EMD分解中端点数据的延长方法问题研究

Research on extending end data in empirical mode decomposition

目前的EMD分解中,延长左右两端数据主要是通过各种数学拟合的方式(镜像延拓、多项式拟合、神经网络延拓等)来实现。在实际中,通过延长信号的采样时间,同样能够使端点数据延长,从而抑制EMD分解时的端点效应。以周期谐波函数为例,通过数值实验,将用数学拟合延长两端数据的方法(以极值点的镜像延拓为例)与直接截取两端数据的方法进行比较。同时,为了比较两种数据延长方法的效果,分别将延长后的数据进行EMD分解,将实际的EMD分解结果作为矩阵,计算与理想分解结果之间的相关系数。得出以下结论:若左右各截取半个信号周期长度的数据信号,则得到的分解结果优于通过端点延拓方法得到的EMD分解结果,且截取的点数越多,得到的结果越接近理想的分解结果。

In Empirical Mode Decomposition（EMD）,to suppress the ending effect,extending the data near the two end points is used by mathematics fitting usually.In practice,extending the sampling-time can also extend the end points and suppress the ending effect.Comparison has been made among the data extending method between the mathematics fitting（the mirror extending method as example） and terminal intercept near the two end points.To test the effect of EMD,the correlation coefficient between the practical results and ideal results are calculated.As a result of simulation and numerical experiment（periodic harmonic function as example）,it is shown that if the signal intercept around half the length of data signals,better results can be obtained than endpoint extending.More the interception of points approximates more ending effect can be effectively restrained.