Approximation of two-dimensional ballistic limit curves in the range of material thickness with stochastic physical-based oversampling

Abstract

In this paper, we propose a method for approximating ballistic curves and determining ballistic limit velocity based on a data-driven approach as a function of two variables: thickness and initial velocity, allowing for the approximation of these parameters for material thicknesses that were not present in the training set. This differs from previous work in this area, where a random division was made between the training and validation sets, which did not guarantee separability in terms of material thickness between the training and validation sets. To prove the effectiveness of this approach, we performed leave-one-out cross-validation. Our method was trained on ballistic experimental data, which was extended using the finite element method. We also proposed a new method of data oversampling based on fitted ballistic curves estimated using the Recht-Ipson method. Oversampling involves the use of stochastic sampling in which the cumulative distribution function is a mixture of uniform sampling and the first and second derivatives derived from ballistic limit curves. We have evaluated several deep neural network architectures. Our experiments have shown that it is possible not only to approximate the shape of the curve but also to accurately predict the ballistic limit velocity for material thicknesses not present in the dataset. The inclusion of information about the first and second derivatives in the stochastic oversampling process allowed for a significant increase in prediction accuracy over uniform sampling.