Quantitative diagnosis of mechanical faults based on generalized fractal dimensions

Abstract

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.