Hilbert-Huang变换方法在Duffing方程和圆柱尾迹流分析中的应用

Application of Hilbert-Huang Transform in Analysis of Duffing Equation and Wake Flow over a Cylinder

本文采用N．E Huang最近提出的Hilbert-Huang变换方法分析了使用三阶Runge-Kutta方法数值求解的 Duffing方程的性质和圆柱绕流尾流特性,分解得到了有限阶经验模态(Empirical Modes)．给出了相应的Hilbert 谱。结果表明,Hilbert-Huang变换得到的主要含能模态物理意义清晰．相应的瞬时频率存在着明显的波内频率调制,很好地刻画了信号的时空局部特性。

The Hilbert-Huang Transform, recently proposed by Norden E Huang, has been used to analyze the properties of Duffing equation, which was solved numerically by using 3^rd-order Runge-Kutta method, and then to the wake flow over a circular cylinder. The signals were successfully decomposed into the summation of five or six empirical modes. The Hilbert spectrum indicates that the energy-containing modes are of physical significance. Besides, the intra-wave frequency modulations are clearly illustrated in the Hilbert spectrum, which well describe the local properties of time-frequency distributions.