应用时频分析方法辨识时变系统的模态参数

应用Gabor展开及Hilbert变换进行时变线性系统模态参数的辨识。利用非平稳信号的Gabor变换将结构响应信号表示在时频面上，并通过Gabor展开重构分离模态分量，建立每一阶模态的时变线性模型。对单模态时变线性模型应用Hilbert变换来辨识随时间变化的模态频率和阻尼。通过对刚度和阻尼慢变的两自由度系统模态参数的仿真辨识验证辨识方法的有效性。仿真结果表明：本文方法为时变线性系统的模态参数辨识提供了一条新的途径。

Identification of Time-Varying Modal Parameters by a Linear Time-Frequency Method

A new method of parametric identification based on linear time-frequency representation and Hilbert transform is proposed in this paper to identify modal parameters of linear time-varying systems from measured vibration responses. With Gabor expansion and synthesis, measured responses are represented in time-frequency domain and the modal components are reconstructed by time-frequency filtering. Hilbert transform is applied to obtain time histories of the amplitude and phase angle of each modal component, from which the time-varying frequencies and the damping ratios are identified. The proposed method is demonstrated with a numerical example in which a linear time-varying system of two degrees of freedom is used to validate the identification scheme. Simulation results indicate that the time-frequency representation can be an effective tool for modal parameter identification of time-varying systems.