Machine learning methods for predicting the outcome of hypervelocity impact events

Abstract

The outcome of projectile impacts on spaced aluminium armour (i.e. Whipple shield) at hypervelocity is traditionally predicted by semi-analytical equations known as ballistic limit equations (BLEs). For spherical aluminium projectiles impacting aluminium Whipple shields, the state-of-the-art BLE has been found to correctly reproduce the perforation/non-perforation result of approximately 75% of tests contained within a database with over 1100 entries. For such high-dimensional, complex problems, machine learning methods may be a superior approach over such semi-analytical/empirical methods. Towards this end an artificial neural network (ANN) and support vector machine (SVM) have been developed to better classify the outcome of hypervelocity impact events on aluminium Whipple shields. The ANN was found to correctly reproduce the perforation/non-perforation result of over 93% of the training exemplars, generalizing at 92.2% when applied with an optimized architecture. The SVM was not able to reach comparable levels of generalization error as the ANN, peaking at 83% after the removal of a small number of test exemplars which induced conflict within the SVM pattern recognition. Although providing a significant improvement in predictive accuracy over the conventional BLE, the performance of both the ANN and SVM were highly sensitive to the population density of the parameter space described by the training data. Within highly populated regions the qualitative trends of the machines are demonstrated to accurately identify patterns associated with projectile fragmentation and melting, while in sparsely populated regions the accuracy significantly decreases and the qualitative trends can become nonsensical. Further improvements in accuracy are limited by the inhomogeneous sampling of the parameter space defined by the current impact test database—a problem expected to be typical of any terminal ballistics problem in which the cost of performing experiments limits their scope to, for example, materials and geometries of interest, impact conditions expected during operation, and a limited range about the perforation threshold (i.e. ballistic limit). A combined novelty-detecting neural net and hetero-associate neural net have been applied to iteratively improve the performance of the ANN without requiring an inordinate number of additional tests. This process, referred to as bootstrapping, has been successfully demonstrated through the design of ‘optimized’ Whipple shields for given impact conditions, hypervelocity impact testing of the designed shields, and re-training of the critic net to incorporate the results of the new impact tests.