Adaptive decomposition and energy-frequency characteristics of high-speed railway train vibration signals on the surface of shallow-buried tunnels - Zhou, Linli; Zheng, Kenan; Jia, Baoxin; Zhou, Zhiyang; Ding, Sihao (Sound & Vibration, 2026)
Vibration signals induced by high-speed railway trains on the surface above shallow-buried tunnels exhibit strong non-stationarity and high background noise due to the coupling of tunnel dynamic response and environmental noise. Traditional signal processing methods struggle to extract key wheel-rail vibration components accurately. To solve this issue, this study proposes an adaptive parameter optimization method for variational mode decomposition (VMD), termed SE-SSA-VMD, based on sample entropy (SE) and the sparrow search algorithm (SSA). By intelligently optimizing the mode number K and penalty factor α, the method improves decomposition objectivity and anti-noise robustness. Simulation results confirm that the method achieves accurate effective mode separation with an average center frequency error below 0.2 Hz at a signal-to-noise ratio of 5 dB. Measured data indicate that vibration energy is mainly concentrated in 35–60 Hz with a Gaussian unimodal distribution, and the adjusted R² of over 95% measuring points exceeds 0.8. Higher train speed significantly increases vertical vibration energy, while longer marshalling mainly strengthens lateral vibration energy; both cause a downward shift of the dominant frequency. Far-field vibration energy does not decay monotonically and shows slight local fluctuations, but remains at a low level owing to strong energy dissipation of overlying artificial fill, regardless of initial speed and near-field energy. This work provides an effective approach and theoretical support for vibration assessment and mitigation design in shallow-buried high-speed railway tunnel sections.