基于张力格林样条的EMD均值曲线插值方法
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摘要
经典经验模式分解采用三次样条插值方法求取信号的均值曲线,其存在较严重的过冲现象,造成最终的分解误差较大。针对上述问题,提出一种基于张力格林样条的均值曲线插值方法。以相邻极值点的中点为插值节点,采用张力格林样条插值直接获得信号的均值曲线。实验结果表明,该方法在保证插值曲线光滑性的基础上,可以消除三次样条在插值节点间出现的过分振荡现象,一定程度上克服过冲问题,基于极值中点的一次插值能进一步降低信号分解的误差。
In the classic EMD,the mean curves are obtained using cubic spline interpolation.However,serious overshoots may often occur,and the decomposition errors are large in the final.In response to these problems,an interpolation method of the mean curve was proposed based on the Green's spline in tension.The midpoints of the adjacent extreme points were used as interpolation nodes,and the mean curve was obtained using Green's spline interpolation in tension.Experimental results show that excessive oscillation of cubic spline between the interpolation nodes can be eliminated without deteriorating the smoothness of the interpolation curve,and serious overshoots disappear to some extent.Moreover,the decomposition errors of signals can be further reduced using one interpolation based on the midpoints of extremes.
In the classic EMD,the mean curves are obtained using cubic spline interpolation.However,serious overshoots may often occur,and the decomposition errors are large in the final.In response to these problems,an interpolation method of the mean curve was proposed based on the Green's spline in tension.The midpoints of the adjacent extreme points were used as interpolation nodes,and the mean curve was obtained using Green's spline interpolation in tension.Experimental results show that excessive oscillation of cubic spline between the interpolation nodes can be eliminated without deteriorating the smoothness of the interpolation curve,and serious overshoots disappear to some extent.Moreover,the decomposition errors of signals can be further reduced using one interpolation based on the midpoints of extremes.
引文
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[8]XU Feng,HE Rizheng,ZHANG Guibin.Green’s functionbased interpolator and its application[J].Progress in Geophysics,2013,28(4):1721-1728(in Chinese).[许丰,贺日政,张贵宾.格林样条插值算法及其应用[J].地球物理学进展,2013,28(4):1721-1728.]
[9]Wessel P,Becker JM.Interpolation using ageneralized Green’s function for a spherical surface spline in tension[J].Geophysical Journal International,2008,174(1):21-28.
[10]ZHU Zheng,WANG Yilin,CAI Ping.A method of obtaining the mean curve for empirical mode decomposition[J].Journal of Harbin Engineering University,2011,32(7):872-876(in Chinese).[朱正,王逸林,蔡平.EMD中的求取均值曲线方法[J].哈尔滨工程大学学报,2011,32(7):872-876.]
[11]Wu Z,Huang NE.Ensemble empirical mode decomposition:A noise assisted data analysis method[J].Advances in Adaptive Data Analysis,2009,1(1):1-41.
[12]Wessel P,Bercovici D.Interpolation with splines in tension:A Green’s function approach[J].Mathematical Geology,1998,30(1):77-94.
[13]DENG Xingsheng,TANG Zhong’an.Study on two dimensional spline interpolation based on moving Green’s function[J].Journal of Geodesy and Geodynamic,2011,31(6):69-72(in Chinese).[邓兴升,汤仲安.移动格林基函数样条二维插值算法研究[J].大地测量与地球动力学,2011,31(6):69-72.]
[2]ZHONG Youming,JIN Tao,QIN Shuren.New envelope algorithm for Hilbert-Huang transform[J].Journal of Data Acquisition&Processing,2005,20(1):13-17(in Chinese).[钟佑明,金涛,秦树人.希尔伯特黄变换中的一种新包络线算法[J].数据采集与处理,2005,20(1):13-17.]
[3]LONG Sisheng,ZHANG Tiebao,LONG Feng.Causes and solutions of overshoot and end swing in Hilbert-Huang transform[J].Acta Seismologica Sinica,2005,27(5):561-568(in Chinese).[龙思胜,张铁宝,龙峰.希尔伯特—黄变换中拟合过冲和端点飞翼的原因及解决办法[J].地震学报,2005,27(5):561-568.]
[4]Chen Qiuhui.A B-spline approach for empirical mode decompositions[J].Advances in Computational Mathematics,2006,24(1-4):171-195.
[5]ZHU Weifang,ZHAO Heming,CHEN Xiaoping.A leastlength constrained envelope approach for EMD[J].Acta Electronica Sinica,2009,40(9):1909-1912(in Chinese).[朱伟芳,赵鹤鸣,陈小平.一种最小长度约束的EMD包络拟合方法[J].电子学报,2009,40(9):1909-1912.]
[6]Wessel P.Interpolation using ageneralized Green’s function for a spherical surface spline in tension[J].Computer&Geosciences,2009,36(6):1247-1254.
[7]XIA Jizhuang.An application of biharmonic spline interpolation to integration of logging and seismic data[J].Oil&Gas Geology,2010,31(2):244-248(in Chinese).[夏吉庄.双调和样条内插方法在测井和地震资料整合中的应用[J].石油与天然气地质,2010,31(2):244-248.]
[8]XU Feng,HE Rizheng,ZHANG Guibin.Green’s functionbased interpolator and its application[J].Progress in Geophysics,2013,28(4):1721-1728(in Chinese).[许丰,贺日政,张贵宾.格林样条插值算法及其应用[J].地球物理学进展,2013,28(4):1721-1728.]
[9]Wessel P,Becker JM.Interpolation using ageneralized Green’s function for a spherical surface spline in tension[J].Geophysical Journal International,2008,174(1):21-28.
[10]ZHU Zheng,WANG Yilin,CAI Ping.A method of obtaining the mean curve for empirical mode decomposition[J].Journal of Harbin Engineering University,2011,32(7):872-876(in Chinese).[朱正,王逸林,蔡平.EMD中的求取均值曲线方法[J].哈尔滨工程大学学报,2011,32(7):872-876.]
[11]Wu Z,Huang NE.Ensemble empirical mode decomposition:A noise assisted data analysis method[J].Advances in Adaptive Data Analysis,2009,1(1):1-41.
[12]Wessel P,Bercovici D.Interpolation with splines in tension:A Green’s function approach[J].Mathematical Geology,1998,30(1):77-94.
[13]DENG Xingsheng,TANG Zhong’an.Study on two dimensional spline interpolation based on moving Green’s function[J].Journal of Geodesy and Geodynamic,2011,31(6):69-72(in Chinese).[邓兴升,汤仲安.移动格林基函数样条二维插值算法研究[J].大地测量与地球动力学,2011,31(6):69-72.]
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