Physical parameter identification of time-varying system based on free response data

A physical parameter identification method is presented in this paper. For an arbitrarily time-varying system, a series of Hankel matrices are established directly from free response data, which have been obtained through only one experiment of the system. The varying equivalent state space system matrices of structures at each moment are then identified by Singular Value Decomposition (SVD) of the Hankel matrix. A varying transformation matrix to transform the identified equivalent system matrices into the physical system matrices is developed to determine the stiffness and damper matrices. Finally, a 2DOF spring-mass-damper model with three kinds of time-varying cases is investigated. Numerical results show that the proposed method is accurate and effective to identify the time-varying physical parameters.