The fault diagnosis of rotating machinery is generally performed using methods that employ vibration and sound. These methods are simple and accurate. However, all of these methods measure vibration data on the basis of the sampling theorem. Thus, they require a high measurement frequency, resulting in a large data volume and expensive measurement equipment. In recent years, a method that uses compressed sensing has been proposed to solve this problem, but it requires dedicated hardware to realize random sampling. To overcome this drawback, we developed a random start uniform sampling method (RSUSM) and combined it with compressed sensing (CS). RSUSM is a method of measuring data at a fixed frequency with a random start time. Numerical experiments demonstrate how the specific constant changes for each RSUSM parameter. This allows us to know the limit of how many measurement points are required for the number of non-zero components. We also applied CS by RSUSM to the sound pressure measurement results of the failed propeller, and found that the signal could be recovered less than 25% error even in a noisy real environment within the aforementioned limit. In this case, we found that the measurement frequency could be compressed to 1/80th of the frequency required by the sampling theorem, and the measurement data size to 1%. This approach is expected to diagnose faults in more rotating machines by significantly reducing the costs associated with data collection and storage.

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