Data-driven rapid assessment of bridge responses under mixed traffic with restricted overloaded vehicles using machine learning

For infrastructure and regional economic development, restricted overload vehicles (ROVs) are an indispensable part. These vehicles are typically of large size and heavy weight, and their impact on bridge structures and other infrastructure is much greater than that caused by the load of ordinary vehicles. Authorization from the competent transportation authority shall be obtained prior to road operation of such vehicles. With the increasing volume of ROVs on highway networks, the safety assessment of bridges under mixed traffic conditions has become a critical yet challenging task. In such scenarios, ROVs coexist with ordinary vehicles under open traffic conditions, which is not adequately addressed by traditional assessment methods. Simplified single-beam models fail to capture spatial load coupling effects, while the high-fidelity finite element simulations are too computationally expensive for rapid and batch processing. To bridge this gap, this study proposes a machine learning-based rapid prediction framework for estimating load effect amplification factors in mixed traffic. A high-fidelity grillage finite element model is established to systematically simulate bridge responses under various combinations of vehicle parameters, bridge types, and standard design loads. An influence surface-based moving load analysis method is employed to efficiently generate a comprehensive database covering over 2,000 ROVs across 17 typical small- and medium-span bridges. Using this database, seven machine learning algorithms are trained to predict the amplification factor from ROVs and bridge features. Results show that tree-based models, especially XGBoost, achieve high prediction accuracy with R2 > 0.98 for most load and response types. SHAP analysis reveals that while axle load has a limited effect under current load limits, the number of trailer axles is critical across all response types, with axle spacing and flexural rigidity governing positive moment and shear amplification, whereas span length and total bridge length predominantly control negative moment amplification. The proposed method allows for rapid estimation of mixed traffic effects by amplifying the single-vehicle response from a simplified model, offering a practical and efficient tool to support intelligent and real-time permit decision-making in bridge safety management.