Compressive sensing for vibration signals in high-speed rail monitoring

The safety and reliability are critical for the high-speed rail system, and axle box accelerations are often utilised for inspections of railways. Due to the Nyquist theorem, there is a compromise between the resolution of defect detection and the amount of recorded data. As an emerging technique, compressive sensing creates the opportunity for sub-Nyquist sampling as long as the target signal has a sparse representation in a known domain. To make use of this advantage, this study proposes a compressive sensing framework for high-speed rail monitoring. In particular, the process of compressive sensing is simulated using the axle box acceleration data acquired from a high-speed train ran on one section of railway in China. The compressed measurements are received by random projection, and the original signals are reconstructed using convex optimisation algorithm. Based on the reconstruction results, the influence of different measuring methods as well as orthogonal bases is evaluated. In addition, a regression model is formulated to give a recommend equivalent sampling rate according to the sparsity and the desired accuracy requirement of the target signal. It is found that the vibration signals are sparser in the discrete cosine transform matrix, leading to better reconstruction, and the performance of different measuring methods is almost identical. More importantly, this study proves that the high-speed rail monitoring data can be satisfactorily obtained through proper sampling rates lower than the Nyquist theorem requires.