The estimation of nonlinear vibration parameters through the segmental use of the harmonic wavelet

In order to perform an accurate evaluation of the dynamic response of a vibration system, it is important to estimate not only the linear vibration parameters but also the nonlinear parameters. Nonlinearities are estimated through time-varying vibration parameters, such as instantaneous damping ratio and instantaneous frequency. In the case of a relatively small nonlinearity, this technique is effective. In this paper, a segmental use of the harmonic wavelet is proposed in order to estimate time-varying parameters. The Hilbert transform is usually employed for the purpose of such estimations. However, it has been pointed out that the Hilbert transform yields unacceptable results with numerical instability under certain conditions. The proposed method shows significantly good results with respect to numerical stability as compared with the simple application of the Hilbert transform and a similar use of another wavelet.