## 1 Introduction  
With the construction and development of railways, it is inevitable that railway lines will pass through areas prone to frequent wind disasters, such as coastal areas and mountainous canyons. At the same time, new high-speed trains (HST) are becoming faster and lighter, which increases the operational risks of trains under strong crosswinds. Train accidents such as overturning and derailments occur frequently. Therefore, ensuring the operational safety of HST under strong wind conditions has become an important concern for high-speed railway operating departments. Compared with establishing a wind monitoring and early warning system and optimizing the aerodynamic shape of HST, setting up wind barriers is considered to be a more economical and applicable method to ensure the safe operation of HST. Therefore, research on the windproof performance of wind barriers is increasingly valued. The shielding effect of wind barriers creates a relatively safe local wind environment for HST [1]. Researchers believe that the reduction of mean wind velocity and the variation of turbulence are two important factors that affect windproof performance [2; 3; 4]. [PERSON] et al. [5] used a visualization method to study the effect of wind barrier height and porosity on the flow field structure around bridges. [PERSON] et al. [6] tested the wind velocity behind the wind barrier through wind tunnel experiments and found that low porosity can reduce wind velocity and lead to high turbulence. [PERSON] et al. [7] observed the distribution of mean wind velocity and vorticity behind the wind barrier using the particle image velocimetry (PIV) method; high turbulence and low wind velocity were observed near the bridge deck, with the wind velocity recovering at a height of 1 m. Similarly, by observing the wake structure after installing four types of wind barriers using the PIV method,Coskun et al. [8] believed that jet-wake-wall interaction had a significant influence on the mean wind characteristics and fluctuating wind characteristics. [PERSON] et al. [9] proposed a corrugated wind barrier and believed that the regular bending of the guide plate could reduce the intensity and kinetic energy of turbulence. Based on this research, [PERSON] et al. [10] conducted wind tunnel experiments considering wind barriers of different lengths and evaluated the influence of wind barrier length on the aerodynamic performance of trains, pointing out that at wind angles of \(20^{\circ}\) and \(30^{\circ}\), the train would obtain relatively unfavorable aerodynamics. [PERSON] et al. [11] evaluated the windproof performance of wind barriers using the data envelopment analysis (DEA) method, indicating that reasonable wind barrier height and porosity would enable HST to have better aerodynamic performance, and other studies have reached similar conclusions [12; 13]. Bridges account for over 50% of newly built railway lines in China, as bridges are better adapted to complex geological structures and provide significantly improved ride comfort. However, the widespread use of bridges also brings new issues. Research by [PERSON] et al. [14] showed that wind barriers transmitted wind loads to bridges, which significantly increased the bridge's lateral force coefficient, as well as the train's lateral force and lift coefficients on the bridge. [PERSON] et al. [15] also pointed out that installing wind barriers will reduce the flutter stability of bridges with typical cross-sections, but the galloping stability remains essentially unchanged. [PERSON] et al. [16] found that the porosity of wind barriers significantly affects the vertical displacement of bridges and the derailment coefficient of trains. [PERSON] et al. [17] found that wind barriers with straight or curved pipes do not significantly change the aerodynamic performance of trains. Additionally, [PERSON] et al. [18] noted that the relative position of trains on bridges has a significant impact on the aerodynamic characteristics of the train-bridge system. [PERSON] et al.