Identification of Time-Variant Modal Parameters Using Time-Varying Autoregressive with Exogenous Input and Low-Order Polynomial Function

This work presents an approach that accurately identifies instantaneous modal parameters of a structure using time-varying autoregressive with exogenous input (TVARX) model. By developing the equivalent relations between the equation of motion of a time-varying structural system and the TVARX model, this work proves that instantaneous modal parameters of a time-varying system can be directly estimated from the TVARX model coefficients established from displacement responses. A moving least-squares technique incorporating polynomial basis functions is adopted to approximate the coefficient functions of the TVARX model. The coefficient functions of the TVARX model are represented by polynomials having time-dependent coefficients, instead of constant coefficients as in traditional basis function expansion approaches, so that only low orders of polynomial basis functions are needed. Numerical studies are carried out to investigate the effects of parameters in the proposed approach on accurately determining instantaneous modal parameters. Numerical analyses also demonstrate that the proposed approach is superior to some published techniques (i.e., recursive technique with a forgetting factor, traditional basis function expansion approach, and weighted basis function expansion approach) in accurately estimating instantaneous modal parameters of a structure. Finally, the proposed approach is applied to process measured data for a frame specimen subjected to a series of base excitations in shaking table tests. The specimen was damaged during testing. The identified instantaneous modal parameters are consistent with observed physical phenomena.