# An Ultrasonic Guided Wave Mode Selection and Excitation Method in Rail Defect Detection
## 1 Introduction  
It is of great significance to discover the internal defects of rails in time for maintaining and ensuring the safety of trains. At present, the hand-push detection vehicle and large-scale detection vehicle are the main tools to detect the defect detection of Continuous Welded Rails [1; 2; 3]. These two kinds of detection vehicles are running in the maintenance time, generally from 12 a.m. to 4 a.m., and cannot be used for real-time monitoring of rail internal defects. Guided waves can propagate a long distance in the rail [4; 5; 6]. Based on the pulse-echo method [7; 8; 9], the on-line monitoring of rail internal defects can be implemented by detecting the echo signals generated at the rail defects during the propagation of the guided waves. In the research of rail defect detection based on guided waves, some scholars selected the suitable modes for rail defect detection by a mode classification method. [PERSON] [10] divided the modes of the rail base into three categories. By analyzing the dispersion characteristics of guided waves, the concept of dominant modes is proposed. In the frequency range of 60-200 kHz, the transverse and vertical vibration modes with smooth dispersion curves of rail base are more suitable for defect detection than the longitudinal vibration modes [11]. A rail base defect of 20 mm in length was successfully detected by exciting the vertical modes. Subsequently, [PERSON] [12] obtained the optimal excitation frequency and pulse period of the propagating modes at the rail base through simulation, and tested oblique cracks at different angles by numerical simulation. The results showthat the detection effect of the vertical vibration modes is better than the transverse vibration modes. [PERSON] et al. [13] excited the vertical vibration modes on the rail head with a kind of mode force hammer. The experimental results show that the vertical vibration modes can effectively detect the transverse crack of the rail head. In addition, some scholars chose the modes to detect the damage of different parts of the rail based on the mode energy distribution. [PERSON] et al. [14] selected the mode with energy concentrated on the rail head to detect the rail head defect. And the signal was excited according to the experimental method. The transverse defect of rail head at a distance of 9 m from the excitation location was successfully identified. In order to distinguish large transverse cracks with a diameter of 30 mm from 6 mm welded seam, [PERSON] and [PERSON] [15] compared the symmetric mode 1 and the antisymmetric mode 2 focusing energy at the rail head, and the symmetric mode 1 successfully distinguished the crack and welded seam at the rail head. Mode 3 and mode 4 focused with energy at the rail web, mode 4 was suitable for detecting the welded seam as well as damage in the rail web. It can be seen that in the research of the excitation mode applied to the detection of rail defects, most of the scholars use the experimental methods to excite the expected modes without specific theoretical guidance and mathematical model. The excitation signal usually contains multiple modes, which also makes it difficult for echo signal analysis and defect location. In view of the above problems, this paper will focus on the guided wave mode selection and excitation methods based on a mathematical model in rail defect detection, by which the modes can be selected and excited with different sensitivities to the defects of the rail head, rail web and rail base, and accordingly the defect position can be rapidly found in different parts of the rail. The paper is organized as follows: A mode selection method is described in Section 1, which is used to select the modes having the concentrated strain energy and small attenuation corresponded to the rail head, rail web and rail base. The mode excitation method is presented in Section 2, to acquire the optimum excitation direction and excitation node of guided wave modes.