基于自回归模型非线性振动模型特性识别

Identification of Nonlinear Vibration System Features Based on Auto-regressive Model

对假定为三次自由衰减非线性系统的识别进行了理论研究。首先,对系统进行非线性分析得到振幅和频率的瞬时关系式。然后,通过引入Hilbert变换获得结构瞬时振幅和瞬时频率,针对Hilbert变换获得的瞬时频率抗噪音能力弱的缺点;基于自回归时间序列模型通过卡尔曼滤波获得结构瞬时频率。最后,通过已获得的瞬时频率、瞬时振幅及二者的关系式建立相应的回归模型,运用最小二乘法可以识别出非线性系统系数。通过数值算例模拟验证算法识别有效。研究为非线性系统的识别提供理论方法。

An application of free-decaying nonlinear vibration system identification method is proposed. Based on nonlinear analysis of the system,the relationship between instantaneous amplitude and frequency is obtained. The method of calculating the instantaneous amplitude based on Hilbert transform was introduced. then,Kalman filter is utilized to estimate the instantaneous frequency. According to the relationship between the instantaneous amplitude and instantaneous frequency,auto-regressive model of nonlinear system is established. Parameter can be estimated using least square method. In numerical simulation,the effect of the new algorithm is validated via the example. The research can provide a effective method to estimate the nonlinear system parameter.