Identification of Time-varying Modal Parameters Using Linear Time-frequency Representation

A new method of parameter identification based on linear time-frequency representation and Hilbert transform is proposed in this paper to identify modal parameters of linear time-varying systems from measured vibration responses. With Gabor expansion and synthesis theory, measured responses are represented in time-frequency domain and modal components are reconstructed by time-frequency filtering. Hilbert transform is applied to obtain time histories of the amplitude and phase angle of each modal component, from which time-varying frequencies and damping ratios are identified. The proposed method has been demonstrated with a numerical example in which a linear time-varying system of two degrees of freedom is used to validate the identification scheme based on time-frequency representation. Simulation results have indicated that time-frequency representation presents an effective tool for modal parameter identification of time-varying systems. NOMENCLATURE ) , ( k n GS Gabor coefficient ) (t gnk Gabor basis ) (k g Synthetic window function ) (k h Analytic widow function ) (t M ) (t C ) (t K Mass ,damping, stiffness matrices r r r p u t a , ), ( rth scale factor, modal vector, eigenvalue r r q t), ( η amplitudes of scale factor and modal vector r r t γ θ ), ( phases of scale factor and modal vector r r β α , Real part and image part of eigenvalue ) (t yr rth modal component ) (i r ω , ) (i r ξ rth modal frequency, damping ratio ) ( ˆ t yr Hilbert transform of ) (t yr