非平稳地震地面运动分析方法及模型综述
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摘要
地震引起的地面运动是短暂的和非平稳的,地面运动的强度和频率都具有时变性,结构的分析和设计必须考虑地面运动的非平稳特性。文中回顾和总结了非平稳地震动分析方法,主要包括短时傅立叶变换、瞬时谱、双频谱法、演变谱法、小波变换、非平稳ARMA模型和HHT变换。同时介绍了常用的非平稳地震地面运动模型。在论述各种方法和非平稳地震动模型的同时,对国内外研究发展状况给出了简要的评述,并对非平稳地震动未来分析方法和模型发展趋势做出了预测和展望。
The earthquake induced ground motions are transient and non-stationary.Both their amplitude and frequency content vary with time.Analysis and design of structures need to consider these non-stationary char- acteristics.In the paper,an overview is given on analysis method of non-stationary earthquake.It includes Short Time Fourier Transform,Wigner-Ville Distribution,Bispectrum,Evolutionary Spectra,Wavelet Trans- form,Non-stationary ARMA model and Hilbert Huang Transform(HHT).The paper also introduces frequent- ly-used model of non-stationary earthquake ground motion.In addition,a comparison is made between the do- mestic and international studies on the aforementioned topics.Finally,recommendations are given for future development of the analysis method and model of non-stationary earthquake ground motion.
The earthquake induced ground motions are transient and non-stationary.Both their amplitude and frequency content vary with time.Analysis and design of structures need to consider these non-stationary char- acteristics.In the paper,an overview is given on analysis method of non-stationary earthquake.It includes Short Time Fourier Transform,Wigner-Ville Distribution,Bispectrum,Evolutionary Spectra,Wavelet Trans- form,Non-stationary ARMA model and Hilbert Huang Transform(HHT).The paper also introduces frequent- ly-used model of non-stationary earthquake ground motion.In addition,a comparison is made between the do- mestic and international studies on the aforementioned topics.Finally,recommendations are given for future development of the analysis method and model of non-stationary earthquake ground motion.
引文
[1]Mark W D.Spectra analysis of the convolution and filtering of non-stationary stochastic process[J].J Sound Vib,1970,11(1):19-63.
[2]Priestly M B.Evolutionary and Non-stationary proces- ses[J].Journal of the Royal Statistical Society, 1965,27:204-237.
[3]何岭松．小波函数性质及其对小波分析结果的影响[J]．振动工程学报，2000，13(1)：143-146．
[4]Huang N E,et al.The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Pro R Soc,1998,454:903- 906.
[5]胡聿贤，周锡元．弹性体系在平稳化地面运动下的反应[C]．地震工程研究报告集(一)，1962：33- 50．
[6]Shinozuka M,Sato Y.Simulation of nonstationary random process[J].Journal of Engineering Mechan- ics Division,ASCE,1967,93(1):11-40.
[7]Levy B,Kozin F,Moorman R B.A Random proces- ses for earthquake simulation[J].Journal of Engi- neering Mechanics Division,ASCE,1971,97(2): 495-517.
[8]Iyengar R N,Iyengar K T.A nonstationary random process model for earthquake accelerations[C]. BSSA,1969(59):1163-1188.
[9]Saragoni G R,Hart G C.Simulation of artificial earthquakes[J].Earthquake Engineering and Struc- tural Dynamics,1974,2(3):249-267.
[10]Jurkevics A,Ulrych T J.Representing and simulating strong ground motion[J].BSSA,1978,68(3):781- 801.
[11]陈永祁，刘锡荟，龚思礼．拟合标准反应谱的人工地震波[J]．建筑结构学报，1981，2(4)：34-42．
[12]宋雅桐，朱继澄．满足规范设计谱的人造地震波及若干结构反应[J]．建筑结构学报，1982，3 (4)：43-54．
[13]霍俊荣，胡聿贤，冯启民．地面运动时程强度包络函数的研究[J]．地震工程与工程振动，1991，11 (1)：1-12．
[14]Ohsaki Y,Watabe M,Tohodo M.Analysis on seis- mic ground motion parameters including vertical com- ponents[C]//Proceedings of the 7~(th)WCEE,Istan- bul,Turkey,1980,2:97-104.
[15]Polhemus N W,Cakmak A S.Simulation on earth- quake ground motions using autoregressive moving average(ARMA)models[J].EESD,1981,9(4): 343-354.
[16]Bolotin V V.Statistical theory of the aseismic design of structures[C]//Pro.2~(nh).World conf.on earth- quake engineering.Tokyo Japan,1960:1365-1374.
[17]Bogdanoff J L,Goldberg J E,Bernard M C.Re- sponse of a simple structrure to a random earthquake- type disturbance[J].Bull Seismol Soc Am,1961, 51:293-310.
[18]Goldberg J E,Bogdanoff J L,Sharpe D R.The re- sponse of simple nonlinear structure to a random dis- turbance of earthquake type[J].Bull Seismol Soc Am,1964,54:263-276.
[19]Amin M,A H-S Ang.A nonstationary random processes[J].J Eng Mech Div ASCE,1967,93(1): 11-40.
[20]Shinozuka M.Engineering modeling of ground motion [C]//Proc of the 9~(th)WCEE,Tokyo-Kyoto Japan, 1988,8:51-62.
[21]Ohsaki Y.On the significance of phase content in earthquake ground motion[J].EESD,1979,7(4): 427-439.
[22]金星，廖振鹏．地震动相位特性的研究[J]．地震工程与工程振动，1993，13(1)：7-13．
[23]胡聿贤，何训．考虑相位谱的人造地震动反应谱拟合[J]．地震工程与工程振动，1986，6(2)：37- 51．
[24]朱昱，冯启民．相位差谱的分布特征和人造地震动[J]．地震工程与工程振动，1992，12(1)：37- 44．
[25]赵风新，胡聿贤．地震动非平稳性与幅值谱和相位差谱的关系[J]．地震工程与工程振动，1994，14(2)：1-6．
[26]Trifunac M D,Brune J N.Complexity of energy re- lease during the imperial vallery earthquake of 1940 [J].BSSA,1970,60(1):137-160.
[27]Kubo T,Watabe M.Simulation of there-dimensional strong ground motions along principal axes,San Fer- nando Earthquake[J].EESD,1979,7:279-294.
[28]Trifunac M D.Response envelope spectrum and in- terpretation of strong ground motion[J].BSSA, 1971,61(2):343-356.
[29]Kameda H.Evolutionary spectra of seismogram by multifilter[J].Journal of Engineering Mechanics di- vision,ASCE,1975,101:787-801.
[30]Schüeller G I,Pradlwarter H J.Estimation of the ev- olutionary process of strongly nonstationary earth- quake records[C]//Proc.of the 9~(th).WCEE,Tokyo- Kyoto,Japan,1988,Vol:777-782.
[31]Conte J P,Pister K S,Mahin S A.Influence of the earthquake ground motion process and structural properties on response characteristics of simple struc- tures[C].Report No.UCB/EERC-90/09,earth- quake engineering research center,university of Cali- fornia,Berkeley,CA,1990.
[32]Der Kiureghian A,Crempien J.An evolutionary model for earthquake ground motion[J].Structural safety,1989,6:235-246.
[33]Li Y,Kareem A.Simulation of multivariate nonsta- tionary random processes by FFT[J].J Engrg Mech,ASCE,1991,117(5):1037-1058.
[34]Kameda H.Evolutionary spectra of seismogram by multifilter[J].J Engrg Mech Div,ASCE,1975:101 (6):787-801.
[35]Scherer R J,Riera J D,Schueller G I.Estimation of the time-dependent frequency content of earthquake accelerations[J].Nuclear Engrg & Des,1982,71: 301-310.
[36]Preumont A.The generation of non-separable artifi- cial earthquake accelerograms for design of nuclear power plants[J].Nuclear Engrg Des,1985,88:59- 67.
[37]Scherer R J.On the frequency dependence of the strong ground motion duration[C].Structural safety and reliability,Schueller,shinozuka,and yao,eds., Balkema publishers,Rotterdam,The Netherlands, 1994:2201-2223.
[38]Grigoriu M.Simulation of nonstationary Gaussian processes by random trigonometric polynomials[J].J Engrg Mech,ASCE,1993,119(2):328-343.
[39]Mark W D.Spectral analysis of the convolution and filtering of non-stationary stochastic processes[J].J Sound Vib,1970,11:19-63.
[40]Crempien-Laborie J E,Orosco L.An evolutionary ground motion model for earthquake analysis of struc- tures in zones with little history[J].Soil Dnamics and Earthquake Engineering,2000,20:373-397.
[41]Kameda H.Evolutionary spectra of seismogram by multifilter[J].J Eng Mech ASCE,1975,101 (EM6):787-801.
[42]Lin Y K,Yong Y.Evolutionary Kanai-Tajimi earth- quake models[J].J Eng Mech ASCE,1987,113 (8):1119-1137.
[43]Fan F G,Ahmadi G.Nonstationary Kanai-Tajimi models for EI Centro 1940 and Mexico City 1985 Earthquake[J].Probabilistic Engrg Meeh,1990,5 (4):171-181.
[44]Yeh C H,Wen Y K.Model of nonstationary earth- quake ground motion and application[C]//Proceed- ings of fourth U.S.national conference on earth- quake engineering,1990,1:505-514.
[45]Gu P.Hilbert-Huang-transform based modeling and simulation of nonstationary processes and applications to earthquake engineering[D].Urbana Illinois:uni- versity of Illinois at Urbana-Champaige,2004.
[46]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．
[47]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．
[48]曾珂，牛荻涛．基于时变ARMA序列的随机地震动模型[J]．工程抗震与加固改造，2005，27(3)：81-86．
[49]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．
[50]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，2000，22，123-127．
[51]Chang M K,Kwiatkowski J W,Nau R F,et al.AB- MA models for earthquake ground motions[C]. Univ.of Calif.Tech.Report ORC 79-1,operations research center,Berkeley,CA,1979.
[52]Kozin F.Estimation and modeling non-stationary time series[C].Proc.Symp.Computer Meth.In Eng. Univ.of southern California,1979.
[53]Ahmet S Cakmak,Russell I S,Glenn E.Modeling earthquake ground motions in California using para- metric time series methods[J].Soil Dynamics and Earthquake Engineering,1985,4(3):124-131.
[54]Conte J P,Prister K S,Mahin S A.Nonstationary ARMA modeling of seismic motions[J].Soil Dy- namics and Earthquake Engineering,1992,11:411- 426.
[55]Deodatis G,Shinozuka M.Auto-regressive model for nonstationary stochastic processes[J].J Eng Mech ASCE,1988,114(11):1995-2012.
[56]Mobarakeh A A,Rofooei F R,Ahmadi G.Simula- tion of earthquake records using time-varying Arma (2,1)model[J].Probabilistic Engineering Me- chanics,2002,17:15-34.
[57]lyama J,Kuwamura H.Application of wavelets to a- nalysis and simulation of earthquake motions[J]. Earthquake Engng Struct Dyn,1999,28:255-272.
[58]Spanos P D,Tezcan J,Tratskas P.Stochastic processes evolutionary spectrum estimation via har- monic wavelets[J].Comput Methods Appl Mech En- grg,2005,194:1367-1383.
[59]Mukherjee S,Gupta V K.Wavelet-based Character- ization of Design Ground Motion[J].Earthquake Engineering and Structural Dynamics,2002,31: 1173-1190.
[60]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)：40- 46．
[61]李英民，赖明．工程地震动模型化研究综述及展望Ⅲ——其他工程学模型与展望[J]．重庆建筑大学学报，1998，20(5)：108-114．
[62]Safak E,Boore D M.On nonstationary stocha stic models for earthquakes[C].Third U.S.national conference on earthquake engineering,1986,1:137- 148.
[63]Elishakoff I,Lyon R H.Random vibration status and recent developments[M].Amsterdam-Oxford-New York-Tokyo:ELSEVIER,1986.
[64]Bendat J S,Piersol A G.Random data analysis and measurement procedures[M].3~(rd)Edition.New York:JOHN EILEY & SONS,INC,2000.
[65]王宏禹．非平稳随机信号分析与处理[M]．北京：国防工业出版社，1999．
[66]Daubechies I．小波十讲[M]．李建平，杨万年，译．北京：国防工业出版社．2004．
[2]Priestly M B.Evolutionary and Non-stationary proces- ses[J].Journal of the Royal Statistical Society, 1965,27:204-237.
[3]何岭松．小波函数性质及其对小波分析结果的影响[J]．振动工程学报，2000，13(1)：143-146．
[4]Huang N E,et al.The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Pro R Soc,1998,454:903- 906.
[5]胡聿贤，周锡元．弹性体系在平稳化地面运动下的反应[C]．地震工程研究报告集(一)，1962：33- 50．
[6]Shinozuka M,Sato Y.Simulation of nonstationary random process[J].Journal of Engineering Mechan- ics Division,ASCE,1967,93(1):11-40.
[7]Levy B,Kozin F,Moorman R B.A Random proces- ses for earthquake simulation[J].Journal of Engi- neering Mechanics Division,ASCE,1971,97(2): 495-517.
[8]Iyengar R N,Iyengar K T.A nonstationary random process model for earthquake accelerations[C]. BSSA,1969(59):1163-1188.
[9]Saragoni G R,Hart G C.Simulation of artificial earthquakes[J].Earthquake Engineering and Struc- tural Dynamics,1974,2(3):249-267.
[10]Jurkevics A,Ulrych T J.Representing and simulating strong ground motion[J].BSSA,1978,68(3):781- 801.
[11]陈永祁，刘锡荟，龚思礼．拟合标准反应谱的人工地震波[J]．建筑结构学报，1981，2(4)：34-42．
[12]宋雅桐，朱继澄．满足规范设计谱的人造地震波及若干结构反应[J]．建筑结构学报，1982，3 (4)：43-54．
[13]霍俊荣，胡聿贤，冯启民．地面运动时程强度包络函数的研究[J]．地震工程与工程振动，1991，11 (1)：1-12．
[14]Ohsaki Y,Watabe M,Tohodo M.Analysis on seis- mic ground motion parameters including vertical com- ponents[C]//Proceedings of the 7~(th)WCEE,Istan- bul,Turkey,1980,2:97-104.
[15]Polhemus N W,Cakmak A S.Simulation on earth- quake ground motions using autoregressive moving average(ARMA)models[J].EESD,1981,9(4): 343-354.
[16]Bolotin V V.Statistical theory of the aseismic design of structures[C]//Pro.2~(nh).World conf.on earth- quake engineering.Tokyo Japan,1960:1365-1374.
[17]Bogdanoff J L,Goldberg J E,Bernard M C.Re- sponse of a simple structrure to a random earthquake- type disturbance[J].Bull Seismol Soc Am,1961, 51:293-310.
[18]Goldberg J E,Bogdanoff J L,Sharpe D R.The re- sponse of simple nonlinear structure to a random dis- turbance of earthquake type[J].Bull Seismol Soc Am,1964,54:263-276.
[19]Amin M,A H-S Ang.A nonstationary random processes[J].J Eng Mech Div ASCE,1967,93(1): 11-40.
[20]Shinozuka M.Engineering modeling of ground motion [C]//Proc of the 9~(th)WCEE,Tokyo-Kyoto Japan, 1988,8:51-62.
[21]Ohsaki Y.On the significance of phase content in earthquake ground motion[J].EESD,1979,7(4): 427-439.
[22]金星，廖振鹏．地震动相位特性的研究[J]．地震工程与工程振动，1993，13(1)：7-13．
[23]胡聿贤，何训．考虑相位谱的人造地震动反应谱拟合[J]．地震工程与工程振动，1986，6(2)：37- 51．
[24]朱昱，冯启民．相位差谱的分布特征和人造地震动[J]．地震工程与工程振动，1992，12(1)：37- 44．
[25]赵风新，胡聿贤．地震动非平稳性与幅值谱和相位差谱的关系[J]．地震工程与工程振动，1994，14(2)：1-6．
[26]Trifunac M D,Brune J N.Complexity of energy re- lease during the imperial vallery earthquake of 1940 [J].BSSA,1970,60(1):137-160.
[27]Kubo T,Watabe M.Simulation of there-dimensional strong ground motions along principal axes,San Fer- nando Earthquake[J].EESD,1979,7:279-294.
[28]Trifunac M D.Response envelope spectrum and in- terpretation of strong ground motion[J].BSSA, 1971,61(2):343-356.
[29]Kameda H.Evolutionary spectra of seismogram by multifilter[J].Journal of Engineering Mechanics di- vision,ASCE,1975,101:787-801.
[30]Schüeller G I,Pradlwarter H J.Estimation of the ev- olutionary process of strongly nonstationary earth- quake records[C]//Proc.of the 9~(th).WCEE,Tokyo- Kyoto,Japan,1988,Vol:777-782.
[31]Conte J P,Pister K S,Mahin S A.Influence of the earthquake ground motion process and structural properties on response characteristics of simple struc- tures[C].Report No.UCB/EERC-90/09,earth- quake engineering research center,university of Cali- fornia,Berkeley,CA,1990.
[32]Der Kiureghian A,Crempien J.An evolutionary model for earthquake ground motion[J].Structural safety,1989,6:235-246.
[33]Li Y,Kareem A.Simulation of multivariate nonsta- tionary random processes by FFT[J].J Engrg Mech,ASCE,1991,117(5):1037-1058.
[34]Kameda H.Evolutionary spectra of seismogram by multifilter[J].J Engrg Mech Div,ASCE,1975:101 (6):787-801.
[35]Scherer R J,Riera J D,Schueller G I.Estimation of the time-dependent frequency content of earthquake accelerations[J].Nuclear Engrg & Des,1982,71: 301-310.
[36]Preumont A.The generation of non-separable artifi- cial earthquake accelerograms for design of nuclear power plants[J].Nuclear Engrg Des,1985,88:59- 67.
[37]Scherer R J.On the frequency dependence of the strong ground motion duration[C].Structural safety and reliability,Schueller,shinozuka,and yao,eds., Balkema publishers,Rotterdam,The Netherlands, 1994:2201-2223.
[38]Grigoriu M.Simulation of nonstationary Gaussian processes by random trigonometric polynomials[J].J Engrg Mech,ASCE,1993,119(2):328-343.
[39]Mark W D.Spectral analysis of the convolution and filtering of non-stationary stochastic processes[J].J Sound Vib,1970,11:19-63.
[40]Crempien-Laborie J E,Orosco L.An evolutionary ground motion model for earthquake analysis of struc- tures in zones with little history[J].Soil Dnamics and Earthquake Engineering,2000,20:373-397.
[41]Kameda H.Evolutionary spectra of seismogram by multifilter[J].J Eng Mech ASCE,1975,101 (EM6):787-801.
[42]Lin Y K,Yong Y.Evolutionary Kanai-Tajimi earth- quake models[J].J Eng Mech ASCE,1987,113 (8):1119-1137.
[43]Fan F G,Ahmadi G.Nonstationary Kanai-Tajimi models for EI Centro 1940 and Mexico City 1985 Earthquake[J].Probabilistic Engrg Meeh,1990,5 (4):171-181.
[44]Yeh C H,Wen Y K.Model of nonstationary earth- quake ground motion and application[C]//Proceed- ings of fourth U.S.national conference on earth- quake engineering,1990,1:505-514.
[45]Gu P.Hilbert-Huang-transform based modeling and simulation of nonstationary processes and applications to earthquake engineering[D].Urbana Illinois:uni- versity of Illinois at Urbana-Champaige,2004.
[46]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．
[47]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．
[48]曾珂，牛荻涛．基于时变ARMA序列的随机地震动模型[J]．工程抗震与加固改造，2005，27(3)：81-86．
[49]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．
[50]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，2000，22，123-127．
[51]Chang M K,Kwiatkowski J W,Nau R F,et al.AB- MA models for earthquake ground motions[C]. Univ.of Calif.Tech.Report ORC 79-1,operations research center,Berkeley,CA,1979.
[52]Kozin F.Estimation and modeling non-stationary time series[C].Proc.Symp.Computer Meth.In Eng. Univ.of southern California,1979.
[53]Ahmet S Cakmak,Russell I S,Glenn E.Modeling earthquake ground motions in California using para- metric time series methods[J].Soil Dynamics and Earthquake Engineering,1985,4(3):124-131.
[54]Conte J P,Prister K S,Mahin S A.Nonstationary ARMA modeling of seismic motions[J].Soil Dy- namics and Earthquake Engineering,1992,11:411- 426.
[55]Deodatis G,Shinozuka M.Auto-regressive model for nonstationary stochastic processes[J].J Eng Mech ASCE,1988,114(11):1995-2012.
[56]Mobarakeh A A,Rofooei F R,Ahmadi G.Simula- tion of earthquake records using time-varying Arma (2,1)model[J].Probabilistic Engineering Me- chanics,2002,17:15-34.
[57]lyama J,Kuwamura H.Application of wavelets to a- nalysis and simulation of earthquake motions[J]. Earthquake Engng Struct Dyn,1999,28:255-272.
[58]Spanos P D,Tezcan J,Tratskas P.Stochastic processes evolutionary spectrum estimation via har- monic wavelets[J].Comput Methods Appl Mech En- grg,2005,194:1367-1383.
[59]Mukherjee S,Gupta V K.Wavelet-based Character- ization of Design Ground Motion[J].Earthquake Engineering and Structural Dynamics,2002,31: 1173-1190.
[60]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)：40- 46．
[61]李英民，赖明．工程地震动模型化研究综述及展望Ⅲ——其他工程学模型与展望[J]．重庆建筑大学学报，1998，20(5)：108-114．
[62]Safak E,Boore D M.On nonstationary stocha stic models for earthquakes[C].Third U.S.national conference on earthquake engineering,1986,1:137- 148.
[63]Elishakoff I,Lyon R H.Random vibration status and recent developments[M].Amsterdam-Oxford-New York-Tokyo:ELSEVIER,1986.
[64]Bendat J S,Piersol A G.Random data analysis and measurement procedures[M].3~(rd)Edition.New York:JOHN EILEY & SONS,INC,2000.
[65]王宏禹．非平稳随机信号分析与处理[M]．北京：国防工业出版社，1999．
[66]Daubechies I．小波十讲[M]．李建平，杨万年，译．北京：国防工业出版社．2004．
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