The investigation of harmonic wavelet analysis revealed good characteristics in vibration signal analysis on partial frequency domain.Harmonic wavelet analysis was applied to the non-linear vibration signal analysis in the low frequency segment of a cracked rotor.The results of theoretical calculation and experiment show that for a cracked rotor,it is possible to obtain the non-linear character spectrum of non-integral multiple period bifurcations with the help of harmonic wavelet analysis on partial frequency domain.Comparison was made between the calculated and experimental results.It was found that the actual vibration signal of a cracked rotor is more complex than that of calculated.The multi-fractal can be used as an index of whether crack exists in a rotor.The singularity spectrum method obtained from Harmonic wavelet transformation can be regarded as a new identification method and it is put forward for non-liner character spectrums of non-integral multiple period bifurcation identification.Using this new method, the vibration signal of an actual cracked rotor was analyzed.The result is satisfactory.