Analysis of Track Irregularity Time-Frequency Characteristics Based on Empirical Mode Decomposition

The measurement of high-speed railway track irregularities is a complex stochastic process, in which many single-component signals of different frequencies and amplitudes are present. In order to analyse the distribution characteristics of track irregularities in the spatial and frequency domains, the Hilbert-Huang transform was used to extract the energy distribution of track irregularity in the time-frequency domain. Track irregularity data was first decomposed into amplitude-frequency modulated multivariate intrinsic mode functions (IMF) at different scales, based on the data-driven filtering characteristics of multivariate empirical mode decomposition (MEMD). The instantaneous frequency of multivariate IMFs at each scale was then calculated by means of a Hilbert transform, from which the frequency and energy distribution characteristics were analysed. The analysis of the track inspection car indicates that the frequency distribution of track irregularities exhibits a characteristic of quasi-dyadic filter banks and that the frequency bandwidth is narrow at each scale. The energy distribution of the track irregularity and corresponding wavelengths can be determined from MEMD-based scalograms at different scales. In the sample track irregularity data, the energy of the gauge and cross level is mainly distributed in the medium and long wavelength frequencies. The energy of the alignment and profile is concentrated in the wavelengths between 4 and 36 m, and the energy of the twist is distributed in two wavelengths of 4.9 m and 7.6 m.