Analysis and control method for track irregularity on kilometer-level span high-speed railway bridges based on multivariate empirical wavelet transform

Abstract To address the challenge that track irregularity on kilometer-level span high-speed railway bridges exhibits significant temperature-dependent time-varying characteristics, while traditional methods are insufficient to achieve modal consistency in decomposition and long-term effective regulation, this paper proposes a multi-dimensional analysis and differential regulation method based on the multivariate empirical wavelet transform (MEWT). An averaged normalized spectrum is constructed from multi-period track vertical deviation data to enable simultaneous decomposition and wavelength alignment of irregularity modes under different temperatures. The optimal unit length of 84 m is determined using weighted joint Shannon entropy, and a feature matrix is established from three dimensions: temperature correlation, historical chord measurement extreme value, and relative energy fluctuation intensity. The HDBSCAN (hierarchical density-based spatial clustering of applications with noise) method classifies bridge units into four categories. Then, a differential regulation strategy and adjustment optimization algorithm is developed for temperature-sensitive modes. Validation using 26 periods of measured data from the Wufengshan Yangtze River Bridge demonstrates that MEWT achieves a coefficient of variation for modal wavelengths below 0.09. Under the reference temperature of 17 °C, the maximum 60-m mid-chord offset is reduced from 10.93 to 1.73 mm, a reduction of 84.17%. Within the extreme temperature range of 0.2–31.5 °C, all regulated chord values are maintained within 2 mm, demonstrating enhanced regularity retention capability. By reasonably retaining long-wave thermal deformation components, invalid adjustments are effectively avoided, reducing engineering complexity and maintenance costs.