The bearing is an important part of mechanical equipment. Its condition directly influences the operation of the entire mechanical equipment. Faults in bearings may induce fatal disasters and heavy economic losses, in worst-case scenarios. In fault diagnosis, many studies have only proposed the characteristics of faults; however, without standards for quantifying the faults, automated diagnosis could not be realized. Based on the generalized fractal dimensions (GFDs) and the receiver operating characteristic (ROC) curve, this study proposed a method to characterize initial failure trends and quantize the bearing failure standard. The size of GFDs was calculated using the vibration signal measured during the operation of a bearing. The optimal classification model was determined based on the ROC curve as the criterion of damage. The model trained by the signals of the training group was used in the check analysis of the signals of the validation group. The accuracy of this quantitative analysis was validated by experimental results. Finally, three bearings in different positions were diagnosed by this model under the same test conditions, and the effectiveness of the quantitative diagnosis of damage proposed in this study was validated.
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.
Fault diagnosis is an important method for maintaining the stable and safe running state of mechanical equipment. As most mechanical equipment faults are induced by the bearing assembly, bearing fault diagnosis is of considerable importance. At present, the mainstream intelligent diagnostic techniques include supervised learning and unsupervised learning. Supervised learning requires manual labeling and data classification, which is unfavorable for massive data amounts. Therefore, how to effectively use labeled data to increase the accuracy of diagnosis is critical, especially when the bearing failure cannot be labeled at the very beginning. This paper proposes a time–frequency analysis of the short-time Fourier transform and wavelet transform methods based on unsupervised learning. The time axis was integrated to obtain the marginal frequency of two frequency domains as a diagnostic feature, and then two clustering centroids were established automatically by the K-means of unsupervised learning. The signals were divided into two classes based on the nearest clustering centroid as the criteria for diagnosis. Finally, other bearings in different positions were classified and diagnosed using the nearest clustering centroid in the same experiment to verify the effectiveness of the method proposed in this study.
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