Machine learning model incorporating domain knowledge for predicting maximum deflection of reinforced concrete beams under low-velocity impact

Maximum deflection has been widely used as a key indicator for evaluating the impact resistance of reinforced concrete (RC) members subjected to low-velocity impact scenarios such as vehicle collisions or rockfalls. To predict the deflection, various methods, including empirical formulas, spring-mass, and energy-based methods, have been proposed. However, these methods are based on simplified assumptions regarding dynamic material behavior, failure mode and impact load transfer, limiting their applicability to a wide range of impact scenarios. As an alternative, machine learning (ML) has emerged, but most existing ML models consider only basic geometric and material properties of RC members, resulting in low interpretability and weak consistency with structural mechanics. To address these challenges, this study proposes a ML model that incorporates domain knowledge through physically meaningful variables representing both impact loading and structural resistance—specifically, impact energy, impact momentum, static flexural capacity, and flexural stiffness. Among these, flexural stiffness—despite its strong relationship with deflection—has been overlooked in prior studies. To expand domain knowledge on flexural stiffness and apply it to the ML model, six drop-weight impact tests were conducted on RC beams with varied stiffness levels, and these results were combined with a literature-based dataset of 157 cases. Model performance evaluation demonstrated that incorporating domain knowledge significantly enhanced both predictive accuracy and model transparency, outperforming existing ML and empirical formulas. Furthermore, considering practical application, a regression formula was proposed based on variables identified as highly important through the ML analysis.