# Dynamic Interaction Analysis of Long-Span Bridges Under Stochastic Traffic and Wind Loads
## 1 Introduction  
With the rapid expansion of global transportation networks, large-span bridges have emerged as a critical infrastructure for connecting key regions [1, 2, 3]. However, the structural response of these bridges in complex geographic environments has become increasingly intricate [4, 5, 6]. This complexity is primarily due to the combined effects of multiple dynamic factors, including wind and vehicular loads, including wind and vehicular loads, which interact with the bridge to induce complex coupled vibration behaviors [7, 8, 9, 10]. These interactions amplify the nonlinearity and uncertainty of the bridge's dynamic response, posing substantial risks to its safety and stability [11, 12, 13, 14, 15]. Therefore, a comprehensive analysis of the dynamic response of large-span bridges under the combined action of wind and stochastic traffic is essential for ensuring the safety of both the bridge structure and the vehicles operating on it. The effects of wind loads or vehicle loads have been widely explored in existing bridge vibration studies. [PERSON] et al. [16] developed an analytical framework for ice-wind-vehicle-bridge interaction, focusing primarily on the effects of ice loading with less emphasis on the coupling effects of wind loading. [PERSON] et al. [17] investigated the dynamic response of bridges under varying wind velocities but did not consider the stochastic nature of traffic flow and its impact on bridge vibrations. [PERSON] et al. [18] developed a coupled wind-vehicle-bridge interaction analysis method incorporating triangular wind barrier shielding effects, demonstrating that optimized barrier geometry significantly mitigates train accelerations with minimal impact on bridge dynamics and vehicle safety indices. This research is crucial for advancing bridge design and safety assessment under challenging conditions. Meanwhile, the impact of stochastic traffic flow on bridges has increasingly attracted attention. Traditional vehicle-bridge coupling models typically assume that traffic flow is a constant load, thereby neglecting its randomness and dynamic nature [19; 20; 21; 22; 23]. In reality, the speed, flow, and distribution of traffic are highly randomized, which can significantly influence the dynamic response of bridges [24; 25; 26]. In practice, the combined effects of variations in traffic flow and wind loads may lead to significant nonlinear vibrations in bridges [27; 28; 29]. Therefore, analyzing the dynamic response of large-span bridges by integrating the randomness of traffic flow with the combined effects of wind loads is crucial for enhancing bridge safety. Recent studies have highlighted the importance of considering the stochastic nature of traffic loads, as well as the directional and nonlinear characteristics of wind forces. For example, a directional wind-vehicle-bridge model has been developed to provide a comprehensive framework for evaluating the dynamic responses of bridges and vehicles under multi-directional and nonlinear wind loads. [PERSON] et al. [30] provided an overview of the role of AI in data-driven structural health monitoring (SHM) systems for bridges, examining recent advancements, conceptual frameworks, advantages, challenges, and potential future research directions. [PERSON] et al. [31] used a U-Net neural network to identify acoustic emission signal onset times as a 1D segmentation task, validated on PLB data for potential real-time monitoring. [PERSON] et al. [32] developed an integrated simulation platform for analyzing bridge-traffic system dynamics under multi-hazard conditions (wind, seismic, road roughness), enabling a concurrent evaluation of structural integrity and vehicle safety. [PERSON] et al. [33] investigated the effects of stochastic traffic flow on long-span suspension bridges but did not consider the coupling effects of the wind loads. [PERSON] et al. [34] analyzed the dynamic response of floating bridges under stochastic traffic flow but did not delve into the combined influence of wind and traffic loads.