Continuous wavelet transform for modal identification using free decay response

This paper deals with the use of the continuous wavelet transform for system identification purposes. The wavelet analysis of the free responses of a linear mechanical system allows the estimation of its natural frequencies, viscous damping ratios and mode shapes, using either the modulus or the phase of the wavelet transform. A complete procedure for modal identification from free responses based on the continuous wavelet transform is presented. Two difficulties during the implementation of this technique are highlighted: the edge effect and the choice of the time–frequency localization of the wavelet transform. Some upper and lower bounds for the mother wavelet's parameters are given in order to improve the numerical computation. Three complex-valued mother wavelets are studied and the full procedure is applied to a damped discrete system. The correct choice of the mother wavelet's parameters leads to an accurate identification of the modal parameters.