Feedforward backpropagation artificial neural networks for predicting mechanical responses in complex nonlinear structures: A study on a long bone

Abstract

Feedforward backpropagation artificial neural networks (ANNs) have been increasingly employed in many engineering practices concerning materials modeling. Despite their extensive applications, how to achieve successfully trained ANNs is not thoroughly explained in the literature, nor are there lucid discussions to delineate influential parameters obtained from analyses. Long bones are composite materials possessing nonhomogeneous and anisotropic properties, and their mechanical responses exhibit dependency on numerous variables. Material complexity hinders researchers from arriving at a consensus in implementing an optimal constitutive model or encourages them to adopt a simple constitutive model including many simplifying assumptions. However, such exceptional features and engineering challenges make long bones materials worth investigating, enriching our comprehension of complex engineering structures using novel techniques where traditional methods may present limitations. This paper reports on the prediction of loading, displacement, load and displacement simultaneously, and strains using feedforward backpropagation ANNs trained with experimental recordings. The technique was used to find optimum network structures (architectures) that encompass the best prediction ability. To enhance predictions, the influence of several elements such as a network training algorithm, injecting noise to datasets prior to training, the level of injected noise which directly affects model fitting and regularization, and data normalization prior to training were investigated and discussed. Essential parameters influencing decision making in identifying well-trained and well-generalized ANNs were elaborated. A considerable emphasis in this study was placed on examining the generalization ability of the already trained and tested ANNs, thus guaranteeing unbiased models that avoided overfitting. Gaining favorable outcomes in this study required three years of performing experiments and data collection before establishing the networks. The subsequent training, testing, and determination of the generalization of more than 60,000 ANNs are promising and will assist researchers in comprehending mechanical responses of complicated engineering structures that exhibit peculiar nonlinear properties.

Keywords: Artificial neural network (ANN); Complex composite structures; Hyperparameters; Load & displacement; Prediction of mechanical properties; Strains.