Subspace-Based Identification of Linear Time-Varying System

Abstract

A physical parameter identification method for the linear time-varying system is presented in this paper. For an arbitrarily time-varying system, a series of Hankel matrices are established directly from the combined measurements of displacement, velocity, and acceleration together with the input excitations from a single experiment with the system. The time-varying equivalent state-space system matrices of the structure at each time instance are then identified by singular value decomposition using the free or random responses. A time-varying transformation matrix for transforming the identified equivalent system matrices into the physical system matrices is developed to determine the mass, stiffness, and damping matrices. Details of the proposed approach are investigated with a two degrees-of-freedom spring-mass-damper system with three kinds of time-varying parameters. Numerical results show that the proposed method is accurate and effective in identifying time-varying physical parameters.