Computational modeling of GMI effect in Co-based amorphous ribbons
© Kaya; licensee Springer 2013
Received: 31 January 2013
Accepted: 28 May 2013
Published: 14 June 2013
This paper presents a prediction of a giant magneto-impedance (GMI) effect on Co-based amorphous ribbons using an artificial neural network (ANN) approach based on a self-organizing feature map (SOFM). The input parameters included the compositions of Fe and Co, ribbon width and magnetizing frequency. The output parameter was the GMI effect. The results show that the proposed model can be used for estimation of the GMI effect in the amorphous ribbons.
Dedicated to Professor Hari M Srivastava
When a soft ferromagnetic conductor is subjected to an alternating current, a large change in the complex impedance of the conductor can be achieved upon applying a magnetic field. This phenomenon is known as the giant magneto-impedance (GMI) effect . This effect has received increasing attention for its potential applications in highly sensitive magnetic sensors .
The ANN is simply a class of mathematical algorithms, since a network can be regarded essentially as a graphic notation for a large class of algorithms. Such algorithms produce solutions to a number of specific problems .
In this investigation, the GMI effects are modeled using self-organizing feature map (SOFM) and previous experimental data [4, 5] of amorphous ribbons made from Co70Fe5Si15B10 and Co70.4Fe4.6Si15B10 alloys.
Self-organizing feature map (SOFM)
Self-organizing feature maps (SOFM), also known as Kohonen maps or topographic maps, were first introduced by von der Malsburg (1973) and in its present form by Kohonen (1982). SOFM is a special neural network that accepts N-dimensional input vectors and maps them to the Kohonen layer, in which neurons are organized in an L-dimensional lattice (grid) representing the feature space. Such a lattice characterizes a relative position of neurons with regards to their neighbors, that is, their topological properties rather than exact geometric locations. In practice, dimensionality of the feature space is often restricted by its visualization aspect and typically is . The objective of the learning algorithm for the SOFM neural networks is formation of the feature map which captures the essential characteristics of the N-dimensional input data and maps them on the typically 1-D or 2-D feature space .
where is the position of the neuron in the lattice .
SOFM training algorithm
Assign small random values to weights ;
Choose a vector from the training set and apply it as input;
- 3.Find the winning output node by the following criterion:
- 4.Adjust the weight vectors according to the following update formula:
Repeat Steps 2 through 4 until no significant changes occur in the weights .
Developed ANN model
Results and discussion
In this study an attempt was made to predict the GMI effect of Co-based amorphous ribbons (Co70Fe5Si15B10 and Co70.4Fe4.6Si15B10) using artificial neural networks. To achieve this goal, magnetizing field (H), ribbon width (l), magnetizing frequency (f), concentration of Co (Co%) and concentration of Fe (Fe%) were used as the input of networks, and GMI% data points were used as the output of these networks. Finally, network was achieved with the least cross validation error for Co-based amorphous ribbons.
These results show that the proposed model is potentially useful for sensor designers in predicting the GMI curves in cases when measurements may be time consuming.
In this study the proposed model was developed from experimental data for the Co-based amorphous ribbons. This study demonstrates the applicability and feasibility of artificial neural network models to predict the GMI effect for Co70Fe5Si15B10 and Co70.4Fe4.6Si15B10 amorphous ribbons which have different ribbon width such as 0.5, 1 and 3 mm and a frequency range of 0.1-1 MHz. The average correlation and prediction error were found to be 99% and 1% for the tested amorphous ribbons, respectively. These results show that the predicted values of these ribbons are in good agreement with the measured ones. Therefore, this model is appropriate for a researcher to evaluate the sensor performance before manufacture.
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