Instantaneous frequency identification of time-varying structures by continuous wavelet transform

Abstract

A method based on the wavelet ridges of continuous wavelet transform is proposed for the instantaneous frequency identification of time-varying structures. To eliminate noise effect, a penalty function is imposed first, and then the dynamic optimization technique is implemented for wavelet ridge extraction. The instantaneous frequencies are then identified from the extracted wavelet ridges. To validate the proposed method, a numerical example of a two degree-of-freedom spring–mass–dashpot system with time-varying stiffness is studied. The numerical results indicated that the proposed method is efficient in extracting wavelet ridges and tracking the instantaneous frequencies of the time-varying system even the numerical responses are contaminated by 10% Gauss white noise. An experiment on the cable with varying tension force is set up in the laboratory. The time-varying natural frequency is achieved by applying linear and sinusoidal varying tension forces respectively. The instantaneous cable frequencies are then identified by the proposed method. The experiment results further verified that the proposed method can effectively identify the instantaneous frequencies of time-varying structures with a high accuracy.