非平稳随机过程功率谱密度估计的小波方法
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摘要
讨论了已有文献中基于一般非正交小波以及广义谐和小波的非平稳随机过程演变功率谱密度(EvolutionaryPower Spectral Density,EPSD)估计的问题。在一种新的非平稳随机过程模型(局部平稳小波过程,Locally Sta-tionary Wavelet Process,LSW)的基础上,提出了一种新的估计非平稳随机过程时变功率谱密度的方法。所建议的新方法能与估计非平稳随机过程EPSD的经典方法统一起来,当以上两种方法均使用广义谐和小波时,二者退化为同一形式。为了验证所建议方法的有效性,给出了基于广义谐和小波的多变量均匀调制下非平稳随机地震动互/自功率谱估计的算例。并以汶川8.0级地震中某近场地及远场地上的地震加速度为例,计算得到了其能量在时-频域上的不同分布。
Reviews on the Evolutionary Power Spectrum Density(EPSD) estimation of stochastic process via wavelets are presented in the paper.Based on a newly proposed Local Stationary Wavelet(LSW) model of non-stationary stochastic process,an approach of estimating the time-varying PSD is developed.The proposed approach can be explained in a unified perspective with the classic one.Both the approaches reduce to a same form when the generalized harmonic wavelet is applied.The auto/cross-EPSD of a multi-variable stochastic process is employed as a numerical example to demonstrate the efficiency of the approach.A real world situation,including both the near-field and far-field ground motions of the Wenchuan,China(05/12/2008),are applied as an example to calculate the energy distribution in time-frequency domain.
Reviews on the Evolutionary Power Spectrum Density(EPSD) estimation of stochastic process via wavelets are presented in the paper.Based on a newly proposed Local Stationary Wavelet(LSW) model of non-stationary stochastic process,an approach of estimating the time-varying PSD is developed.The proposed approach can be explained in a unified perspective with the classic one.Both the approaches reduce to a same form when the generalized harmonic wavelet is applied.The auto/cross-EPSD of a multi-variable stochastic process is employed as a numerical example to demonstrate the efficiency of the approach.A real world situation,including both the near-field and far-field ground motions of the Wenchuan,China(05/12/2008),are applied as an example to calculate the energy distribution in time-frequency domain.
引文
[1]Trifunac M D.Response envelope spectrum and inter-pretation of strong earthquake ground motion[J].Bulletin of the Seismological Society of America,1971,61(2):343—356.
[2]Wang J,Fan L,Qian S,et al.Simulations of non-sta-tionary frequency content and its importance to seismicassessment of structures[J].Earthquake Engineering&Structural Dynamics,2002,31(4):993—1 005.
[3]Qian S.Introduction to Time-Frequency and WaveletTransforms[M].Pretice Hall,2001.
[4]Qian S,Chen D.Joint Time-frequency Analysis:Methods and Applications[M].New Jersey:PrenticeHall PTR,1996.
[5]Gabor D.Theory of communication[J].Journal ofthe IEEE,1946,93(III):429—457.
[6]Wexler J,Raz S.Discrete Gabor Expansions[J].Sig-nal Processing,1990,21(3):207—220.
[7]Qian S,Chen D.Discrete Gabor Transform[M].New York,NY,ETATS-UNIS:Institute of Electricaland Electronics Engineers,1993.
[8]Wigner E P.On the quantum correction for the ther-modynamic equilibrium[J].Physics Review,1932,40:749—759.
[9]Ville J.Theorie at applications de la notion de signalanalytique[J].Cables Transm,1948(2):61—74.
[10]Newland D E.An Introduction to Random Vibrations,Spectral and Wavelet Analysis[M].New York:Longman Scientific&Technical,1993.
[11]Daubechies I.Ten Lectures on Wavelets[M].Phila-delphia:Society for Industrial and Applied Mathemat-ics,1992.
[12]Mallat S.Multiresolution approximation and wavelets[J].Tansation of America Mathematics Society,1989,315:69—88.
[13]Grossmann A,Morlet J.Decomposition of Hardyfunction into square intergrable wavelets of constantshape[J].SIAM J.Mathematics Anual,1984,15:723—736.
[14]Basu B.Wavelet-based stochastic seismic response of aduffing oscillator[J].Journal of Sound and Vibration,2001,245(2):251—260.
[15]Basu B,Gupta V K.Stochastic seismic response ofsingle-degree-of-freedom systems through wavelets[J].Engineering Structures,2000,22(12):1 714—1 722.
[16]Basu B,Gupta V K.Seismic response of SDOF sys-tems by wavelet modeling of nonstationary processes[J].Journal of Engineering Mechanics,1998,124(10):1 142—1 150.
[17]Iyama J,Kuwamura H.Application of wavelets to a-nalysis and simulation of earthquake motions[J].Earthquake Engineering&Structural Dynamics,1999,28(3):255—272.
[18]Liang J-W,Chaudhuri S R,Shinozuka,M.Simulationof nonostationary stochastic process by spectral repre-sentation[J].Journal of Engineering Mechanics,2007,133(6):616—627.
[19]Huang G,Chen X.Wavelets-based estimation of mul-tivariate evolutionary spectra and its application tononstationary downburst winds[J].EngineeringStructures,2009,31(4):976—989.
[20]Newland D E.Practical signal analysis:Do waveletsmake any difference?[A].Proceedings of the 16thASME Biennial Conference on Vibration and Noise[C].Sacramento,1997.
[21]Newland D E.Harmonic and musical wavelets[A].Proceedings:Mathematical and Physical Sciences[C].1994a:605—620.
[22]Newland D E.Harmonic wavelet analysis[A].Pro-ceedings of the Royal Society of London.Series A:Mathematical and Physical Sciences[C].1993:203—225.
[23]Spanos P,Tezcan J,Tratskas P.Stochastic processesevolutionary spectrum estimation via harmonic wave-lets[J].Computer Methods in Applied Mechanics andEngineering,2005,194(12-16):1 367—1 383.
[24]Tratskas P,Spanos P D.Linear multi-degree-of-free-domsystem stochastic response by using the harmonicwavelet transform[J].Journal of Applied Mechanics,2003,70(5):724.
[25]Tratskas P.Wavelet-based excitation representationand response determination of linear and nonlinear sys-tems[D].Houston:Rice University,2001.
[26]Spanos P D,Kougioumtzoglou I A.Harmonic wave-let-based statistical linearlization for response evolu-tionary power spectrum determination.[J].Probabi-listic Engineering Mechanics,2011,doi:10.1016/j.probengmech.2011.05.008.
[27]Priestley M B.Spectral Analysis and Time Series[M].Academic Press,1981.
[28]Priestley M B.Evolutionary spectra and non-stationaryprocess[J].Journal of the Royal Statistical Society,Series B,1965,27:204—237.
[29]Spanos P D,Failla G.Evolutionary spectra estimationusing wavelets[J].Journal of Engineering Mechanics,2004,130(8):952—960.
[30]Chakraborty A,Basu B.Nonstationary response anal-ysis of long span bridges under spatially varying differ-ential support motions using continuous wavelet trans-form[J].Journal of Engineering Mechanics,ASCE,2008,134(2):155—162.
[31]Failla G,Pappatico M,Cundari G A.A wavelet-basedspectrum for non-stationary processes[J].MechanicsResearch Communications,2011,38(5):361—367.
[32]Eckley I A,Nason G P,Treloar R L.Locally station-ary wavelet fields with application to the modeling andanalysis of image texture[J].Applied Statistics,2010,59:595—616.
[33]Nason G P,von Sachs R,Kroisandt G.Waveletprocesses and adaptive estimation of the evolutionarywavelet spectrum[J].Journal of the Royal StatisticalSociety:Series B(Statistical Methodology),2000,62(2):271—295.
[34]Matz G,Hlawatsch F,Kozek W.Generalized evolu-tionary spectral analysis and the Weyl spectrum ofnonstationary random processes[M].New York,NY,ETATS-UNIS:Institute of Electrical and Elec-tronics Engineers,1997.
[35]Dahlhaus R.Fitting time series models to non-station-ary processes[J].The Annals of Statistics,1997,25:1—37.
[36]Ombao H,Raz J,Von Sachs R,et al.The SELXmodel of a non-stationary random process[J].Annalsof the Institute of Statistical Mathematics,2002,54:171—200.
[37]Rao M R,Bopardkar S A.Wavelet Transforms:In-troduction to Theory and Applications[M].Massa-chusetts:Addison Wesley Longman,1998.
[38]Deodatis G.Non-stationary stochastic vector proces-ses:seismic ground motion applications[J].Probabi-listic Engineering Mechanics,1996,11(3):149—167.
[2]Wang J,Fan L,Qian S,et al.Simulations of non-sta-tionary frequency content and its importance to seismicassessment of structures[J].Earthquake Engineering&Structural Dynamics,2002,31(4):993—1 005.
[3]Qian S.Introduction to Time-Frequency and WaveletTransforms[M].Pretice Hall,2001.
[4]Qian S,Chen D.Joint Time-frequency Analysis:Methods and Applications[M].New Jersey:PrenticeHall PTR,1996.
[5]Gabor D.Theory of communication[J].Journal ofthe IEEE,1946,93(III):429—457.
[6]Wexler J,Raz S.Discrete Gabor Expansions[J].Sig-nal Processing,1990,21(3):207—220.
[7]Qian S,Chen D.Discrete Gabor Transform[M].New York,NY,ETATS-UNIS:Institute of Electricaland Electronics Engineers,1993.
[8]Wigner E P.On the quantum correction for the ther-modynamic equilibrium[J].Physics Review,1932,40:749—759.
[9]Ville J.Theorie at applications de la notion de signalanalytique[J].Cables Transm,1948(2):61—74.
[10]Newland D E.An Introduction to Random Vibrations,Spectral and Wavelet Analysis[M].New York:Longman Scientific&Technical,1993.
[11]Daubechies I.Ten Lectures on Wavelets[M].Phila-delphia:Society for Industrial and Applied Mathemat-ics,1992.
[12]Mallat S.Multiresolution approximation and wavelets[J].Tansation of America Mathematics Society,1989,315:69—88.
[13]Grossmann A,Morlet J.Decomposition of Hardyfunction into square intergrable wavelets of constantshape[J].SIAM J.Mathematics Anual,1984,15:723—736.
[14]Basu B.Wavelet-based stochastic seismic response of aduffing oscillator[J].Journal of Sound and Vibration,2001,245(2):251—260.
[15]Basu B,Gupta V K.Stochastic seismic response ofsingle-degree-of-freedom systems through wavelets[J].Engineering Structures,2000,22(12):1 714—1 722.
[16]Basu B,Gupta V K.Seismic response of SDOF sys-tems by wavelet modeling of nonstationary processes[J].Journal of Engineering Mechanics,1998,124(10):1 142—1 150.
[17]Iyama J,Kuwamura H.Application of wavelets to a-nalysis and simulation of earthquake motions[J].Earthquake Engineering&Structural Dynamics,1999,28(3):255—272.
[18]Liang J-W,Chaudhuri S R,Shinozuka,M.Simulationof nonostationary stochastic process by spectral repre-sentation[J].Journal of Engineering Mechanics,2007,133(6):616—627.
[19]Huang G,Chen X.Wavelets-based estimation of mul-tivariate evolutionary spectra and its application tononstationary downburst winds[J].EngineeringStructures,2009,31(4):976—989.
[20]Newland D E.Practical signal analysis:Do waveletsmake any difference?[A].Proceedings of the 16thASME Biennial Conference on Vibration and Noise[C].Sacramento,1997.
[21]Newland D E.Harmonic and musical wavelets[A].Proceedings:Mathematical and Physical Sciences[C].1994a:605—620.
[22]Newland D E.Harmonic wavelet analysis[A].Pro-ceedings of the Royal Society of London.Series A:Mathematical and Physical Sciences[C].1993:203—225.
[23]Spanos P,Tezcan J,Tratskas P.Stochastic processesevolutionary spectrum estimation via harmonic wave-lets[J].Computer Methods in Applied Mechanics andEngineering,2005,194(12-16):1 367—1 383.
[24]Tratskas P,Spanos P D.Linear multi-degree-of-free-domsystem stochastic response by using the harmonicwavelet transform[J].Journal of Applied Mechanics,2003,70(5):724.
[25]Tratskas P.Wavelet-based excitation representationand response determination of linear and nonlinear sys-tems[D].Houston:Rice University,2001.
[26]Spanos P D,Kougioumtzoglou I A.Harmonic wave-let-based statistical linearlization for response evolu-tionary power spectrum determination.[J].Probabi-listic Engineering Mechanics,2011,doi:10.1016/j.probengmech.2011.05.008.
[27]Priestley M B.Spectral Analysis and Time Series[M].Academic Press,1981.
[28]Priestley M B.Evolutionary spectra and non-stationaryprocess[J].Journal of the Royal Statistical Society,Series B,1965,27:204—237.
[29]Spanos P D,Failla G.Evolutionary spectra estimationusing wavelets[J].Journal of Engineering Mechanics,2004,130(8):952—960.
[30]Chakraborty A,Basu B.Nonstationary response anal-ysis of long span bridges under spatially varying differ-ential support motions using continuous wavelet trans-form[J].Journal of Engineering Mechanics,ASCE,2008,134(2):155—162.
[31]Failla G,Pappatico M,Cundari G A.A wavelet-basedspectrum for non-stationary processes[J].MechanicsResearch Communications,2011,38(5):361—367.
[32]Eckley I A,Nason G P,Treloar R L.Locally station-ary wavelet fields with application to the modeling andanalysis of image texture[J].Applied Statistics,2010,59:595—616.
[33]Nason G P,von Sachs R,Kroisandt G.Waveletprocesses and adaptive estimation of the evolutionarywavelet spectrum[J].Journal of the Royal StatisticalSociety:Series B(Statistical Methodology),2000,62(2):271—295.
[34]Matz G,Hlawatsch F,Kozek W.Generalized evolu-tionary spectral analysis and the Weyl spectrum ofnonstationary random processes[M].New York,NY,ETATS-UNIS:Institute of Electrical and Elec-tronics Engineers,1997.
[35]Dahlhaus R.Fitting time series models to non-station-ary processes[J].The Annals of Statistics,1997,25:1—37.
[36]Ombao H,Raz J,Von Sachs R,et al.The SELXmodel of a non-stationary random process[J].Annalsof the Institute of Statistical Mathematics,2002,54:171—200.
[37]Rao M R,Bopardkar S A.Wavelet Transforms:In-troduction to Theory and Applications[M].Massa-chusetts:Addison Wesley Longman,1998.
[38]Deodatis G.Non-stationary stochastic vector proces-ses:seismic ground motion applications[J].Probabi-listic Engineering Mechanics,1996,11(3):149—167.
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