The purpose of this paper is to provide a modal expression of a time-varying MDOF system and to develop an identification method for it. The single-input-multi-output relation of a time-varying N-DOF system is expressed as a superposition of N time-varying SDOF subsystems in the time domain, where the expansion coefficients represent the time-varying mode-shapes, and the natural frequency and the damping ratio of each subsystem represent the time-varying modal parameters of each mode. Then we define the SDOF wavelets, which correspond to the time-varying impulse responses of SDOF subsystems and show that the output of the entire system can be expressed by a superposition of SDOF wavelets. Then, the identification problem is reduced to an atomic decomposition problem of choosing the nearly best set of SDOF wavelets and determining the expansion coefficients. We develop a modified matching pursuit algorithm, called modal pursuit, to solve the problem. Basic examples are numerically examined to show that the proposed modal representation and the identification method are applicable to track the modal characteristics of time-varying systems.

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