基于目标功率谱和包线的地震动合成
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摘要
本文给出了以目标功率谱和目标包线函数为双目标函数的人工地震动合成方法,使人工地震动不仅符合目标功率谱,还基本符合目标包线函数,并对加速度基线进行了调整,使速度时程和位移时程更为合理。作者认为如果用反应谱作为目标谱,生成的人工地震动时程可能会弱化地震动的随机特性,用这样的人工地震动时程作为输入来分析建筑结构的非线性动力反应,不是理想的选择。对建筑结构进行非线性时程分析时,用基于功率谱的人工地震动作为输入,应当是一种更为合理的方法。作者认为平方和具有明确的物理意义,是随机信号的总能量参数,并通过理论分析和数值计算,对于一定持时的随机平稳信号样本,平方和(持时×平方平均值)对振幅起重要控制作用。平方和、归一化功率谱、时域包线函数是基于功率谱模型的地震动三要素。
This article presents a method that takes the power spectrum and the enveloping curve as double target functions to synthesize the artificial ground motion.The method not only makes the spectrum of the artificial ground motion comply with the target spectrum,but also in the iterative process adjusts the ground motion wave-shape to conform to the goal enveloping curve function approximately,and eliminates the base-line shift in the acceleration time history,then makes the velocity and displacement time histories of ground motion more reasonable.The authors argue that the synthetic method based on the response spectrum may weaken the random characteristics of ground motion,and hence it may be imperfect to use the artificial ground motion based on response spectrum as an input to analyze the elastic-plastic structures.Using the artificial ground motion based the power spectrum model in elastic-plastic structure dynamic analysis may be one more reasonable alternative.The authors see that the sum of squares has the explicit physics significance,which is the total energy parameter of random signal.Through the the-oretical analysis and the numerical calculation,the authors think that the sum of squares(Means of squares multiplied by duration)is an important control factor in the amplitude of a stochastic statistical signal sample with certain duration.Consequently,the sum of squares,the normalized power spectrum,and the enveloping curve function in time domain are three essential factors of the ground motion based on the power spectrum model.
This article presents a method that takes the power spectrum and the enveloping curve as double target functions to synthesize the artificial ground motion.The method not only makes the spectrum of the artificial ground motion comply with the target spectrum,but also in the iterative process adjusts the ground motion wave-shape to conform to the goal enveloping curve function approximately,and eliminates the base-line shift in the acceleration time history,then makes the velocity and displacement time histories of ground motion more reasonable.The authors argue that the synthetic method based on the response spectrum may weaken the random characteristics of ground motion,and hence it may be imperfect to use the artificial ground motion based on response spectrum as an input to analyze the elastic-plastic structures.Using the artificial ground motion based the power spectrum model in elastic-plastic structure dynamic analysis may be one more reasonable alternative.The authors see that the sum of squares has the explicit physics significance,which is the total energy parameter of random signal.Through the the-oretical analysis and the numerical calculation,the authors think that the sum of squares(Means of squares multiplied by duration)is an important control factor in the amplitude of a stochastic statistical signal sample with certain duration.Consequently,the sum of squares,the normalized power spectrum,and the enveloping curve function in time domain are three essential factors of the ground motion based on the power spectrum model.
引文
[1]Chopra A K,Goel R K.Capacity-demand-diagram methods for estimating seismic deformation of inelastic structures:SDF systems[R].Berke-ley:Pacific Earthquake Engineering Research Center,College of Engineering University of California,1999.
[2]Fajfar P.Capacity spectrum method based on inelastic demand spectra[J].Earthquake Engineering and Structural Dynamics,1999,28:979-993.
[3]Housner G W.Characteristics of strong motion of earthquakes[J].BSSA,1947,37(1):19-31.
[4]Kanai K.Semi-empirical formula for the seismic characteristics of ground motion[M].Bull.Earthq.Res.Inst.,Tokyo University,1957,35:306-325.
[5]胡聿贤,周锡元.弹性体系在平稳和非平稳化地面运动下的反应[C]∥地震工程研究报告集第一集.北京:科学出版社,1962:33-50.
[6]Clough R W,Penzien J.Dynamics of structures[M].New York:Mc Graw-Hill,1993.
[7]欧进萍,牛荻涛,杜修力.设计用随机地震动模型及其参数的确定[J].地震工程与工程振动,1991,11(3):45-54.
[8]杜修力,胡晓,陈厚群.强震地运动随机过程模拟[J],地震学报,1995,17(1):103-109.
[9]Ohsaki Y.On the significance of phase content in earthquake ground motions[J].Earthquake Engineering&Structural Dynamics,1979,7(5):427-439.
[10]胡聿贤,何训.考虑相位谱的人造地震动反应谱的拟合[J].地震工程与工程震动,1986,6(2):37-51.
[11]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.
[12]金星,廖振鹏.地震动强度包线函数的理论研究[J].地震学报,1994,16(4):519-525.
[13]金星,廖振鹏.强地震动相位特征的统计规律性[J].地震学报,1994,16(1):106-110.
[14]霍俊荣,胡聿贤,冯启民.地面运动时程强度包线函数的研究[J].地震工程与工程振动,1991,11(1):1-12.
[15]Priestley M B.Evolutionary spectra and non-stationary random process[J].Statst.J,R,Soc.Ser.B,1965,28(2):204-230.
[16]Priestley M B,Power spectral analysis of non-stationary processes[J].J Sound Vibra.,1967,6(1):86-97.
[17]梁建文.非平稳地震动过程模拟方法(I)[J].地震学报,2005,27(2):213-228.
[18]梁建文.非平稳地震动过程模拟方法(II)[J].地震学报,2005,27(3):346-351.
[19]张翠然,陈厚群,李敏.根据渐近谱的统计规律生成地震动加速度时程[J].地震学报,2007,29(4):409-418.
[20]徐国栋,周锡元,郭明珠,等.典型振动信号时-频分析方法研究[J].世界地震工程,2007,23(2):26-36.
[21]徐国栋,强震地面运动超随机特性的若干研究[D].北京:北京工业大学,2006.
[22]徐国栋,周锡元,董娣,等.强震地面运动的超随机特性研究[J].地震工程与工程振动,2005,25(2):1-9.
[23]徐国栋,周锡元,闫维明,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.
[24]徐国栋,周锡元,闫维明.强震地面运动超随机特性的几点注记[J].地震工程与工程振动,2007,27(1):7-15.
[25]Boore D M.Simulation of ground motion using the stochastic method[J].Pure Appl.Geophys,2003(160):635-676.
[26]Wang Guoquan,Boore D M,Igel H.Some observations on colocated and closely-spaced strong ground motion records of the1999,Chi-Chi Tai-wan Earthquake[J].Bull.Seism.Soc.Am.,2003,93:674-693.
[27]Trifunac M D.A method for synthesizing realistic strong ground motion[J].Bull.Seism.Soc.Amer.,1971,61:1739-1753.
[28]Wong H L,Trifunac M D.Generation of artificial strong motion accelerograms[J].Earthq.Eng.Struct.Dyn.,1979,7:509-528.
[29]蔡长青,沈建文.人造地震动的时域叠加法和反应谱整体逼近技术[J].地震学报,1997,19(1):71-78.
[30]赵凤新,张郁山.拟合峰值速度与目标反应谱的人造地震动[J].地震学报,2006,28(4):429-437.
[31]徐国栋,史培军,周锡元.基于目标反应谱和包线的地震动合成[J].地震工程与工程振动,2010,30(1):1-7.
[2]Fajfar P.Capacity spectrum method based on inelastic demand spectra[J].Earthquake Engineering and Structural Dynamics,1999,28:979-993.
[3]Housner G W.Characteristics of strong motion of earthquakes[J].BSSA,1947,37(1):19-31.
[4]Kanai K.Semi-empirical formula for the seismic characteristics of ground motion[M].Bull.Earthq.Res.Inst.,Tokyo University,1957,35:306-325.
[5]胡聿贤,周锡元.弹性体系在平稳和非平稳化地面运动下的反应[C]∥地震工程研究报告集第一集.北京:科学出版社,1962:33-50.
[6]Clough R W,Penzien J.Dynamics of structures[M].New York:Mc Graw-Hill,1993.
[7]欧进萍,牛荻涛,杜修力.设计用随机地震动模型及其参数的确定[J].地震工程与工程振动,1991,11(3):45-54.
[8]杜修力,胡晓,陈厚群.强震地运动随机过程模拟[J],地震学报,1995,17(1):103-109.
[9]Ohsaki Y.On the significance of phase content in earthquake ground motions[J].Earthquake Engineering&Structural Dynamics,1979,7(5):427-439.
[10]胡聿贤,何训.考虑相位谱的人造地震动反应谱的拟合[J].地震工程与工程震动,1986,6(2):37-51.
[11]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.
[12]金星,廖振鹏.地震动强度包线函数的理论研究[J].地震学报,1994,16(4):519-525.
[13]金星,廖振鹏.强地震动相位特征的统计规律性[J].地震学报,1994,16(1):106-110.
[14]霍俊荣,胡聿贤,冯启民.地面运动时程强度包线函数的研究[J].地震工程与工程振动,1991,11(1):1-12.
[15]Priestley M B.Evolutionary spectra and non-stationary random process[J].Statst.J,R,Soc.Ser.B,1965,28(2):204-230.
[16]Priestley M B,Power spectral analysis of non-stationary processes[J].J Sound Vibra.,1967,6(1):86-97.
[17]梁建文.非平稳地震动过程模拟方法(I)[J].地震学报,2005,27(2):213-228.
[18]梁建文.非平稳地震动过程模拟方法(II)[J].地震学报,2005,27(3):346-351.
[19]张翠然,陈厚群,李敏.根据渐近谱的统计规律生成地震动加速度时程[J].地震学报,2007,29(4):409-418.
[20]徐国栋,周锡元,郭明珠,等.典型振动信号时-频分析方法研究[J].世界地震工程,2007,23(2):26-36.
[21]徐国栋,强震地面运动超随机特性的若干研究[D].北京:北京工业大学,2006.
[22]徐国栋,周锡元,董娣,等.强震地面运动的超随机特性研究[J].地震工程与工程振动,2005,25(2):1-9.
[23]徐国栋,周锡元,闫维明,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.
[24]徐国栋,周锡元,闫维明.强震地面运动超随机特性的几点注记[J].地震工程与工程振动,2007,27(1):7-15.
[25]Boore D M.Simulation of ground motion using the stochastic method[J].Pure Appl.Geophys,2003(160):635-676.
[26]Wang Guoquan,Boore D M,Igel H.Some observations on colocated and closely-spaced strong ground motion records of the1999,Chi-Chi Tai-wan Earthquake[J].Bull.Seism.Soc.Am.,2003,93:674-693.
[27]Trifunac M D.A method for synthesizing realistic strong ground motion[J].Bull.Seism.Soc.Amer.,1971,61:1739-1753.
[28]Wong H L,Trifunac M D.Generation of artificial strong motion accelerograms[J].Earthq.Eng.Struct.Dyn.,1979,7:509-528.
[29]蔡长青,沈建文.人造地震动的时域叠加法和反应谱整体逼近技术[J].地震学报,1997,19(1):71-78.
[30]赵凤新,张郁山.拟合峰值速度与目标反应谱的人造地震动[J].地震学报,2006,28(4):429-437.
[31]徐国栋,史培军,周锡元.基于目标反应谱和包线的地震动合成[J].地震工程与工程振动,2010,30(1):1-7.
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