I recently rode in the above French TER, Electric Train, Model Z 24500, Lyon to Annecy.
A sample accelerometer time history is shown above. The sensor was mounted on a passenger car floor, a Slam Stick X, sampled at 400 samples/sec.
The spectrogram of the accelerometer data shows a cluster of peaks from 1 to 2 Hz. These are mostly likely due to the interaction between the wheels and the track joint gaps. The track length and the train speed would need to be identified in order to resolve this. But here is a rough estimate using assumed values for speed and length:
speed/length = (25 m/sec) / 20 m = 1.25 Hz
Minor speed variations would cause the peaks to have some drift.
Some intermittent peaks also occur near 8 Hz. Here is another rough calculation. Assume that the wheels have a 1-meter diameter, with a circumference of pi meters.
speed/circumference = (25 m/sec) / (pi meters) = 8 Hz.
So the peaks near 8 Hz appear to be due to wheel static imbalance.
Also note that the electrical power frequency is 50 Hz, so the engine may have a component at this frequency.
Matlab Data: French_train.mat
– Tom Irvine