A Graphical Analysis Method of Guided Wave Modes in Rails

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.