消除EMD端点效应的PSO-SVM方法研究
|
摘要
经验模态分解(empirical mode decomposition,简称EMD)的端点效应使得EMD分解结果产生严重失真,为了减小分解过程中产生的端点效应,将支持向量机(SVM)这一智能算法引入EMD,提出采用SVM模型解决分解中产生的端点效应问题.通过支持向量机对其原始数据两端进行延拓,以获得一个或者多个极大值和极小值.为了使端点处的延拓交得更加合理,引入粒子群(PSO)智能算法对支持向量机算法参数进行优化,使其两个端点处的数据延拓得更加准确,从而使得三次样条曲线在端点处不会发生大的摆动,实现EMD分解的固有模态函数(IMF)更加准确可靠.通过对仿真信号的研究表明,基于PSO-SVM方法的延拓方法能够很好地抑制了分解的端点效应.
End effects of EMD(empirical mode decomposition) make a serious distortion of the decomposition result.In order to reduce the end effects in the process of decomposition,support vector machine (SVM) which is a kind of intelligent algorithm is combined with EMD,then a solution to the end effects problem during the course of decomposition using SVM model is proposed.Firstly,one or more extreme values are obtained by extending two endpoints of the original data with SVM.Moreover,in order to get more reasonable extension at endpoint,SVM algorithm is combined with particle swarm algorithm(PSO) to optimize the parameters,and the extension of two endpoints will be more accurate,then the end-points of cubic spline curve will not have large swing so as to achieve that intrinsic mode functions(IMF) of EMD are more accurate and reliable.Simulation results indicate that the extension method for data based on PSO-SVM method can restrain the end effects effectively.
End effects of EMD(empirical mode decomposition) make a serious distortion of the decomposition result.In order to reduce the end effects in the process of decomposition,support vector machine (SVM) which is a kind of intelligent algorithm is combined with EMD,then a solution to the end effects problem during the course of decomposition using SVM model is proposed.Firstly,one or more extreme values are obtained by extending two endpoints of the original data with SVM.Moreover,in order to get more reasonable extension at endpoint,SVM algorithm is combined with particle swarm algorithm(PSO) to optimize the parameters,and the extension of two endpoints will be more accurate,then the end-points of cubic spline curve will not have large swing so as to achieve that intrinsic mode functions(IMF) of EMD are more accurate and reliable.Simulation results indicate that the extension method for data based on PSO-SVM method can restrain the end effects effectively.
引文
[1]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis[C]// Proceedings of the Royal Society of London Series A,1998,454(12): 903-995.
[2]黄大吉,赵进平,苏纪兰.希尔伯特-黄变换的端点延拓.海洋学报[J],2003,25(1):1-11. Huang D J,Zhao J P,Su J L.Practical implementation of the Hilbert-Huang transform algorithm[J].Acta Oceanologica Sinica,2003,25(1):1-11.
[3]邓拥军,王伟,钱成春,等.EMD方法及Hilbert变换中边界问题的处理[J].科学通报,2001,46(3):257-263.
[4]瞿伟廉,程磊.应用径向基函数神经网络处理EMD方法中的边界问题[J].华中科技大学学报:城市科学版,2006,23(4): 1-4. Qu W L,Cheng L.Disposal of boundary problem in EMD method applying RBF neural network[J].Journal of Huazhong University of Science and Technology:Urban Science Edition,2006,23(4):1-4.
[5]杨建文,贾民平.希尔伯特-黄谱的端点效应分析及处理方法研究[J].振动工程学报,2006,19(2):283-288. Yang J W,Jia M P.Study on processing method and analysis of end problem of Hilbert-Huang spectrurn[J]. Journal of Vibration Engineering,2006,19(2):283-288.
[6]刘慧婷,张曼,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用,2004,40(16):84-86. Liu H T,Zhang M,Cheng J X.Dealing with the end issue of EMD based on polynomial fitting algorithm[J]. Computer Engineering and Applications,2004,40(16):84-86.
[7]胡爱军,安连锁,唐贵基.Hilbert-Huang变换端点效应处理新方法[J].机械工程学报,2008,44(4):154-158. Hu A J,An L S,Tang G J.New process method for end effects of Hilbert-Huang transform[J].Chinese Journal of Mechanical Engineering,2008,44(4):154-158.
[8]张郁山,梁建文,胡聿贤.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展,2003,13(10):1054-1059.
[9]罗奇峰,石春香.Hilbert-Huang变换理论及其计算中的问题[J].同济大学学报,2003,31(6):647-640. Luo Q F,Shi C X.Hilbert-Huang transform and several problems in its calculation method[J].Journal of Tongji University,2003,31(6):647-640.
[10]Rilling G,Flandrin P,Goncalves P.On empirical mode decomposition and its algorithms[C]// IEEE EURASIP Workshop on Nonlinear Signal and Image Processing,Grado(I),2003.
[11]张义平,李夕兵,左宇军.爆破振动信号的HHT分析与应用[M].北京:冶金工业出版社,2008.
[12]李夕兵,张义平.基于HHT方法的爆破地震信号分析[J].工程爆破,2005(1):1-7. Li X B,Zhang Y P.Analysis of blasting vibration signal based on HHT method[J].Engineering Blasting,2005(1): 1-7.
[13]李顺国,卢新元.基于粗糙集和SVM的工程项目投标风险研究[J].计算机工程与应用,2008,44(17):224-227. Li S G,Lu X Y.Research of constructional engineering project bidding risk analysis based on rough sets and support vector machine[J].Computer Engineering and Applications,2008,44(17):224-227.
[14]苏怀智,温志萍,吴中如.基于SVM理论的大坝安全预警模型研究[J].应用基础与工程科学学报,2009,17(1):40-47. Su H Z,Wen Z P,Wu Z R.An early-warning model of dam safety based on SVM theory[J].Journal of Basic Science and Engineering,2009,17(1):40-47.
[15]郑一华,徐立中,黄风辰.基于支持向量分类的水质分析应用研究[J].仪器仪表学报,2006,27(6):291-293. Zheng Y H,Xu L Z,Huang F C.Study of water quality analysis based on support vector classification[J].Chinese Journal of Scientific Instrument,2006,27(6):291-293.
[16]Vapnik V N.The nature of statistical learning theory[M].New York:Springer-Verlag,1995.
[17]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000(1):32-42. Zhang X G.Introduction to statistical learning theory and support vector machines[J].Acta Automatica Sinica, 2000(1):32-42.
[18]周涛,张艳宁,袁和金,等.基于改进粒子群算法的支持向量机[J].计算机工程与应用,2007,43(15):44-49. Zhou T,Zhang Y N,Yuan H J,et al.SVM based on improvement particle swarm optimization algorithm[J]. Computer Engineering and Applications,2007,43(15):44-49.
[19]陈炳瑞,冯夏庭.压缩搜索空间与速度范围粒子群优化算法[J].东北大学学报:自然科学版,2005,26(5):488-491. Chen B R,Feng X T.Particle swarm optimization with contracted ranges of both search space and velocity[J]. Journal of Northeastern University:Natural Science Edition,2005,26(5):488-491.
[20]吴启迪,汪镭.智能微粒群算法研究及应用[M].南京:江苏教育出版社,2005.
[21]Kennedy J,Eberhart R C.Particle swarm optimization[C]// Proc IEEE Int Conf Neutral Networks,1995,4: 1942-1948.
[22]Van den Bergh F.An analysis of particle swarm optimizers[D].University of Pretoria,South Africa,2002.
[2]黄大吉,赵进平,苏纪兰.希尔伯特-黄变换的端点延拓.海洋学报[J],2003,25(1):1-11. Huang D J,Zhao J P,Su J L.Practical implementation of the Hilbert-Huang transform algorithm[J].Acta Oceanologica Sinica,2003,25(1):1-11.
[3]邓拥军,王伟,钱成春,等.EMD方法及Hilbert变换中边界问题的处理[J].科学通报,2001,46(3):257-263.
[4]瞿伟廉,程磊.应用径向基函数神经网络处理EMD方法中的边界问题[J].华中科技大学学报:城市科学版,2006,23(4): 1-4. Qu W L,Cheng L.Disposal of boundary problem in EMD method applying RBF neural network[J].Journal of Huazhong University of Science and Technology:Urban Science Edition,2006,23(4):1-4.
[5]杨建文,贾民平.希尔伯特-黄谱的端点效应分析及处理方法研究[J].振动工程学报,2006,19(2):283-288. Yang J W,Jia M P.Study on processing method and analysis of end problem of Hilbert-Huang spectrurn[J]. Journal of Vibration Engineering,2006,19(2):283-288.
[6]刘慧婷,张曼,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用,2004,40(16):84-86. Liu H T,Zhang M,Cheng J X.Dealing with the end issue of EMD based on polynomial fitting algorithm[J]. Computer Engineering and Applications,2004,40(16):84-86.
[7]胡爱军,安连锁,唐贵基.Hilbert-Huang变换端点效应处理新方法[J].机械工程学报,2008,44(4):154-158. Hu A J,An L S,Tang G J.New process method for end effects of Hilbert-Huang transform[J].Chinese Journal of Mechanical Engineering,2008,44(4):154-158.
[8]张郁山,梁建文,胡聿贤.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展,2003,13(10):1054-1059.
[9]罗奇峰,石春香.Hilbert-Huang变换理论及其计算中的问题[J].同济大学学报,2003,31(6):647-640. Luo Q F,Shi C X.Hilbert-Huang transform and several problems in its calculation method[J].Journal of Tongji University,2003,31(6):647-640.
[10]Rilling G,Flandrin P,Goncalves P.On empirical mode decomposition and its algorithms[C]// IEEE EURASIP Workshop on Nonlinear Signal and Image Processing,Grado(I),2003.
[11]张义平,李夕兵,左宇军.爆破振动信号的HHT分析与应用[M].北京:冶金工业出版社,2008.
[12]李夕兵,张义平.基于HHT方法的爆破地震信号分析[J].工程爆破,2005(1):1-7. Li X B,Zhang Y P.Analysis of blasting vibration signal based on HHT method[J].Engineering Blasting,2005(1): 1-7.
[13]李顺国,卢新元.基于粗糙集和SVM的工程项目投标风险研究[J].计算机工程与应用,2008,44(17):224-227. Li S G,Lu X Y.Research of constructional engineering project bidding risk analysis based on rough sets and support vector machine[J].Computer Engineering and Applications,2008,44(17):224-227.
[14]苏怀智,温志萍,吴中如.基于SVM理论的大坝安全预警模型研究[J].应用基础与工程科学学报,2009,17(1):40-47. Su H Z,Wen Z P,Wu Z R.An early-warning model of dam safety based on SVM theory[J].Journal of Basic Science and Engineering,2009,17(1):40-47.
[15]郑一华,徐立中,黄风辰.基于支持向量分类的水质分析应用研究[J].仪器仪表学报,2006,27(6):291-293. Zheng Y H,Xu L Z,Huang F C.Study of water quality analysis based on support vector classification[J].Chinese Journal of Scientific Instrument,2006,27(6):291-293.
[16]Vapnik V N.The nature of statistical learning theory[M].New York:Springer-Verlag,1995.
[17]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000(1):32-42. Zhang X G.Introduction to statistical learning theory and support vector machines[J].Acta Automatica Sinica, 2000(1):32-42.
[18]周涛,张艳宁,袁和金,等.基于改进粒子群算法的支持向量机[J].计算机工程与应用,2007,43(15):44-49. Zhou T,Zhang Y N,Yuan H J,et al.SVM based on improvement particle swarm optimization algorithm[J]. Computer Engineering and Applications,2007,43(15):44-49.
[19]陈炳瑞,冯夏庭.压缩搜索空间与速度范围粒子群优化算法[J].东北大学学报:自然科学版,2005,26(5):488-491. Chen B R,Feng X T.Particle swarm optimization with contracted ranges of both search space and velocity[J]. Journal of Northeastern University:Natural Science Edition,2005,26(5):488-491.
[20]吴启迪,汪镭.智能微粒群算法研究及应用[M].南京:江苏教育出版社,2005.
[21]Kennedy J,Eberhart R C.Particle swarm optimization[C]// Proc IEEE Int Conf Neutral Networks,1995,4: 1942-1948.
[22]Van den Bergh F.An analysis of particle swarm optimizers[D].University of Pretoria,South Africa,2002.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心