## 1 Introduction  
In recent years, high-speed rail has developed rapidly around the world. The development of high-speed rail in northwest China is also underway, and the operation of high-speed rail is bound to bring great convenience to cities along the route. However, the operating environment of high-speed trains in northwest China is not optimistic. [PERSON] et al. [1] found that the environment in northwest China is harsh, mostly desert and strong winds. Particularly, [PERSON] et al. [2] found that the Baili wind area, one of the five windy areas through which the Lanzhou-Xinjiang high-speed railway (maximum operating speed of 250 km/h) passes, has large wind speed changes, which brings great challenges to the safe operation of high-speed trains. [PERSON] et al. [3] found that the change in wind speed along the railway line is particularly serious in windy areas, and according to incomplete statistics, more than 170 sections of the Lanzhou-Xinjiang high-speed railway line exhibit the phenomenon of \"car swaying\". According to [PERSON] et al. [4], strong crosswinds caused at least 26 serious train safety accidents from 1956 to 2000 on the Lanzhou-Xinjiang railway. [PERSON] et al. [5] found that to maintain safety under crosswinds, trains need to slow down to pass safely and then accelerate to the normal speed, which may result in frequent acceleration and deceleration processes. As shown in Figure 1, when the train passes through curved tracks under crosswinds, the possibility of derailment and overturning is greatly increased, and the safety risk is greatly increased. A large number of scholars have performed studies on the safety of trains under crosswinds. [PERSON] et al. [6] focused on the effect of changing wind speeds on a train's operational safety and obtained many important research results. [PERSON] et al. [3] analyzed the roll angle and lateral displacement of car-body gravity by performing a field measurement along the Lanzhou-Xinjiang high-speed railway in China. [PERSON] et al. [7] evaluated the derailment risk of an HS train crossing the future Volga River railway bridge by using a stochastic wind model and found that the unloading ratio was most critical for train speeds below 300 km/h. [PERSON] et al. [8] analyzed the dynamic of metro vehicles traveling on a high-pier viaduct under cross-wind in Chongqing. [PERSON] et al. [9] verified the accuracy of the train dynamic model by a real vehicle test. They studied the dynamic response of the train passing through the curve track under changing wind speed cases by combining it with the gust model. [PERSON] et al. [10] studied the influence of Chinese hat gust wind on the passing dynamics of train curves through wind tunnel tests and dynamic simulations. And they found that the wind direction reversal had a great impact on the safety of train overturning. Vehicle system dynamics has developed rapidly in recent decades, and many scholars have published a large number of related research papers and established mature vehicle-dynamics models, including single-vehicle models and multi-vehicle models [11; 12; 13; 14]. A multi-section vehicle-dynamics model is used in this article. Most of the world's high-speed trains are designed with inter-vehicle shock absorbers, tight-lock devices, and inter-vehicle windshields, such as Japan's Shinkansen, Germany's Inter City Express 3, and China's CRH2. The purpose of these devices is to absorb vibrations between vehicles and improve the overall dynamics of the vehicle. Therefore, when the train is running in a complex environment, such as a crosswind area, the role of the IVS device cannot be ignored when studying the vehicle-dynamics problems of multi-car trains. The train must slow down to reach safe travel criteria when passing through a drastically changing wind zone and then accelerate back to normal travel speed when the wind speed decreases.