Non-regular Sampling and Compressive Sensing for Gearbox Monitoring

Vibration-based condition monitoring is a powerful field to achieve preventive maintenance and control the efficiency of mechanical systems. The common monitoring scheme consists of capturing vibration signals at a sufficiently high sampling frequency to consider the dynamic and kinematic properties of the machine, and then condition indicators are constructed and saved or sent to a ground-based surveillance station. A major drawback of such an approach is that these indicators may not be sufficient to establish an accurate diagnosis, and the signal itself is needed in various situations. As the frequency rate of vibration signals and, consequently, their size highly depends on the highest frequency to be monitored, it is generally set high in order to respect the Nyquist theorem. As a consequence, sending these data can be compromised because of the limited bandwidth of the transmission channel. This paper proposes a non-regular sampling strategy via compressive sensing to significantly reduce the sampling frequency (below the Nyquist limit) and the data size, while preserving enough information for diagnosis. It is based on the hypothesis that the measured signal consists of a sum of sinusoids corrupted by some random Gaussian noises. The signal recovery problem from random samples is then formulated through an \({{\ell }}_{{{2}}} - {{\ell }}_{{{1}}}\) optimization problem, which is solved via the iterative shrinking-thresholding algorithm. At last, the potentiality of the suggested approach is demonstrated on real vibration signals measured from a spur gearbox with a spalling fault that progresses over 12 days.