基于数据/极值联合对称延拓的端点效应处理及其应用

A process method for end effects of HHT based on data/extrema symmetrical extension and its application

Hilbert-Huang变换在EMD分解中因端点非极值点,无法满足样条插值的要求导致包络线异常,产生端点飞翼;在Hilbert变换中又因卷积计算和Fourier变换能量泄露的原因,也使端点产生飞翼。提出数据/极值联合对称延拓的方法,通过端部数据对称延拓,把EMD分解和Hilbert变换过程中产生的端点效应释放到数据外端,一举解决两阶段的端点飞翼问题;通过极值点对称延拓进一步控制三次样条包络曲线的走势,使原始数据的包络曲线更加准确。经仿真信号验证,联合对称延拓的方法具有良好的抑制效果。当该方法应用于结构动力响应非线性特征分析时,不仅具有明确的物理意义,而且能较准确地表征结构进入非线性状态时出现"频带扩展"和"主导频率飘移"的力学特征。

End effects appear in EMD decomposition because an end point is not an extreme point and the requirements of spline interpolation can not be met. End effects are produced in Hilbert transform due to the convolution calculation and the energy leakage of Fourier transform. In this paper,a data/extrema symmetrical extension method was proposed to solve the problem. Using end data symmetrical extension,the end swings resulted from EMD and Hilbert transform could be released to the outside of the data. Through extrema symmetrical extension,the shape of the cubic spline envelope curve was further controlled and the envelope curve of the original data was more accurate. The simulation demonstrates the effectiveness of the method. When this method is applied to the structural dynamic non-linear characteristics analysis,clear physical meaning and two non-linear mechanical characteristics including ＂ frequency band extension＂ and ＂ main frequency drift＂ can be described accurately.