An approach is presented for treating the local minima problem in the Hopfield neural network. The proposed technique is based on scaling the input signal of the network with different scaling factors, then the output for each scaled input is measured and the average of these outputs is computed. The purpose of the present paper is to investigate the Hopfield neural network as a flexible detection method of Ferro-magnetic sources from magnetic anomaly data. The observed magnetic anomaly is approximated over a steel drum by an equivalent dipole source. The Hopfield network was used to obtain the magnetic moment at a set of regular locations. For each location, the Hopfield network reaches its stable state and the location of minimum Hopfield energy signifies the target location. To escape from the local minima of the network energy function, the successively scaled input technique is proposed.
The performance of the proposed technique was tested using theoretical and field examples. The method detected the location of the targets with a degree of accuracy sufficient in environmental investigations for the detection of Ferro-metallic objects. The results show that the proposed scaled technique increases the correlation between the practical and expected outputs of the network from 91.8 % to 100 % at noise-free input. Also, when the input signal is contaminated with a random noise, the proposed technique increases the correlation between the actual output and the expected output from 88.1% to 99.5 % when the standard deviation of the added noise is 1.0.
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