希尔伯特-黄变换端点效应的自适应端点相位正弦延拓方法

针对希尔伯特-黄变换（Hilbert Huang Transform，HHT）的端点效应问题，提出一种自适应端点相位正弦延拓经验模态分解（Empirical Mode Decomposition，EMD）方法.该方法根据端点附近数据变化趋势，通过在信号两端自适应加上相位、幅值和频率适当的正弦延拓函数，使得原端点的包络线顺着端点附近波形延展，以改进EMD分解精度.为满足EMD内禀模态分量（Intrinsic Mode Function，IMF）与原信号的相关性精度和EMD较低迭代次数的要求，引入能表征EMD性能的目标函数.该函数可通过迭代次数、IMF个数和有效IMF的相关系数大小等来衡量.由于该方法的边界延拓参数是根据延拓周期比例系数、延拓信号长度系数和采样频率自动确定的，故其分解过程完全是一个自适应过程，不需要人为设置，具有较好的实用性.仿真和液压系统实例分析表明，该方法不仅能较好地解决HHT的端点效应，而且相对现有的延拓方法而言，筛选次数更少，能显著提高信号EMD分解精度，且减小Hilbert谱的端点效应，更加精确地提取了液压系统齿轮泵振动信号的故障特征，取得了较好的应用效果.

Processing Method for Hilbert-Huang Transform End Effects Self-Adaptive Endpoint-Phase Sinusoidal Extension

For the Hilbert-Huang Transform(HHT) endpoint effect problem, a self-adaptive method of endpoint-phase sinusoidal extension was presented. This method adaptively adds sinusoidal extension function of phase, amplitude and frequency to improve decomposition precision according to the data trend near the end. Then the object function to represent empirical mode decomposition(EMD) performance was introduced to satisfy the pertinence precision between intrinsic mode function(IMF) and original signal and low iterations of EMD. The boundary extension parameter decomposition is an adaptive process with better practicability. The simulation and example of hydraulic system show that this approach can not only solve HHT end effect, but also improve EMD decomposition precision with less filtration and reduce Hilbert spectrum end effect. Finally, it can extract the fault characteristics of gear pump vibration signal and get a good application effect.