Application of Vibration Signals for the Quantitative Analysis of the Optimal Threshold of Bearing Failure

This study established the prognostics and health management system for bearing failure. The vibration signals measured during the bearing operation were used for prognostics. First, the time-domain signal of vibration was calculated through generalized fractal dimensions, and the relationship diagram of generalized fractal dimensions and time was obtained. Then, the trend of bearing failure was compared by the GFDal results. However, the results can only be used for qualitative feature extraction. The bearing failure at the beginning cannot be determined by qualitative methods. Therefore, this study further converted the calculation results of GFDs into a Gauss distribution curve based on the statistical method under normal operation of the bearing. The Gauss distribution curve of the bearing under normal operation and at different time was overlapped. The overlap rate of the bearing area under different times was calculated. The minimum value was taken as the diagnostic standard, which was the optimal threshold of bearing failure defined in this study and was used as the quantitative basis for bearing failure. Therefore, the comparison of the area overlap rate under the Gauss distribution curve between the normal bearing and the bearing under test could provide diagnosis to the bearing failure. Moreover, the time point of the initial failure of the bearing could also be estimated based on the optimal failure threshold.