This paper proposes a rail defect location method based on a single mode extraction algorithm (SMEA) of ultrasonic guided waves. Simulation analysis and verification were conducted. The dispersion curves of a CHN60 rail were obtained using the semi-analytical finite element method, and the modal data of the guided waves were determined. According to the inverse transformation of the excitation response algorithm, modal identification under low-frequency and high-frequency excitation was realized, and the vibration displacements at other positions of a rail were successfully predicted. Furthermore, an SMEA for guided waves is proposed, through which the single extraction results of four modes were successfully obtained when the rail was excited along different excitation directions at a frequency of 200 Hz. In addition, the SMEA was applied to defect location detection, and the single reflection mode waveform of the defect was extracted. Based on the group velocity of the mode and its propagation time, the distance between the defect and the excitation point was measured, and the defect location was predicted as a result. Moreover, the SMEA was applied to locate the railhead defect. The detection mode, the frequency, and the excitation method Were selected through the dispersion curves and modal identification results, and a series of signals of the sampling nodes were obtained using the three-dimensional finite element software ANSYS. The distance between the defect and the excitation point was calculated using the SMEA result. When compared with the structure of the simulated model, the errors obtained were all less than 0.5 m, proving the efficacy of this method in precisely locating rail defects, thus providing an innovated solution for rail defect location.
The cross-section of a rail has a complex geometry, and there are many propagating modes of ultrasonic guided waves in a rail. The analysis of mode shapes or the cross-sectional wave structure is of high significance to the design of an appropriate wave excitation approach for long-range defect detection of a rail. Traditionally, the semi-analytical finite elements (SAFE) method is used to obtain ultrasonic guided waves’ dispersion curves of a rail. Then, through solving the eigenvectors, it is able to calculate the displacement values of discrete nodes in three degrees of freedom (DOFs) and further obtain the wave structures. In this paper, a graphical analysis method of guided wave mode shapes is proposed. The displacements of each node in three DOFs are converted into Red Green Blue (RGB) image pixels, and the complex vibration vector data is expressed by an image. Therefore, the graphical analysis of mode shapes can be realized by using conventional image processing methods without the design of special data processing algorithms. This will improve the processing efficiency, and it is more intuitive and easier to analyze the vibration displacements represented by the image. The simulation results show that the proposed graphical analysis method can quickly and precisely locate the excitation position of the guided wave mode in the rail. By adopting image processing methods, such as the K-means clustering algorithm, the guided wave modes at a 35 kHz frequency in a rail are classified according to their mode shapes. Classification is essential for exploring the relations and fundamentals of vibrations in modes. The graphical analysis method proposed in this paper provides a novel method for the mode analysis of guided waves in rails.
The cross-sectional geometry of a rail is complex, and numerous guided wave modes can be propagated in rails. In order to select a mode which is the most suitable for detecting a specific crack on a rail, a mathematical model of guided wave mode selection is constructed. The model is composed of a modal vibration factor and a modal orthogonal factor. By setting a reasonable vibration coefficient and orthogonal coefficient, the mode with the highest sensitivity to cracks is selected for crack detection. Taking a vertical crack on the rail bottom as an example, mode 1 at a frequency of 60 kHz is selected as the most suitable detection mode. At the same time, mode 7 and mode 11 are selected as comparative modes, and these three modes are simulated to detect rail cracks. Among them, mode 1 is the best, which verifies the correctness of the mode selection model. In addition, vertical cracks are manufactured artificially on the side of the rail bottom. The cracks are successfully detected by mode 1, and the positioning error is 0.07 m. After correction, the error is reduced to 0.02 m. The model can effectively select guided wave modes suitable for detecting arbitrary cracks on rails, which provides a theoretical solution for rail crack detection.
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