# Prediction of giant magneto-impedance effect in amorphous glass-coated micro-wires using artificial neural network

- Asli Ayten Kaya
^{1}Email author

**2013**:216

https://doi.org/10.1186/1029-242X-2013-216

© Kaya; licensee Springer 2013

**Received: **31 January 2013

**Accepted: **19 April 2013

**Published: **30 April 2013

## Abstract

This paper deals with a prediction of a giant magneto-impedance (GMI) effect on amorphous micro-wires using an artificial neural network (ANN). The prediction model has three hidden layers with fifteen neurons and full connectivity between them. The ANN model is used to predict the GMI effect for Co_{70.3}Fe_{3.7}B_{10}Si_{13}Cr_{3} glass-coated micro-wire. The results show that the ANN model has a 98.99% correlation with experimental data.

### Keywords

giant magneto-impedance effect amorphous micro-wires modeling artificial neural network## Introduction

where $\frac{\mathrm{\Delta}Z}{Z}$, $Z(H)$ and $Z({H}_{max})$ are the GMI ratio, magneto impedance at magnetic field *H*, and magneto impedance at maximum magnetic field, respectively. The discovery of the giant magneto-impedance (GMI) effect in soft ferromagnetic amorphous micro-wires makes them very attractive candidate material for making high-performance magnetic sensors [1–6]. The use of such micro-wires could also have implications for the next generation of electronic devices, which will involve increasingly smaller components [7–9]. The GMI effect is termed the giant variation of impedance of a ferromagnetic conductor with an ac current in an applied dc magnetic field [10, 11].

Artificial neural networks are increasingly becoming useful in prediction of magnetic performance in electromagnetic devices. The ANN operates like a human brain. ANNs have been applied in many areas (such as electronics, forecasting, banking and aerospace) because of these features. The available ANN software today provides many neural network architectures and learning algorithms, and it also helps users to apply ANN to their specific problems easily [12, 13].

In this investigation, the GMI effects are modeled using self-organizing feature map (SOFM) and previous experimental data [11] of Co_{70.3}Fe_{3.7}B_{10}Si_{13}Cr_{3} amorphous glass-coated micro-wire.

## Experimental procedure

### Kohonen neural network

The ideas of self-organizing feature map (SOFM) are rooted in competitive learning networks. The SOFM transforms the input of an arbitrary dimension into a one- or two-dimensional discrete map subject to a topological (neighborhood-preserving) constraint. The feature maps are computed using Kohonen unsupervised learning. The output of the SOFM can be used as the input to a supervised classification neural network [14].

### ANN model for glass-coated amorphous micro-wire

The input parameters were magnetizing field $(H)$, wire length $(l)$ and frequency $(f)$. A total of 1,200 input vectors obtained from varied samples [11] were available in the training data. The number of hidden layers and neurons in each layer were determined through trial and error to be optimal including different transfer functions such as hyperbolic tangent, sigmoid and hybrid. After the network was trained, a better result was obtained from the network formed by the hyperbolic tangent transfer function in the hidden and output layers. The number of epochs was 10^{6} for training.

## Results and discussion

_{70.3}Fe

_{3.7}B

_{10}Si

_{13}Cr

_{3}amorphous glass-coated micro-wires [11] have been used for the experimental confirmation of the proposed model. The agreement between the experimental observations and the network output (predictions) for training is shown in Figure 2. As shown in Figure 2, the values obtained through the training of the ANN model are very close to experimental results, indicating a strong correlation between the input and output parameters of the ANN model. The statistical value of R

^{2}found from ANN training is 0.994.

**Comparison of predicted and measured GMI% values**

Wire length-frequency | Max GMI% (measured) | Max GMI% (predicted) |
---|---|---|

10 mm-1 MHz | 70.00 | 71.62 |

10 mm-2 MHz | 117.14 | 118.05 |

10 mm-4 MHz | 181.82 | 181.43 |

10 mm-10 MHz | 265.63 | 267.29 |

All statistical values prove that the proposed ANN model is suitable to predict the GMI values very close to the experimental results.

## Conclusions

The proposed model developed from experimental data obtained previously can be used to predict more easily the GMI curves for Co_{70.3}Fe_{3.7}B_{10}Si_{13}Cr_{3} amorphous glass-coated micro-wires (5, 10 and 15 mm length) at 1, 2, 4 and 10 MHz. According to the results obtained from modeling a neural network, the neural network with the architecture of the ANN method is suitable for predicting the GMI values of Co-based amorphous glass-covered micro-wire. The overall prediction error is about 1% compared with the measured GMI values.

## Declarations

### Acknowledgements

Dedicated to Professor Hari M Srivastava.

## Authors’ Affiliations

## References

- Knobel M, Pirota KR: Giant magnetoimpedance: concepts and recent progress.
*J. Magn. Magn. Mater.*2002, 242–245: 33–40. Part 1View ArticleGoogle Scholar - Knobel M, Vazquez M, Kraus L 15. In
*Handbook of Magnetic Materials*Edited by: Buschow KH. 2003.Google Scholar - Phan M-H, Peng H-X: Giant magnetoimpedance materials: fundamentals and applications.
*Prog. Mater. Sci.*2008, 53(2):323–420. 10.1016/j.pmatsci.2007.05.003View ArticleGoogle Scholar - Zhukov A, Ipatov M, Gonzalez J, Blanco JM, Zhukova V: Recent advances in studies of magnetically soft amorphous microwires.
*J. Magn. Magn. Mater.*2009, 321(7):822–825. 10.1016/j.jmmm.2008.11.068View ArticleGoogle Scholar - Zhukov A, Zhukova V:
*Magnetic Properties and Applications of Ferromagnetic Mircowires with Amorphous and Nanocrystalline Structure*. Nova Science Publishers, New York; 2009.Google Scholar - Chiriac H, Ovari TA: Amorphous glass-covered magnetic wires: preparation, properties, applications.
*Prog. Mater. Sci.*1996, 40(5):333–407. 10.1016/S0079-6425(97)00001-7View ArticleGoogle Scholar - Mohri K, Uchiyama T, Shen LP, Cai CM, Panina LV, Honkura Y, Yamamoto M: Amorphous wire and CMOS IC-based sensitive micromagnetic sensors utilizing magnetoimpedance (MI) and stress-impedance (SI) effects.
*IEEE Trans. Magn.*2002, 38(5):3063–3068. 10.1109/TMAG.2002.802438View ArticleGoogle Scholar - Mohri K, Tsuyoshi U, Panina LV: Recent advances of micro magnetic sensors and sensing application.
*Sens. Actuators A*1997, 59(1–3):1–8. 10.1016/S0924-4247(97)80141-0View ArticleGoogle Scholar - Mohri K, Panina LV, Uchiyama T, Bushida K, Noda M: Sensitive and quick response micro-magnetic sensor utilizing magneto-impedance in Co-rich amorphous wires.
*IEEE Trans. Magn.*1995, 31(2):1266–1275.View ArticleGoogle Scholar - Panina LV, Mohri K: Magneto-impedance effect in amorphous wires.
*Appl. Phys. Lett.*1994, 65(9):1189–1191. 10.1063/1.112104View ArticleGoogle Scholar - Qin FX, Peng HX, Phan MH: Wire-length effect on GMI in Co
_{70.3}Fe_{3.7}B_{10}Si_{13}Cr_{3}amorphous glass-coated microwires.*Mater. Sci. Eng.*2010, 167: 129–132. 10.1016/j.mseb.2010.01.039View ArticleGoogle Scholar - Kucuk I: Multilayered perceptron neural networks to compute energy losses in magnetic cores.
*J. Magn. Magn. Mater.*2006, 307: 53–61. 10.1016/j.jmmm.2006.03.043View ArticleGoogle Scholar - Kucuk I: Estimation of thermally stimulated current in as grown TlGaSeS layered single crystals by multilayered perceptron neural network.
*Expert Syst. Appl.*2011, 38: 7192–7194. 10.1016/j.eswa.2010.12.040View ArticleGoogle Scholar - Kohonen T: The self-organizing map.
*Proc. IEEE*1990, 78(9):1464–1480. 10.1109/5.58325View ArticleGoogle Scholar

## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.