运用希尔伯特黄变换进行多分量信号的频散分析
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摘要
基于谱分析原理将希尔伯特黄变换应用于多分量信号的频散分析,通过希尔伯特时频能量谱获得每个单分量信号的能量分布和群速度,通过希尔伯特时频相位谱获得每个单分量信号的相速度。在相速度的计算过程中提出异步相差和校正相差的算法,可以有效避免相位解缠。仿真结果表明,上述方案可以获得较为准确的频散分析结果。
The Hilbert-Huang transform is used to analyse frequency dispersion of multi-component signal based on SASW(Spectral Analysis of Surface Waves).The group velocity and energy distribution of every single component signal can be obtained from the Hilbert time-frequency-energy spectrum.The phase velocity of every single component signal can be obtained from the Hilbert time-frequency-phase spectrum.In the process of calculating the phase velocity,the algorithm of asynchronous phase difference and emendation phase difference is advanced to solve the problem of phase unwrapping.The simulation results indicate that both above methods can lead to more satisfactory results in analysis of frequency dispersion.
The Hilbert-Huang transform is used to analyse frequency dispersion of multi-component signal based on SASW(Spectral Analysis of Surface Waves).The group velocity and energy distribution of every single component signal can be obtained from the Hilbert time-frequency-energy spectrum.The phase velocity of every single component signal can be obtained from the Hilbert time-frequency-phase spectrum.In the process of calculating the phase velocity,the algorithm of asynchronous phase difference and emendation phase difference is advanced to solve the problem of phase unwrapping.The simulation results indicate that both above methods can lead to more satisfactory results in analysis of frequency dispersion.
引文
[1]Dong-Soo Kim,Hyung-Choon Park.Determination of dis-persive phase velocities for SASW method using harmonicwavelet transform[J].Soil Dynamics and Earthquake Engi-neering,2002,22(8):675-684.
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[5]Norden E Huang,Zheng Shen,Steven RLong.The empiricalmode decomposition and the Hilbert spectrumfor nonlinearand non-stationarytime series analysis[J].Proceedings ofthe Royal Society A:Mathematical Physical and EngineeringSciences,1998,454(1971):903-995.
[6]Norden Huang,Zhengshen,Steven R Long.Anewviewofnonlinear water waves:The Hilbert Spectrum[J].Annual Re-viewof Fluid Mechanics,1999,31(1):417-457.
[7]Chau-Huei Chen,Cheng-Pling Li,Ta-Liang Teng.Sur-face-Wave Dispersion Measurements Using Hilbert-HuangTransform[J].Terrestrial,Atmospheric and Ocean Sciences,2002,13(2):171-184.
[8]李白基,师洁珊,宋子安,等.地震面波的数字计算[J].地球物理学报,1977,20(4):283-298.LI Bai-ji,SHI Jie-shan,SONG Zi-an,et al.DigitalProcessing for Seismic Surface Wave Dispersion[J].ActaGeophysica Sinica,1977,20(4):283-298.(in Chinese)
[9]LI Jiang,XU Yixian.Analysis of dispersion of phase veloci-ties using empirical mode frequency decomposition on SASW[C]//Proceedings of Near-Surface Geophysics and Geo-hazards.Chengdu:Science Press,2010:225-231.
[10]程乾生,武连文.时间序列的经验模态频率分解EMFD[J].数学的实践与认识,2005,36(5):151-153.CHENG Qian-sheng,WU Lian-wen.The EmpiricalMode Frequency Decomposition for Time Series Analysis[J].Mathematics in Practice and Theory,2005,36(5):151-153.(in Chinese)
[2]Jianghai Xia,Richard D Miller,Choon B Park,et al.Compar-ing shear-wave velocity profiles from MASW with boreholemeasurementsin unconsolidated sediments[J].Journal of Envi-ronmental and Engineering Geophysics,2000,5(3):1-13.
[3]科恩.时频分析:理论与应用[M].白居宪,译.西安:西安交通大学出版社,1998.Leon Cohen.Time-Frequency Analysis:Theory and Appli-cations[M].Translated by BAI Ju-xian.Xi′an:Xi′anJiaotong University Press,1998.(in Chinese)
[4]Norden E Huang,Zhaohua Wu.A Review on Hilbert-Huang Transform:Method anIts Applicationsto GeophysicalStudies[J].Reviews of Geophysics,2008,46(2):1-23.
[5]Norden E Huang,Zheng Shen,Steven RLong.The empiricalmode decomposition and the Hilbert spectrumfor nonlinearand non-stationarytime series analysis[J].Proceedings ofthe Royal Society A:Mathematical Physical and EngineeringSciences,1998,454(1971):903-995.
[6]Norden Huang,Zhengshen,Steven R Long.Anewviewofnonlinear water waves:The Hilbert Spectrum[J].Annual Re-viewof Fluid Mechanics,1999,31(1):417-457.
[7]Chau-Huei Chen,Cheng-Pling Li,Ta-Liang Teng.Sur-face-Wave Dispersion Measurements Using Hilbert-HuangTransform[J].Terrestrial,Atmospheric and Ocean Sciences,2002,13(2):171-184.
[8]李白基,师洁珊,宋子安,等.地震面波的数字计算[J].地球物理学报,1977,20(4):283-298.LI Bai-ji,SHI Jie-shan,SONG Zi-an,et al.DigitalProcessing for Seismic Surface Wave Dispersion[J].ActaGeophysica Sinica,1977,20(4):283-298.(in Chinese)
[9]LI Jiang,XU Yixian.Analysis of dispersion of phase veloci-ties using empirical mode frequency decomposition on SASW[C]//Proceedings of Near-Surface Geophysics and Geo-hazards.Chengdu:Science Press,2010:225-231.
[10]程乾生,武连文.时间序列的经验模态频率分解EMFD[J].数学的实践与认识,2005,36(5):151-153.CHENG Qian-sheng,WU Lian-wen.The EmpiricalMode Frequency Decomposition for Time Series Analysis[J].Mathematics in Practice and Theory,2005,36(5):151-153.(in Chinese)
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