Estimation of time-varying vibration parameters by the segmental use of the harmonic wavelet

Estimation of time-varying vibration parameters, that is, instantaneous damping and frequencies by the wavelet transform is based on the ridge identification and the phase extraction in the time-frequency map. However, there are some problems in easiness to operate the technique. The process of the ridge identification is rather complicated, and the most suitable mother wavelet to yield a time-frequency map for the efficient identification is not determinately chosen. In this paper, we propose a segmental use of the harmonic wavelet in order to estimate the time-varying vibration parameters. The segmental harmonic wavelet is implemented in combination with the Fourier transform, which is utilized to set bounds to frequency range. It shows significantly good results compared with the simple application of the Hubert transform. The time-varying parameters pertaining to nonlinearities are successfully estimated by the proposed method. A possibility of the proposed method to a diagnosis of a mechanical element is also demonstrated.