Application of regularization dimension to gear damage assessment

Fractal dimension provides a measure of the complexity of a dynamic system, and contains the health information of a machine. The basics of regularization dimension and the effects of Gaussian kernel parameters on the regularization of a signal are introduced. Regularization dimension has advantages over other fractal dimensions because the scale-independent range can be selected according to the signal frequency components of interest. Experimental gearbox vibration signals are analyzed by means of spectral analysis firstly, and then according to the spectral structure, the scale-independent range is selected for computing the regularization dimension, which increases monotonically with increasing gear damage degree. Comparison with correlation dimension and kurtosis shows the advantages of regularization dimension in assessing the localized gear damage.