Machine learning for predicting the outcome of terminal ballistics events

Machine learning(ML) is well suited for the prediction of high-complexity,high-dimensional problems such as those encountered in terminal ballistics.We evaluate the performance of four popular ML-based regression models,extreme gradient boosting(XGBoost),artificial neural network(ANN),support vector regression(SVR),and Gaussian process regression(GP),on two common terminal ballistics’ problems:(a)predicting the V50ballistic limit of monolithic metallic armour impacted by small and medium calibre projectiles and fragments,and(b) predicting the depth to which a projectile will penetrate a target of semi-infinite thickness.To achieve this we utilise two datasets,each consisting of approximately 1000samples,collated from public release sources.We demonstrate that all four model types provide similarly excellent agreement when interpolating within the training data and diverge when extrapolating outside this range.Although extrapolation is not advisable for ML-based regression models,for applications such as lethality/survivability analysis,such capability is required.To circumvent this,we implement expert knowledge and physics-based models via enforced monotonicity,as a Gaussian prior mean,and through a modified loss function.The physics-informed models demonstrate improved performance over both classical physics-based models and the basic ML regression models,providing an ability to accurately fit experimental data when it is available and then revert to the physics-based model when not.The resulting models demonstrate high levels of predictive accuracy over a very wide range of projectile types,target materials and thicknesses,and impact conditions significantly more diverse than that achievable from any existing analytical approach.Compared with numerical analysis tools such as finite element solvers the ML models run orders of magnitude faster.We provide some general guidelines throughout for the development,application,and reporting of ML models in terminal ballistics problems.

Adaptive optimisation of explosive reactive armour for protection against kinetic energy and shaped charge threats

We evaluate an adaptive optimisation methodology,Bayesian optimisation(BO),for designing a minimum weight explosive reactive armour(ERA)for protection against a surrogate medium calibre kinetic energy(KE)long rod projectile and surrogate shaped charge(SC)warhead.We perform the optimisation using a conventional BO methodology and compare it with a conventional trial-and-error approach from a human expert.A third approach,utilising a novel human-machine teaming framework for BO is also evaluated.Data for the optimisation is generated using numerical simulations that are demonstrated to provide reasonable qualitative agreement with reference experiments.The human-machine teaming methodology is shown to identify the optimum ERA design in the fewest number of evaluations,outperforming both the stand-alone human and stand-alone BO methodologies.From a design space of almost 1800 configurations the human-machine teaming approach identifies the minimum weight ERA design in 10 samples.

Stability analyses of the mass abrasive projectile high-speed penetrating into a concrete target Part III: Terminal ballistic trajectory analyses

During the high-speed penetration of projectiles into concrete targets （the impact velocity ranges from 1.0 to 1.5 km/s）, important factors such as the incident oblique and attacking angles, as well as the asymmetric abrasions of the projectile nose induced by the target-projectile interactions, may lead to obvious deviation of the terminal ballistic tra- jectory and reduction of the penetration efficiency. Based on the engineering model for the mass loss and nose-blunting of ogive-nosed projectiles established, by using the Differ- ential Area Force Law （DAFL） method and semi-empirical resistance function, a finite differential approach was pro- grammed （PENTRA2D） for predicting the terminal ballistic trajectory of mass abrasive high-speed projectiles penetrating into concrete targets. It accounts for the free-surface effects on the drag force acting on the projectile, which are attributed to the oblique and attacking angles, as well as the asymmetric nose abrasion of the projectile. Its validation on the prediction of curvilinear trajectories of non-normal high-speed pene- trators into concrete targets is verified by comparison with available test data. Relevant parametric influential analyses show that the most influential factor for the stability of ter- minal ballistic trajectories is the attacking angle, followed by the oblique angle, the discrepancy of asymmetric nose abrasion, and the location of mass center of projectile. The terminal ballistic trajectory deviations are aggravated as the above four parameters increase.

Experiment/simulation correlation-based methodology for metallic ballistic protection solutions

A methodology is developed based on the coupling of a finite element code with an optimisation module for the design of land vehicle armouring composed of lightweight aluminium alloy and high strength steel plate.Following an experiment/simulation correlation,a numerical model has been built and calibrated considering monolithic plates and then verified considering a bi-metal protection against tungsten carbide projectile mimicking the core of a 7.62×51 AP8 ammunition.In addition,a method is proposed to obtain the v_(res)-v_(i) curve for the full 7.62×51 AP8 bullet from the v_(res)-v_(i) curve obtained from the core only.

Dimensional analysis and extended hydrodynamic theory applied to long-rod penetration of ceramics

Principles of dimensional analysis are applied in a new interpretation of penetration of ceramic targets subjected to hypervelocity impact. The analysis results in a power series representation – in terms of inverse velocity – of normalized depth of penetration that reduces to the hydrodynamic solution at high impact velocities. Specifically considered are test data from four literature sources involving penetration of confined thick ceramic targets by tungsten long rod projectiles. The ceramics are AD-995 alumina, aluminum nitride, silicon carbide, and boron carbide.Test data can be accurately represented by the linear form of the power series, whereby the same value of a single fitting parameter applies remarkably well for all four ceramics. Comparison of the present model with others in the literature(e.g., Tate's theory) demonstrates a target resistance stress that depends on impact velocity, linearly in the limiting case. Comparison of the present analysis with recent research involving penetration of thin ceramic tiles at lower typical impact velocities confirms the importance of target properties related to fracture and shear strength at the Hugoniot Elastic Limit(HEL) only in the latter. In contrast, in the former(i.e., hypervelocity and thick target) experiments, the current analysis demonstrates dominant dependence of penetration depth only by target mass density. Such comparisons suggest transitions from microstructure-controlled to density-controlled penetration resistance with increasing impact velocity and ceramic target thickness.Production and hosting by Elsevier B.V. on behalf of China Ordnance Society.

Ballistic response of armour plates using Generative Adversarial Networks

It is important to understand how ballistic materials respond to impact from projectiles such that informed decisions can be made in the design process of protective armour systems. Ballistic testing is a standards-based process where materials are tested to determine whether they meet protection, safety and performance criteria. For the V50ballistic test, projectiles are fired at different velocities to determine a key design parameter known as the ballistic limit velocity(BLV), the velocity above which projectiles perforate the target. These tests, however, are destructive by nature and as such there can be considerable associated costs, especially when studying complex armour materials and systems. This study proposes a unique solution to the problem using a recent class of machine learning system known as the Generative Adversarial Network(GAN). The GAN can be used to generate new ballistic samples as opposed to performing additional destructive experiments. A GAN network architecture is tested and trained on three different ballistic data sets, and their performance is compared. The trained networks were able to successfully produce ballistic curves with an overall RMSE of between 10 and 20 % and predicted the V50BLV in each case with an error of less than 5 %. The results demonstrate that it is possible to train generative networks on a limited number of ballistic samples and use the trained network to generate many new samples representative of the data that it was trained on. The paper spotlights the benefits that generative networks can bring to ballistic applications and provides an alternative to expensive testing during the early stages of the design process.