Singularity localization and characterization based on continuous wavelet transform for vibration signals with impacts

Vibration signals tested from mechanical components usually contain a great deal of information about the properties and status of the mechanical parts or even the whole mechanical system, which is worthy of further analysis. A method based on continuous wavelet transform to localize and characterize the singularities of vibration signals with impacts is introduced in this paper. Continuous wavelet transform was first performed to the signal, and then the ridges and ridge functions of the absolute value of the wavelet coefficients were extracted. By tracking the ridge lines from large-scale to small-scale, the singular points of the signal can be localized quite precisely, which is corresponding to the times when mechanical impacts occur. By performing a double logarithmic linear regression of the ridge functions, we got use the slopes and the intercepts of the regressed lines, which can be used as features to characterize the singularity of the impacts. This work provides a reliable and effective method for signal truncation and singular feature extraction, which will benefit the subsequent signal analysis works.