Compressed Sensing of Vibration Signal for Fault Diagnosis of Bearings, Gears, and Propellers Under Speed Variation Conditions

In the fields of fault diagnosis and structural health monitoring using sound and vibration, there is increasing interest in data compression techniques based on Compressed Sensing (CS). However, conventional CS approaches that use standard bases such as Fourier or wavelets are unable to achieve sparse representations of operational vibrations in rotating machinery with speed variations, leading to significantly reduced compression performance. To overcome this limitation, this study introduces a CS approach that incorporates order analysis, a technique commonly used in the analysis of rotating machinery. The method constructs an order basis using randomly sampled rotational speed data, enabling sparse observation of operational vibrations through CS. This represents a novel approach for efficiently capturing the essential features of vibration signals under rotational speed variations. The proposed method was validated through numerical experiments. The results showed that for rotational vibrations with speed variations of approximately 10% of the average speed, the compression performance was 20 times higher than that of conventional methods using the Fourier basis. Furthermore, evaluations using simulated vibration signals from eccentric faulty gears, as well as experimental data from defective propellers and bearings with outer ring defects, demonstrated that the proposed method could successfully reconstruct signals even under conditions with substantial speed variation—conditions under which conventional Fourier-based methods fail. Due to its superior compression performance and its ability to handle unknown operational vibrations, the proposed method is highly suitable for applications in fault diagnosis, structural health monitoring, and vibration measurement.