Comparative Study of Machine-Learning Frameworks for the Elaboration of Feed-Forward Neural Networks by Varying the Complexity of Impedimetric Datasets Synthesized Using Eddy Current Sensors for the Characterization of Bi-Metallic Coins

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.