关于非线性系统辨识的恢复力曲面法和希尔伯特变换法

本文针对均匀薄板和压电双晶薄板进行了非线性辨识实验，比较了两种方法——恢复力曲面法和希尔伯特变换法。针对辨识数据的函数逼近问题，提出将位移-刚度函数而非位移-恢复力函数用于数据拟合。通过均匀薄板和压电双晶薄板的实验结果，验证了位移-刚度函数确实能提高小位移处的函数逼近精度并更加准确展现系统的非线性特性。本文还对比了恢复力曲面法和希尔伯特变换法在辨识精度和数据利用率方面的区别，结果显示希尔伯特变换法能有效抑制小位移处位移—刚度曲线的不规则振荡，并有着较高的数据利用率。
Abstract：Two nonlinear system identification methods including the restoring force surface method and Hilbert transform one were compared based on experiments of a homogeneous plate and a piezoelectric bimorph one.The stiffness-displacement function was proposed to be used for data fitting instead of the restoring force-displacement function in the function approximation process.The experiment results of a homogeneous plate and a piezoelectric bimorph one showed that using the stiffness-displacement function can improve the function approximation accuracy at small displacements.The identification accuracy and data utilization rate obtained by the restoring force surface method were compared with those obtained by Hilbert transform one.The results showed that Hilbert transform method can effectively suppress irregular oscillations of the stiffness-displacement curve at small displacements, and it has a higher data utilization rate.