基于系统响应瞬时特性的非线性系统识别

Nonlinear system identification based on instantaneous characteristics of dynamic response

在Krylov-Bogoliubov-Mitropolski(KBM)法的基础上,提出一种基于系统响应瞬时特性的非线性系统识别方法.该方法通过建立系统响应瞬时特性与系统参数之间的函数关系,从而一次性识别出所有系统参数.采用归一化Hilbert变换(normalized Hilbert transform,NHT)和广义过零(generalized zero-crossing,GZC)法求解信号瞬时振幅和瞬时频率,通过算例验证了两种方法的效果.以Duffing方程和Vanderpol方程两类非线性振动系统为例,验证了所提系统识别方法的精度.算例表明,即使在系统响应受到较大噪声污染时,该方法也有很好的识别精度.

In the light of the Krylov-Bogoliubov-Mitropolski（KBM）method,a nonlinear system identification method is developed based on the instantaneous characteristics of the dynamic response of the system.The method identifies all the system parameters through establishing function relationship connecting system transient response characteristics with system parameters. The normalized Hilbert transform（NHT）and the generalized zero-crossing（GZC）method are introduced to calculate the instantaneous amplitude and frequency of the dynamic response.An example is applied to verify the efficiencies of these two methods.The proposed system identification method is applied to the nonlinear vibration systems of the Duffing and Vanderpol equations.Experimental results show that the method has good identification accuracy even when the dynamic responses are largely polluted by noises.