## 1 Introduction
[10] studied the contact pressure distribution of the brake friction pair based on a multi-body dynamics approach and proposed that fluctuations in braking pressure can lead to the occurrence of vibration. [PERSON] et al. [11] explored the cause of brake vibration from the perspective of vibration energy and found that the brake disc is the main component that vibrates during the braking process. [PERSON] et al. [12] studied the mechanism of friction vibration by combining complex eigenvalue analysis and transient dynamic analysis methods and proposed that the repeated separation-reattachment process of friction pairs is an important mechanism leading to vibration. To study the mechanism  
Figure 1: High-speed train disc brake: (**a**) disc brakes installed on high-speed trains, (**b**) non-uniform temperature distribution on the friction surface during braking. of disc brake vibration, [PERSON] et al. [13] conducted finite element analysis under different braking conditions and proposed that there is a coherent relationship between braking pressure and initial braking speed. The friction pair's relative velocity and the contact pressure of the contact interface are not linear during the braking operation. The disc brake will vibrate while working because of the friction force and the thermal-mechanical coupling effect during the braking operation. High-speed train disc brake braking efficiency might decline due to brake vibration that causes relative displacement between the brake disc and brake pad. In some cases, the brake disc may even be unable to complete the braking process. Scholars have carried out many studies on the vibration characteristics of disc brakes to reveal the influence of braking vibration on the braking performance of disc brakes. [PERSON] et al. [14] proposed a two-degree-of-freedom disc brake model and obtained the influence of brake pressure and speed on vibration stability. [PERSON] et al. [15] used a two-degree-of-freedom dynamic model to explore the influence of braking parameters on the vibration characteristics of the brake disc and pads and found that the vibration amplitude of the brake increased with the increase of the braking load. [PERSON] et al. [16] applied the complex eigenvalue analysis to the finite element model of the disc brake and found that the braking parameters and the contact stiffness of the friction pair have a significant impact on the vibration of the disc brake. [PERSON] et al. [17] studied the relationship between the vibration response of the brake and the interface contact behavior and proposed that the friction coefficient and contact angle of the brake pair are important factors affecting its vibration characteristics. [PERSON] et al. [18] investigated the effect of braking parameters on the vibration characteristics and stability of the brake based on the finite element numerical simulation method. The results showed that the brake vibration was aggravated by the increase in the braking load and speed. [PERSON] et al. [19] studied the effect of radial stiffness on the vibration stability of a disc brake system under different friction conditions. [PERSON] et al. [20] established a rigid-flexible vehicle dynamics model and a finite element model of the braking system. The results showed that the wheel flat directly induced the elastic vibration of the brake disc and further affected the disc contact, resulting in a significant increase in the contact force, contact stress, friction force, and vibration acceleration between the braking interfaces. [PERSON] et al. [21] established a six-degree-of-freedom nonlinear dynamics model of the disc brake system to reduce the generation of vibration and analyzed its vibration characteristics under different braking pressures and braking speeds. In summary, it can be seen that factors such as braking pressure and braking speed have a great impact on the vibration of the brake. Excessive speed and pressure will easily cause the brake to vibrate violently and reduce its braking efficiency.