Objectives  Nowadays, most 3D laser scanning in subway tracks is used to survey the tracks' diameter convergence so as to determine whether section deformation takes place between different periods. However, no measurement has been conducted on the subway track deformation with this method.

  Methods  Therefore, using wavelet analysis and Wigner-Ville distribution, this paper carries out the locating research on subway track relative deformation based on point cloud data. The first step is data preprocessing. On the basis of the subway point cloud data acquired by 3D laser scanners, sections are intercepted continuously in equal intervals, and track traits are recognized in section point cloud for track elevation extraction. Then, we define the partial relative deformation fluctuation indexes of the linear structure to describe the relative spatial relationships of partial tracks between different stages. Last but not least, this paper presents an extraction method for abnormal partial relative deformation based on wavelet analysis and smoothed pseudo Wigner-Ville distribution (SPWVD). First, we need to choose a suitable basic function and decomposition level, decompose relative deformation fluctuation by the wavelet method, and calculate the characteristic wavelength based on the fast Fourier transform of signals in different levels. Second, the SPWVD value of decomposed-then-reconstructed signals and the energy corresponding to different mileages in the characteristic wavelength should be determined, and the energy threshold should be set based on the 3σ criterion to locate the relative deformation wave. Third, the range of relative deformations should be settled in relative deformation fluctuations.

  Results  This paper verifies the feasibility of this algorithm using simulated data and concrete example analysis. Through the calculation of simulated data, the waveform detected by this method has an approximate location and range with the preset value. By the concrete example analysis, two results are obtained. After the comparison of the design value with the concrete scanning value of the same track, relevant information of relative deformation in characteristic wavelengths is successfully detected. With the scanning point cloud data in two periods that have short time intervals, relative deformation in any characteristic wavelength can hardly be detected.

  Conclusions  The calculation results prove the feasibility of this algorithm, show the energy distribution of track relative deformation in both time and frequency domains, and effectively extract the relevant information of track relative deformations, providing a new method to monitor the track relative deformation.