Hmax exprérimental

Jiles Atherton Preisach

Figure 8. Comparison between Preisach and Jiles-Atherton Model for Sample (A)

We can summarize the results in the following table:

sample relative error

(simulation)

mean error (optimization)

identification Sample [A]

Jiles-Atherton model 8.3851% 0.12 Iterative optimization process for 5 parameters.

Sample [A]

Preisach model 8.42% 0.25 Interpolation methods

II. CONCLUSION

We have used a natural selection method for identification and optimization of parameters based on genetic algorithms. Excellent agreement has been found between obtained results by this method and those measured. The GA is a powerful and flexible tool for the identification of non-linear systems and can be used in the identification of systems with hysteresis in particular for the Jiles-Atherton model which is based on energy considerations. In this case, the problem of identification involves the approximation parameters for GA. The results show good precision with the experimental data.

The accuracy of the constructed model would determine the magnetic material parameters and thus their characterizations which would determine the nondestructive evaluation of materials behavior in specific cases.

REFERENCES

[1] D.C. Jiles et J.L. Atherton. "Theory of ferromagnetic hysteresis", Journal of Magnetism and Magnetic Materials,Vol. 61, pp. 48-60, 1986.

[2] F. Liorzou, B. Phelps, D. L. Atherton, « Macroscopic Models of Magnetization », IEEE. Trans. Magn. Vol. 36, N°. 2, March 2000.

[3] R.C. Smith, J.E. Massad, Technical Report CRSC-TR-01-10, North Carolina State University, 2001

[4] F.T. Calkins, R.C. Smith, A.B. Flatau, NASA/CR-97-206246, ICASE Report No. 97–60, 1999.

Sample B C

α 0,003978 8×10-3

a 7,4158 73.21

c 0,3541 0.001

k 62,6106 179.63

Ms 7847,1855 25405.19

Mean error 3.0929e-04 0.12