Abstract
A suitable framework for the development of artificial neural networks is important because it decides the level of accuracy, which can be reached for a certain dataset and increases the certainty about the reached classification results. In this paper, we conduct a comparative study for the performance of four frameworks, Keras with TensorFlow, Pytorch, TensorFlow, and Cognitive Toolkit (CNTK), for the elaboration of neural networks. The number of neurons in the hidden layer of the neural networks is varied from 8 to 64 to understand its effect on the performance metrics of the frameworks. A test dataset is synthesized using an analytical model and real measured impedance spectra by an eddy current sensor coil on EUR 2 and TRY 1 coins. The dataset has been extended by using a novel method based on interpolation technique to create datasets with different difficulty levels to replicate the scenario with a good imitation of EUR 2 coins and to investigate the limit of the prediction accuracy. It was observed that the compared frameworks have high accuracy performance for a lower level of difficulty in the dataset. As the difficulty in the dataset is raised, there was a drop in the accuracy of CNTK and Keras with TensorFlow depending upon the number of neurons in the hidden layers. It was observed that CNTK has the overall worst accuracy performance with an increase in the difficulty level of the datasets. Therefore, the major comparison was confined to Pytorch and TensorFlow. It was observed for Pytorch and TensorFlow with 32 and 64 neurons in hidden layers that there is a minor drop in the accuracy with an increase in the difficulty level of the dataset and was above 90% until both the coins were 80% closer to each other in terms of electrical and magnetic properties. However, Pytorch with 32 neurons in the hidden layer has a reduction in model size by 70% and 16.3% and predicts the class, 73.6% and 15.6% faster in comparison to TensorFlow and Pytorch with 64 neurons.
Highlights
Four different machine-learning frameworks ‘Keras with TensorFlow at the backend, Pytorch, TensorFlow, and Cognitive Toolkit (CNTK)’ are selected for quantitative comparison based on different performance metrics for a trained neural network (NN) model
‘Keras with TensorFlow at the backend, Pytorch, TensorFlow, and CNTK’ for a feed-forward neural network model based on the sensor dataset with different difficulty levels of the bi-metallic coins
Since the sensor dataset based on bi-metallic coins for model training is not readily available, for this purpose, the application of eddy current sensor was used to artificially synthesize the dataset, which implies the use of two bi-metallic coins ‘EUR 2 and TRY 1’ with similar physical and mechanical properties
Summary
Bi-metallic coins comprise different types of metals within the layered structure, embedded with different security features depending upon the fused metal composition and their magnetic properties. To access the magnetic properties from different layers of these coins, multi-frequency excitation signals can be used to excite an eddy current sensor coil in the presence of the coin. Depending upon the used frequencies, a particular penetration depth of the eddy current effect in the coin can be achieved, measuring the response in the form of inductance from the varying properties of a coin at different layers. The multi-frequency inductive response of the bi-metallic coins can be further used for their classification into different classes
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