基于Hilbert-Huang变换理论的非线性系统分析

介绍了Hilbert-Huang变换(HHT)这一全新的处理非线性、非平稳信号数据的方法,将其用于分析典型的非线性系统-Duffing方程,通过对使用三阶Runge-Kutta法求解而得到的Duffing方程数值解分解后,得到了4个固有模态函数分量和1个残余量,给出了相应的能量-频率-时间分布图-Hilbert谱,并将其边际谱与Fourier谱作了比较。结果表明,此方法具有更好的局部特性分辨以及瞬时频率分解效果,经HHT变换得到的主要固有模态函数分量具有明确的物理意义,体现在Hilbert谱上的系统固有频率存在明显的波内调制机制,分析结果充分保留了系统的非线性特征。

Nonlinear system analysis based on Hilbert-Huang transform theory

A new method for nonlinear and non-stationary data processing,the Hilbert-Huang transform(HHT),is applied to analyze a typical nonlinear system,Duffing equation.Four intrinsic mode function(IMF)components and one residual component are gained through decomposition on the numerical results of Duffing equation using third-order Runge-Kutta method.The corresponding energy-frequency-time distribution designated as the Hilbert spectrum was given.Comparison between marginal spectrum and Fourier spectrum shows that HHT offers much better local characteristic identifications and instantaneous frequency resolutions.The main IMF components have distinct physical senses.Besides,the intra-wave frequency modulations of system intrinsic frequency are clearly illustrated in the Hilbert spectrum and the nonlinear characteristics are reserved adequately by analysis results.