Track irregularities are perhaps the main excitations of vehicle–track systems and cause dynamic wheel–rail responses, but track irregularities and vehicle responses do not always correspond to each other. In this study, the interrelations between track irregularities and vehicle responses in a multi-scale framework were investigated using measured data. Firstly, the track irregularity and vehicle response data were separated into modes on different time scales using multivariate empirical mode decomposition, and the energy distribution of each wavelength component was determined. Then, the local correlations between irregularity–response mode pairs were examined via time-dependent intrinsic correlation (TDIC) analysis. The irregularity–response interrelation was not always unique, but rather varied in both time scale and time domain, and positive–negative correlation reversals frequently occurred, causing a low overall correlation and coherence. TDIC analysis can elucidate the wavelengths and positions of track irregularities that affect vehicle responses.

轨道不平顺可能是车辆-轨道系统的主要激励因素，并导致动态轮轨响应，但轨道不平顺和车辆响应并不总是相互对应。在这项研究中，使用测量数据研究了多尺度框架中轨道不规则和车辆响应之间的相互关系。首先，利用多元经验模态分解将轨道不平顺和车辆响应数据分成不同时间尺度的模态，并确定每个波长分量的能量分布。然后，通过时间相关内在相关性 (TDIC) 分析检查不规则-响应模式对之间的局部相关性。不规则性 - 响应相互关系并不总是唯一的，而是在时间尺度和时域上变化，正负相关反转频繁发生，导致整体相关性和连贯性较低。TDIC 分析可以阐明影响车辆响应的轨道不规则的波长和位置。