基于EMD和VARMA模型的地震动仿真
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摘要
通过EMD方法将地震动分解成若干固有模态函数,提出了用固有模态函数的时变VARMA建模实现地震动仿真的思路。算例分析表明,该方法充分利用了固有模态函数的特性,解决了直接基于ARMA或VARMA模型建模的仿真方法所面临的模型判阶的难题,并可同时考虑地震动的强度和频率非平稳特性,使仿真地震动与实际地震动在能量时频分布特性上具有较好的一致性且样本统计性较好,弹性及弹塑性反应谱拟合精度较高。
By using the empirical mode decomposition(EMD) method to decompose the earthquake ground motion to a finite set of intrinsic mode functions(IMFs),a simulation method based on the time varying VARMA modeling of IMFs is proposed.The numerical results indicate that having advantage of the characteristics of IMFs the method resolves the problem of model order selection,with which the ARMA or VARMA model based methods are confronted and can simultaneously take into account the nonstationarity in amplitude and frequency contents of earthquake ground motions.It is also confirmed that the method has an agreement in energy-time-frequency distribution between the synthesized and the actual ground motions and gives a good performance in sample characteristics and compatibility of elastic and elasto-plastic response spectra.
By using the empirical mode decomposition(EMD) method to decompose the earthquake ground motion to a finite set of intrinsic mode functions(IMFs),a simulation method based on the time varying VARMA modeling of IMFs is proposed.The numerical results indicate that having advantage of the characteristics of IMFs the method resolves the problem of model order selection,with which the ARMA or VARMA model based methods are confronted and can simultaneously take into account the nonstationarity in amplitude and frequency contents of earthquake ground motions.It is also confirmed that the method has an agreement in energy-time-frequency distribution between the synthesized and the actual ground motions and gives a good performance in sample characteristics and compatibility of elastic and elasto-plastic response spectra.
引文
[1]李英民.工程地震动的模型化研究[D].重庆:重庆建筑大学,1999.
[2]Papageorgiou A S.Analysis and simulation of earthquake strong ground motion for earthquake engineering applications[R].Report No.MCEER-04-SP01,Multidisciplinary Center for Earthquake Engineering Research,State University of New York at Buffalo,Buffalo,NY,2004.
[3]徐国栋,周锡元,阎维明,等.考虑超随机特性的人工地震动合成[J].地震工程与工程振动,2005,25(4):11-17.
[4]李英民,董银峰,夏洪流,等.考虑频率非平稳特性的地震波ARMA模型仿真方法[J].重庆建筑大学学报,2000,22(S1):123-127.
[5]董银峰.ARMA模型在地震动仿真和谱估计中的应用[D].重庆:重庆建筑大学.2000.
[6]Conte J P,Pister KS,Mahin S A.Influence of the earthquake ground motion process and structural properties on response characteristics of sim-ple structures[R].Report No.UCB/EERC-90/09,Earthquake Engineering Research Center,University of California,Berkeley,CA,1990.
[7]Dong Y F,Ji S Y,Xiao MK.Simulation of ground motions using time varying vector ARMAmodel[C]//Proc.of the 13thWorld Conference onEarthquake Engineering,2004,PN1469.
[8]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series a-nalysis[J].Proc.of the Royal Society of London,Series A,1998,454(1971):903-995.
[9]Huang N E,Shen Z,Long S R.A new view of nonlinear water waves:the Hilbert spectrum[J].Annu.Rev.Fluid Mech.,1999,31:417-457.
[10]Pandit S M.Modal and spectrum analysis:data dependent systems in state space[M].New York:John Wiley,1991.
[11]Andersen P,Brincker R,Kirkegaard P.Theory of covariance equivalent ARMAV models of civil engineering structures[C]//Proceedings ofIMAC 14,1996,518-524.
[12]Andersen P.Identification of civil engineering structures using ARMA models[D].Aalborg:Aalborg University,1997.
[13]Kalman R E.Anewapproach to linear filtering and prediction problems[J].Journal of Basic Engineering,Transactions of the ASME,Series D,1960,82:35-45.
[14]Ljung L.System Identification—Theory for the User[M].2ndEdition.Upper Saddle River,N.J:PTR Prentice Hall,1999.
[15]Haykin S.Kalman filtering and neural networks[M].New York:John Wiley,2001.
[16]Dong Y F,Zhen NN,Lai M,et al.Estimation of instantaneous spectrum of earthquake ground motions using neural networks[C]//Proc.of the13thWorld Conference on Earthquake Engineering,2004,PN1446.
[2]Papageorgiou A S.Analysis and simulation of earthquake strong ground motion for earthquake engineering applications[R].Report No.MCEER-04-SP01,Multidisciplinary Center for Earthquake Engineering Research,State University of New York at Buffalo,Buffalo,NY,2004.
[3]徐国栋,周锡元,阎维明,等.考虑超随机特性的人工地震动合成[J].地震工程与工程振动,2005,25(4):11-17.
[4]李英民,董银峰,夏洪流,等.考虑频率非平稳特性的地震波ARMA模型仿真方法[J].重庆建筑大学学报,2000,22(S1):123-127.
[5]董银峰.ARMA模型在地震动仿真和谱估计中的应用[D].重庆:重庆建筑大学.2000.
[6]Conte J P,Pister KS,Mahin S A.Influence of the earthquake ground motion process and structural properties on response characteristics of sim-ple structures[R].Report No.UCB/EERC-90/09,Earthquake Engineering Research Center,University of California,Berkeley,CA,1990.
[7]Dong Y F,Ji S Y,Xiao MK.Simulation of ground motions using time varying vector ARMAmodel[C]//Proc.of the 13thWorld Conference onEarthquake Engineering,2004,PN1469.
[8]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series a-nalysis[J].Proc.of the Royal Society of London,Series A,1998,454(1971):903-995.
[9]Huang N E,Shen Z,Long S R.A new view of nonlinear water waves:the Hilbert spectrum[J].Annu.Rev.Fluid Mech.,1999,31:417-457.
[10]Pandit S M.Modal and spectrum analysis:data dependent systems in state space[M].New York:John Wiley,1991.
[11]Andersen P,Brincker R,Kirkegaard P.Theory of covariance equivalent ARMAV models of civil engineering structures[C]//Proceedings ofIMAC 14,1996,518-524.
[12]Andersen P.Identification of civil engineering structures using ARMA models[D].Aalborg:Aalborg University,1997.
[13]Kalman R E.Anewapproach to linear filtering and prediction problems[J].Journal of Basic Engineering,Transactions of the ASME,Series D,1960,82:35-45.
[14]Ljung L.System Identification—Theory for the User[M].2ndEdition.Upper Saddle River,N.J:PTR Prentice Hall,1999.
[15]Haykin S.Kalman filtering and neural networks[M].New York:John Wiley,2001.
[16]Dong Y F,Zhen NN,Lai M,et al.Estimation of instantaneous spectrum of earthquake ground motions using neural networks[C]//Proc.of the13thWorld Conference on Earthquake Engineering,2004,PN1446.
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