Identification of modal parameters of a time variant structure via TVARX model

The time varying autoregressive with exogenous input (TVARX) model is often used to describe input-output relationship of a linear time variant structure system from its dynamic responses and input forces. This work presents a procedure of determine the instantaneous modal parameters of a time variant system. A weighted basis function technique is applies to estimate the time dependent coefficients of the TVARX model. The time varying coefficients of the TVARX model are expanded by basis functions. Then, the expansion coefficients for the basis functions are estimated through a weighted least-squares approach. Final, the instantaneous natural frequencies, damping ratios and mode shapes of the structural system can be directly determined. The proposed procedure is applied to process the dynamical responses of a five-story steel frame, subjected to 10% and 60% of the strength of the Kobe earthquake, in shaking table tests. The steel frame responded nonlinearly when it subjected to 60% Kobe earthquake, while it responded linearly when it subjected to 10% Kobe earthquake. This work thoroughly investigates the differences in instantaneous modal parameters identified from the responses corresponding to different strengths of the Kobe earthquake.