Identification of structural parameters from free vibration data using Gabor wavelet transform

Abstract

This paper elucidates the roles of signal and wavelet functions in continuous wavelet transform (CWT) for identifying structural parameters from a free vibration signal. Through separation of variables, the CWT of a signal can be expressed as the weighted sum of the analytic components of the signal. Weight functions are related to the scale, frequency, and damping ratio of the signal but not to time. The characteristics of the Gabor wavelet and its weight function are studied in this context. Using the weight function, the resolution capability of the CWT can be evaluated accurately, and its parameters can be selected to balance the time–frequency resolution trade-off appropriately. The drawback of the conventional wavelet ridge-based method is discussed. To address the trade-off problem and the edge effect, four new methods that do not rely on ridge extraction are presented: the differential-scale, differential-variance, differential-frequency, and recursive Gabor-wave methods. The parametric identification capabilities of the proposed methods are verified via numerical and experimental tests. The results indicate that the proposed methods have a wider scope of application than the ridge-based method do. The recursive Gabor-wave method exhibits the best parametric identification capability and is not vulnerable to changes in sample size.