Multi-scale fractal dimension based on morphological covering for gear fault diagnosis

Fractal dimension (FD) is one of the most utilized parameters for characterizing and discriminating vibration signals in gear fault detection. However, most of the natural signals are not critical self-similar fractals; the assumption of a constant FD at all scales may not be appropriate. Motivated by this fact, this article explores the capacity of the multi-scale fractal dimension (MFD) to represent the complexity of vibration signals for gear fault diagnosis. We select the morphological covering method to calculate the MFD. Vibration signals measured from a gear test rig with five states are employed to evaluate the effectiveness of the presented method. Experimental results reveal that the vibration signals acquired from gear with five states demonstrate different fractal structures when the visualization scales are changed. The MFD can provide more information about the signals and yield a higher classification rate than the FD and traditional statistical parameters. It is very reasonable to apply the MFD to vibration signal analysis for improving the performance of the gear fault diagnosis.