基于经验包络法的非线性系统参数识别

摘要

An efficient nonlinear system parameter identification method is developed on the basis of the relationship between the instantaneous characteristics of the system response and system parameters,which is derived by the averaging method.The instantaneous characteristics are calculated by the empirical envelope method (EE),and the superiority of EE compared with the traditional Hilbert transform (HT) is illustrated.The identification accuracy of the developed identification method is verified by numerical example.The influences of the signal length,initial condition,sampling frequency and the ratio of noise are analyzed.Results show that the linear parameters are immune from these factors,while the nonlinear parameters are sensitive to them;the proposed method shows excellent performance and the identification accuracy can be guaranteed even when the system response contains high noise pollution.%基于平均法导出了Van der Pol-Duffing类振子响应时程瞬时特性与系统参数间的函数关系,在此基础上提出一种高效的非线性系统参数识别方法.借助经验包络法EE(Empirical Envelope Method)求解了响应时程瞬时特性,验证了EE相对传统Hilbert变换HT(Hilbert Transform)方法在求解瞬时频率上的优势.通过数值算例验证了本文方法的识别精度.分析了信号长度、初始条件、采样频率和噪声比例四种因素对识别精度的影响.结果表明,线性参数识别精度不受上述因素影响,非线性刚度项系数识别精度受各因素影响较为明显;本文方法具有良好的抗噪声性能,即使系统响应受到10％的噪声污染,本文方法也具有很好的识别精度.