A Simulation Study on Characterizing Transfer Functions of Railway Tracks Using Train-Borne Laser Doppler Vibrometer

Abstract

Due to train load and aging, the dynamic properties of railway tracks degrade over time and deviate over space, which should be monitored to facilitate track maintenance decisions. A train-borne laser Doppler vibrometer (LDV) can directly measure track vibrations in response to the moving train load, which can be potentially applied to large-scale rail infrastructure monitoring. This paper characterizes track structures as a distributed system by estimating transfer functions between the wheel-rail force and the response of each sleeper measured by a train-borne LDV. A challenge with this technique is that a train-borne LDV measures only a fragment of the response for each sleeper while the train load is moving. To investigate the feasibility of this technique and the influence of key factors, we perform numerical simulations using a vehicle-track model and analyze the estimation performance through comparison with simulated impact hammer tests. We find that the transfer function estimated under a moving excitation is close to but noisier than that estimated under an impact load. Partial measurement affects the estimation performance significantly, and a wider sleeper provides a better estimate and a higher frequency resolution. Train speed is a crucial factor for a train-borne LDV system. As the vehicle speed increases, the estimation performance gets better at high frequencies but worse at low frequencies.

Railway sleeper vibration measurement by train‐borne laser Doppler vibrometer and its speed‐dependent characteristics

“…Therefore, the measured sleeper vibrations can be used to monitor the dynamic properties of track structures. To tackle the challenge induced by the amplitude and frequency variation of the excitation from the vehicle to the track, wheel‐rail force or vehicle vibration signals can be incorporated to normalize the train‐borne LDV signals and estimate the transfer functions of track structures (Zeng, Núñez, et al., 2023). The deviation in the estimated transfer functions can reflect the difference in track stiffness and damping, which can be further used for anomaly detection in railway tracks.…”

“…This research first uses modeling and simulation to characterize train‐borne LDV measurement and generate signals of sleeper vibration and speckle noise. A vertical train‐track model is built to simulate sleeper vibration measurement using a train‐borne LDV (Zeng, Núñez, et al., 2023), as shown in Figure 2. The train is modeled as a quarter vehicle as follows, $$$$\begin{equation}{m}_{\mathrm{v}}{\ddot{z}}_{\mathrm{v}}(t) + {k}_{\mathrm{v}}\left[ {{z}_{\mathrm{v}}(t) - {z}_{\mathrm{w}}(t)} \right] + {c}_{\mathrm{v}}\left[ {{{\dot{z}}}_{\mathrm{v}}(t) - {{\dot{z}}}_{\mathrm{w}}(t)} \right] = 0\end{equation}$$$$ $$$$\begin{eqnarray} && {m}_{\mathrm{w}}{\ddot{z}}_{\mathrm{w}} - {k}_{\mathrm{v}}\left[ {{z}_{\mathrm{v}}(t) - {z}_{\mathrm{w}}(t)} \right] - {c}_{\mathrm{v}}\left[ {{{\dot{z}}}_{\mathrm{v}}(t) - {{\dot{z}}}_{\mathrm{w}}(t)} \right]\nonumber\\ &&\quad +\, {F}_{\mathrm{c}}(t) = 0 \end{eqnarray}$$$$where m v and m w are the masses of the vehicle and the wheel, respectively, z v and z w are their vertical displacements, respectively, k v and c v are the stiffness and damping of the suspension, respectively, and F c is the wheel‐r...…”

“…Table A1 lists the parameters for simulating the vehicle‐track dynamics. The vertical irregularity of the rail z e is generated by applying a low‐pass Butterworth infinite impulse response filter to Gaussian white noise (Zeng, Núñez, et al., 2023). Such an artificial spectrum is defined by a passband wavelength λ pass , a stopband wavelength λ stop , and a stopband attenuation h stop , and it is smoothly monotonic and maximally flat in the passband.…”

“…A train‐borne LDV can target its laser spot on tracks and directly measure track vibrations in response to the moving train. In simulation studies, train‐borne LDVs are used to identify bridge mode shapes (OBrien & Malekjafarian, 2016) and estimate transfer functions of track structures (Zeng, Núñez, et al., 2023). In experimental studies, train‐borne LDVs measure rail vibrations to identify rail bending modes (Kaynardag et al., 2021) and detect welds (Kaynardag et al., 2023).…”