地震波时变谱估计方法比较研究
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摘要
利用小波变换、S变换、Hilbert-Huang变换(HHT)、自适应Chirplet变换等现代时频分析技术对Kobe波及El Centro波进行时变谱估计。通过对比分析表明具有自适应分解形式的HHT、Chirplet变换,排除了窗函数、交叉项等造成的种种干扰,具有较高的时频分辨率;S变换对低频分量分辨率较低;小波变换虽然在高频段存在能量泄露现象,但其具有较好的时间分辨率。通过对比Kobe波及El Centro波的时变谱图,可以得到,Kobe波相对于El Centro波具有短持时高能量的特点,由HHT三维图可得到较清晰的局部细节时频特征,了解序列能量在时间-频率平面上的分布情况。
Using modern time-frequency analysis methods:wavelet transform,S-transform,Hilbert-Huang transform and adaptive Chirplet transform,time-varying spectrum estimation was done on Kobe accelerogram record and El Centro accelerogram record.By comparing the analyses,it is showed that the Hilbert-Huang transform and Chirplet transform with the form of adaptive decomposition rules out a variety of interferences caused by the window functions and cross-term and has a high time-frequency resolution;S-transform has low-resolution to a low-frequency component;Although the wavelet transform exists energy leakage in a high-frequency band,it has good temporal resolution.By comparing the time-varying spectrum of the Kobe accelerogram record and El Centro accelerogram record,it is concluded that the Kobe accelerogram record has short duration and high energy characteristics compared with the El Centro accelerogram record,and it could get a clearer time-frequency characteristics of local details by HHT three-dimensional map to understand the distribution of the sequence of energy in terms of a time-frequency plane.
Using modern time-frequency analysis methods:wavelet transform,S-transform,Hilbert-Huang transform and adaptive Chirplet transform,time-varying spectrum estimation was done on Kobe accelerogram record and El Centro accelerogram record.By comparing the analyses,it is showed that the Hilbert-Huang transform and Chirplet transform with the form of adaptive decomposition rules out a variety of interferences caused by the window functions and cross-term and has a high time-frequency resolution;S-transform has low-resolution to a low-frequency component;Although the wavelet transform exists energy leakage in a high-frequency band,it has good temporal resolution.By comparing the time-varying spectrum of the Kobe accelerogram record and El Centro accelerogram record,it is concluded that the Kobe accelerogram record has short duration and high energy characteristics compared with the El Centro accelerogram record,and it could get a clearer time-frequency characteristics of local details by HHT three-dimensional map to understand the distribution of the sequence of energy in terms of a time-frequency plane.
引文
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[2]Wang Junjie,Fan Lichu,Qian Shie.Simulations of non-stationary frequency content and its importance to seismic assessment of structures[J].Earthquake Engineering and Structural Dynamics,2002,31:993―1005.
[3]Mukherjee S,Gupta V K.Wavelet-based characterization of design ground motions[J].Earthquake Engineering and Structural Dynamics,2002,31:1173―1190.
[4]Iyama J,Kuwamura H.Application of wavelets to analysis and simulation of earthquake motions[J].Earthquake Engineering and Structural Dynamics,1999,28:255―272.
[5]Tezcan J.Evolutionary power spectrum estimation using harmonic wavelets[J].Seismic Design and Analysis of Structures,1999,6:37―41.
[6]Spanos P D,Giaralis A,Politis N P.Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition[J].Soil Dynamics and Earthquake Engineering,2007,27:675―689.
[7]曹晖,赖明,白绍良.基于小波变换的地震地面运动仿真研究[J].土木工程学报,2002,35(4):41―46.Cao Hui,Lai Ming,Bai Shaoliang.Study on the simulation of earthquake ground motions based on wavelet transform[J].China Civil Engineering Journal,2002,35(4):41―46.(in Chinese)
[8]Sejdic E,Djurovic I,Jiang J.Time-frequency feature representation using energy concentration:An overview of recent advances[J].Digital Signal Processing,2009,19:153―183.
[9]Basu B,Gupta V K.Wavelet-based stochastic seismic response of a duffing oscillator[J].Journal of Sound and Vibration,2001,245(2):251―260.
[10]Stockwell R G,Mansinha L,Lowe R P.Localization of the complex spectrum:The S transform[J].IEEE Transactions on Signal Processing,1996,44(4):998―1001.
[11]Huang N E,Shen Z,Long S R.The empirical mode decomposition and Hilbert spectrum for Nonlinear and non-stationary time series analysis[J].Proc R Soc Lond A,1998(454):903―995.
[12]Mann S,Haykin S.The chirplet transform:Physical considerations[J].IEEE Transactions on Signal Processing,1995,41(11):2745―2761.
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