ANN Architecture Specifications for Modelling of Open-Cell Aluminum under Compression

Abstract

The knowledge on strength properties of porous metals in compression is essential in tailored application design, as well as in elaboration of general material models. In this article, the authors propose specification details of the ANN architecture for adequate modelling of the phenomenon of compressive behaviour of open-cell aluminum. In the presented research, an algorithm was used to build different structures of artificial neural networks (ANNs), which approximated stress-strain relations of an aluminum sponge subjected to compression. Next, the quality of the built approximations was appraised. The mean absolute relative error (MARE), coefficient of determination between outputs and targets R2, root mean square error (RMSE), and mean square error (MSE) were assumed as criterial measures for the assessment of the fitting quality. The studied neural networks (NNs) were two-layer feedforward networks with different numbers of neurons in the hidden layer. A set of experimental stress-strain data from quasistatic uniaxial compression tests of open-cell aluminum of various apparent densities was used as data for training of neural networks. Analysis was performed in two modes: in the first one, all samples were taken for training, and in the second case, one sample was left out during training in order to play the role of external data for testing the trained network later. The taken out samples were maximum and minimum density samples (for extrapolation) and one random from within the density interval. The results showed that good approximation on the engineering level MARE<5% was reached for teaching networks with ≥7 neurons in the hidden layer for the first studied case and with ≥8 neurons for the second. Calculations on external data proved that 8 neurons are enough to actually obtain MARE<10%. Moreover, it was shown that the quality of approximation can be significantly improved to MARE≈7% (tested on external data) if the initial region of the stress-strain relation is modelled by an additional network.