基于非线性自回归时序模型的振动系统辨识

针对线性和弱非线性振动系统进行了研究，提出采用非线性自回归时序(GNAR)模型进行系统频率辨识和判断系统性或非线性基本特征的方法。首先根据摄动法求解非线性微分方程的理论，论证GNAR模型与线性和弱非线性系统之间的本质联系，推导出GNAR模型系数与线性和非线性系统频率之间的解析关系，然后给出由GNAR模型系数和结构判断系统是否存在非线性，及辨识系统频率和非线性项基本特征的方法。最后，以单自由度线性振动系统和无阻尼Duffing振动系统为算例验证该辨识方法的有效性和准确性。实验结果表明，基于GNAR模型的振动系统基本特征辨识方法具有较好的识别精度，能用于估计系统的动力学特性。

Identification Based on GNAR model for Vibration System

A method based on GNAR model was proposed to identify the essential characteristics of linear and weak nonlinear vibration systems. Firstly, the relationship between GNAR model and weak nonlinear system was proved according to perturbation method of solving nonlinear differential equation and the analytic expressions between GNAR model coefficients and the system frequency were deduced. Then the identification method based on GNAR model coefficients and its structure was extracted to determine whether there was a linear or nonlinear system, and to identify the system frequency and the basic characteristics of nonlinear term. Finally single degree freedom linear vibration systems and undamped Duffing vibration systems were analyzed to test the effectiveness and accuracy of the identification method. The experimental results show that the proposed method has high accuracy and efficiency, and can be used to estimate the system dynamic characteristics.