Instantaneous frequency identification of a time varying structure using wavelet-based state-space method

This paper presents a method to identify the instantaneous frequency of the time varying structures based on wavelet and state space methods by using free and forced vibration response data. Firstly, the second-order vibration differential equations are rewritten as the first-order state equations using state space theory. Secondly, both excitation and response signals are projected by the Daubechies wavelet scaling functions. Thus, the first-order state equations are transformed into linear algebraic equations using the orthogonality of the scaling functions. Lastly, the equivalent time varying state space system matrices of time varying structure are extracted directly by solving the linear equations. The instantaneous frequencies are determined via eigenvalue decomposition of the state space system matrices. The proposed identification algorithm is investigated with a four degrees-of-freedom spring-mass-damper model. Numerical simulations demonstrate that the proposed method is robust and effective for identification of the abruptly, smoothly and periodically changing instantaneous frequencies of time varying structures.