Development of a machine learning-driven formula for calculating fragment velocity

• Determined the dimensionless factors influencing fragment velocity. • Proposed the optimal configuration for the ANN prediction model of spatial distribution parameters . • Established a calculation formula for spatial distribution parameters. • Optimized the calculation formula for fragment velocity. Fragment velocity is a critical parameter for assessing the damage potential of cased charges, and its accurate prediction has been a focal point in the field of engineering protection. To develop a more widely applicable and accurate fragment velocity calculation formula, this study integrates experimental and numerical simulation results to construct an artificial neural network (ANN) predictive model for the spatial distribution parameters of fragment velocity. Based on this, a calculation formula that considers spatial distribution parameters and fragment velocity distribution is derived. The results indicate that fragment velocity is positively correlated with the charge mass ratio, end cap thickness ratio, and aspect ratio, with the mass ratio having the most significant impact. The spatial distribution parameter is negatively correlated only with the end cap thickness ratio. The developed fragment velocity formula yields an average error of 6.2 % for the charge with end caps and 4.4 % without end caps, reducing the average error by 3.9 % and 1.1 %, respectively, compared to the formula established by Liao et al. Overall, the neural network model developed in this study effectively predicts spatial distribution parameters of fragment velocity, and the resulting fragment velocity formula offers broad applicability and enhanced accuracy.