The Application Of Wavelet In Parameter Identification Of Mechanical Systems

Wavelet transformation is a time-frequency signal analysis. It has many desirable properties, and has been widely applied in many fields of engineering. In this thesis, the theory based on wavelet transform is introduced into area of parameter identification. Two wavelet-based procedures are presented for identifying the mechanical parameters of linear and non-linear systems according to the time response respectively. The first part of the thesis is mainly concern with the modal parameter identification of linear systems. In this part the Morlet wavelet is used to decompose the denoised response of the system into the time-scale domain at first, then the so-called wavelet ridge is obtained from the wavelet transform, at last the modal frequency and dumping ratio can be identified by the obtained ridge. Both simulation and experiment results based on cantilever beam show the efficiency of this approach. The technique proposed in the second part consists of projecting the governing differential equation associated with a linear time-varying or a non-linear model on a subspace spanned by a finite number of Daubechies wavelets, the resulting algebraic equations are then rewritten with the parameters of the system as unknowns. The core of the identification algorithm is the estimation of the parameters of the equations from input and output measurements. Fist, the parameters over tiny time intervals are identified, and then the evolution of the parameters over the whole duration can be estimated. Numerical simulations demonstrating the applicability of the method to single and multi-degree-of freedom dynamical systems are presented.