Identification of Time-Varying Modal Parameters for Thermo- Elastic Structure Subject to Unsteady Heating

A time-varying modal parameter identification method combined with Bayesian information criterion （BIC） and grey correlation analysis （GCA） is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field. To demonstrate the method, the thermo-elastic structure to be identified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field, and the dynamic outputs of the beam are first simulated as the meas- ured data for the identification. Then, an improved time-varying autoregressive （TVAR） model is generated from the simulated input and output of the system. The time-varying coefficients of the TVAR model are expahded as a finite set of time basis functions that facilitate the time-varying coefficients to be time invariant. According to the BIC for preliminarily determining the scope of the order number, the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree （AGCD）. Finally, the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method. The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.