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.