Interpretable machine learning models for predicting penetration depth in ultra‐high‐performance concrete under ballistic impact

Abstract The process of rigid projectiles penetrating concrete is governed by a range of factors, such as the material strength of the concrete and the properties of the projectile. This study focuses on developing precise models to predict penetration depth (PD) in ultra‐high‐performance concrete (UHPC) targets subjected to projectile impact, utilizing three machine learning (ML) techniques: multi‐expression programming (MEP), decision tree (DT), and gene expression programming (GEP). The research employed a dataset comprising 103 data points and 10 input features, and various statistical metrics were applied to evaluate model performance. The proposed models were also compared with existing empirical formulas to assess their accuracy and reliability. Additionally, SHapley Additive exPlanations (SHAP) were employed for model interpretability. While all models demonstrated strong predictive capabilities, the DT model achieved the highest accuracy, with a correlation coefficient ( R ) of 0.999 and a mean absolute error (MAE) of 0.588. The MEP and GEP models also performed well, with R values of 0.995 and 0.987 and MAE values of 3.118 and 5.416, respectively. Furthermore, empirical equations based on GEP and MEP were derived, providing a straightforward and practical method for estimating PD. The evaluation of the proposed ML models against existing empirical formulas revealed that the ML models significantly outperformed empirical approaches in predictive accuracy. The SHAP analysis identified impact energy, velocity, and diameter as the most influential factors in determining PD, while compressive strength and fiber aspect ratio also played a notable role. Overall, this study demonstrates that ML significantly enhances the accuracy of PD predictions, outperforming traditional empirical methods and offering a robust approach for estimating PD in UHPC targets.