Data-efficient computational framework for multi-objective design of explosively formed projectiles using space-filling sampling and Bayesian optimization

Designing Explosively Formed Projectiles (EFP) presents a significant challenge due to the complex hydro-elasto-plastic behaviors under high-strain-rate loading, typically incurring prohibitive computational costs when relying solely on traditional numerical simulations. This paper proposes an efficient hybrid computational framework integrating high-fidelity Finite Element Method ( FEM ) simulations with Bayesian Optimization (BO) to address the multi-objective optimization of a 54 mm EFP. A key contribution of this work is the implementation of an intelligent Space-Filling Design strategy utilizing Maximin Latin Hypercube Sampling. This approach enables the construction of a representative design space with only 64 points, reducing the computational burden by over 75% compared to Full Factorial Design. Based on this dataset, a Gaussian Process ( GP ) surrogate model with a Matern 5/2 kernel was trained to approximate the highly nonlinear dependencies between geometric variables ( h / d , δ 1 ​/ d , δ 2 ​/ d , l / d ) and warhead performance. Results demonstrate that the GP model achieves high accuracy, with prediction errors maintained below 2.5% against numerical verification. The BO algorithm successfully identified the best Pareto compromise configuration yielding a projectile velocity of 2728 m/s, which constitutes a 30.2 % increase over the empirical baseline, while simultaneously maximizing penetration width ( W p ≈ 37 mm) and ensuring robust structural integrity without fragmentation risks. Consequently, the proposed framework offers a highly sample-efficient alternative to traditional stochastic search methods which are often computationally prohibitive for high-fidelity hydrocode simulations due to their requirement for extensive function evaluations.