调幅-调频信号的经验模态分解包络技术和模态混叠

Empirical Mode Decomposition Envelope Technique and Mode Mixing Problem in Amplitude Modulation-frequency Modulation Signals

经验模态分解(Empirical mode decomposition,EMD)是一种数据驱动的自适应非线性非平稳数据处理方法。包络技术和模态混叠问题是EMD研究的重要课题。将非线性非平稳信号定义为多成分调幅-调频(Amplitude modulation-frequency modulation,AM-FM)信号模型,而EMD分解的每一个固有模态函数为单一的AM-FM信号。通过研究单成分AM-FM信号的包络以及多成分AM-FM信号EMD分解引起的模态混叠问题,提出新的EMD包络条件,并给出新包络算法的数值计算方法。基于新条件包络算法,提出单成分AM-FM信号相位和瞬时频率的新估计算法。提出解决多成分AM-FM信号EMD分解的模态混叠问题的新方法,并通过几组仿真信号和一组实测的转子碰摩数据验证了方法的有效性。

Empirical mode decomposition （EMD） is a self-adaptive method and suitable to analysing the non-stationary and nonlinear signals.The envelope technique and mode-mixing problem are the most important topics of the EMD. A nonlinear and nonstationary signal is modeled as a multicomponent amplitude modulation-frequency modulation （AM-FM） signal and each intrinsic mode function （IMF） of the EMD will be modeled as a single AM-FM signal. Through studying the envelope technique of single AM-FM signal and the mode-mixing problem caused by separating multicomponent AM-FM signals with the EMD algorithm, a new necessary condition of envelope and the numerical calculation method of the new conditional envelope algorithm are presented. Based on the new conditional envelope algorithm, a new estimation algorithm for phase and instantaneous frequency of single component AM-FM signal is proposed. A solution is presented to the mode-mixing problem that occurs when multicomponent AM-FM signals are separated. The efficacy of the proposed method is verified by several simulation signals and a measured data of rubbing fault of rotor system.