新型随机地震动模型
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摘要
在研究结构的随机地震反应时,要用大量的符合场地条件的地震记录作为输入数据。但强震历史记录却不是每个地区都有的,因此根据符合场地条件的现有地震记录建立随机地震动模型具有重要意义。本文利用中国抗震规范2001版修正选取的样本波作为目标波,考虑了幅值和频率的双重非平稳性,建立了新型随机地震动模型———改进的时变ARMA模型随机地震动模型。通过使用残差的卡方检验法,对多种非平稳ARMA模型生成的模拟波进行检验;同时又比较了模拟波与目标波的功率谱密度图和反应谱图。结果证明:此法能够更精确地反映不同场地条件地震动的频谱和幅值的真实内容,从而建立符合目标场地条件的更为有效的模拟地震动,为相关研究与工程设计架起一座桥梁。
When the stochastic seismic response of the structures is studied,lots of the earthquake records fit for the selected site are necessary to be used for initial data for structure model analysis.In the given site it always hasn't the strong earthquake records,thus it's very significant to make satisfactory model used to describe realistic earthquake ground motion time history matching the location condition.In this paper,using the sample records reformed by Chinese code 2001 version for seismic design of buildings as target earthquake records,the modified discrete time-varying ARMA model is made.Both amplitude and frequency nonstationarities are incorporated in the model.Chi-Square verification tests are performed in the different nonstationary ARMA model.Applications of these verification procedures are given and show that the proposed models are able to reflect accurately the nonstationary features of real earthquake accelerogram,including both the time-variation of the frequency and amplitude content.Thus the more efficiently simulated earthquake records matching the site's condition are made.It sets up a bridge from the research to civil engineering design.
When the stochastic seismic response of the structures is studied,lots of the earthquake records fit for the selected site are necessary to be used for initial data for structure model analysis.In the given site it always hasn't the strong earthquake records,thus it's very significant to make satisfactory model used to describe realistic earthquake ground motion time history matching the location condition.In this paper,using the sample records reformed by Chinese code 2001 version for seismic design of buildings as target earthquake records,the modified discrete time-varying ARMA model is made.Both amplitude and frequency nonstationarities are incorporated in the model.Chi-Square verification tests are performed in the different nonstationary ARMA model.Applications of these verification procedures are given and show that the proposed models are able to reflect accurately the nonstationary features of real earthquake accelerogram,including both the time-variation of the frequency and amplitude content.Thus the more efficiently simulated earthquake records matching the site's condition are made.It sets up a bridge from the research to civil engineering design.
引文
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[2]Nau R F,O liver R M,P ister K S.S imu lating and analyzing artificial nonstationary earthquake ground motions[R].1980,Report No.UCB/EERC-80/36,Earthquake Engineering Research Center,Un iversity of Californ ia,Berkeley,CA,1980.
[3]Polhemus N W,Cakmak A S.S imu lation on earthquake ground motions using autoregressive moving average(ARMA)models[J].EESD,1981,9(4):343~354.
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[5]蒋溥,梁小华,雷军.工程地震动时程合成与模拟[M].北京:地震出版社,1991.33~36.
[6]李英民.地震波仿真及多刚体离散模型在剪切型结构地震反应分析中的应用[D].重庆:重庆建筑大学,1992
[7]胡孔国,陈小兵,岳清瑞.随机地震动模拟的时间序列法及其工程应用[J].世界地震工程,2003.19,(1):141~153.
[8]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(Sup.):123~127.
[9]ChangM K,Kw iatkowsk i JW,Nau R F,et al.ARMA Models for Earthquake G round Motions[R].Un iv.of Calif.Tech.ReportORC 79-1,Operations Research Center,Berkeley,CA,1979.
[10]Kozin F.Estimation,Modeling ofNon-Stationary Tim e Series[A].Proc.Symp.ComputerM eth.in Eng.Un iv.of Southern Californ ia[C].LosAngeles,1979.
[11]Ahm et S Cakmak,Russell I.Sherif and G lenn ellis.Modeling earthquake ground motions in Californ ia using param etric tim e seriesm ethods[J].Soil Dynam ics and Earthquake Engineering,1985,4(3):124~131.
[12]Conte JP,P isterKS,Mah in SA.Nonstationary ARMA modeling of seism ic motions[J].Soil Dynam ics and Earthquake Engineering,1992,11:411~426.
[13]AghababaiiMobarakeh A,Rofooei F R,Ahmad i G.S imu lation of earthquake records using tim e-varying Arma(2,1)model[J].Probab ilisticEngineeringM echan ics,2002,17:15~34.
[14]章在墉.地震危险性分析及其应用[M].上海:同济大学.1996.
[15]GB 50011-2001,建筑抗震规范[S].
[16]陈兆国.时间序列及其谱分析[M].北京:科学出版社,1988.
[2]Nau R F,O liver R M,P ister K S.S imu lating and analyzing artificial nonstationary earthquake ground motions[R].1980,Report No.UCB/EERC-80/36,Earthquake Engineering Research Center,Un iversity of Californ ia,Berkeley,CA,1980.
[3]Polhemus N W,Cakmak A S.S imu lation on earthquake ground motions using autoregressive moving average(ARMA)models[J].EESD,1981,9(4):343~354.
[4]Conte J P,P isterK S,Mah in,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,Un iversity of Californ ia,Berkeley,CA.1990.1~25.
[5]蒋溥,梁小华,雷军.工程地震动时程合成与模拟[M].北京:地震出版社,1991.33~36.
[6]李英民.地震波仿真及多刚体离散模型在剪切型结构地震反应分析中的应用[D].重庆:重庆建筑大学,1992
[7]胡孔国,陈小兵,岳清瑞.随机地震动模拟的时间序列法及其工程应用[J].世界地震工程,2003.19,(1):141~153.
[8]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(Sup.):123~127.
[9]ChangM K,Kw iatkowsk i JW,Nau R F,et al.ARMA Models for Earthquake G round Motions[R].Un iv.of Calif.Tech.ReportORC 79-1,Operations Research Center,Berkeley,CA,1979.
[10]Kozin F.Estimation,Modeling ofNon-Stationary Tim e Series[A].Proc.Symp.ComputerM eth.in Eng.Un iv.of Southern Californ ia[C].LosAngeles,1979.
[11]Ahm et S Cakmak,Russell I.Sherif and G lenn ellis.Modeling earthquake ground motions in Californ ia using param etric tim e seriesm ethods[J].Soil Dynam ics and Earthquake Engineering,1985,4(3):124~131.
[12]Conte JP,P isterKS,Mah in SA.Nonstationary ARMA modeling of seism ic motions[J].Soil Dynam ics and Earthquake Engineering,1992,11:411~426.
[13]AghababaiiMobarakeh A,Rofooei F R,Ahmad i G.S imu lation of earthquake records using tim e-varying Arma(2,1)model[J].Probab ilisticEngineeringM echan ics,2002,17:15~34.
[14]章在墉.地震危险性分析及其应用[M].上海:同济大学.1996.
[15]GB 50011-2001,建筑抗震规范[S].
[16]陈兆国.时间序列及其谱分析[M].北京:科学出版社,1988.
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