基于功率谱的三参量人工地震动合成
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摘要
常用的地震动功率谱模型及其人工地震动合成方法在功率谱大小量度、引入时域包线造成功率谱的改变、自相关函数随机噪声成分或功率谱随机波动成分的模拟等方面还存在一些不足。细化地震动的功率谱模型,详细论述平方和作为功率谱强度参数的合理性,提出包含随机波动成分的目标功率谱或包含随机噪声成分的目标自相关函数的数学模型及模拟方法,在目标功率谱中引入随机波动成分。给出了利用地震动功率谱数学模型的3个控制物理量(包含随机波动成分的归一化功率谱、平方和、时域包线函数)合成人工地震动的方法,使合成出的人工地震动时程在能量上严格符合平方和,在频域上严格符合归一化目标功率谱,在时域波形上近似符合目标包线函数,并通过算例演示了给出的人工地震动功率谱模型更加符合实际情况。研究表明平方和、归一化功率谱或归一化自相关函数和时域包线函数是地震动功率谱模型的3个重要物理统计量。
There are some shortcomings in the common power spectrum models of ground motion and in the corresponding synthesis of artificial ground motion,such as the irrationality of the measurement of the size of the power spectrum,the conversion to the power spectrum when leading into the time-domain envelope,and the ignorance of fluctuating ingredient in power spectrum or of random noise part in autocorrelation function.This article elaborated the rationality that the sum of squares should be taken as the measurement of the size of power spectrum.The article discussed that the sum of squares had explicit physics significance,and was the total energy parameter of random stationary signal.A more accurate mathematical model was developed in order to simulate the random fluctuating ingredient of target power spectrum,or the stochastic noise part of corresponding target autocorrelation function,and proposed the non-stationary ground motion’s mathematical model,which was based on power spectrum and included three main controlling physical statistics: the normalized power spectrum containing random fluctuating ingredient,the sum of squares and the time-domain envelope function.Using the synthesis method of ground motion developed by the article,the total energy of artificial ground motion accords with the target sum of squares exactly,the frequent characteristics of the artificial ground motion are in accordance with the normalized target power spectrum accurately,and the wave-shape of the artifical ground motion in time domain accords with the target envelope function approximately.Studies show that the sum of squares,the normalized power spectrum,and the time-domain envelope function are three essential physical statistics of ground motion based on power spectrum model.
There are some shortcomings in the common power spectrum models of ground motion and in the corresponding synthesis of artificial ground motion,such as the irrationality of the measurement of the size of the power spectrum,the conversion to the power spectrum when leading into the time-domain envelope,and the ignorance of fluctuating ingredient in power spectrum or of random noise part in autocorrelation function.This article elaborated the rationality that the sum of squares should be taken as the measurement of the size of power spectrum.The article discussed that the sum of squares had explicit physics significance,and was the total energy parameter of random stationary signal.A more accurate mathematical model was developed in order to simulate the random fluctuating ingredient of target power spectrum,or the stochastic noise part of corresponding target autocorrelation function,and proposed the non-stationary ground motion’s mathematical model,which was based on power spectrum and included three main controlling physical statistics: the normalized power spectrum containing random fluctuating ingredient,the sum of squares and the time-domain envelope function.Using the synthesis method of ground motion developed by the article,the total energy of artificial ground motion accords with the target sum of squares exactly,the frequent characteristics of the artificial ground motion are in accordance with the normalized target power spectrum accurately,and the wave-shape of the artifical ground motion in time domain accords with the target envelope function approximately.Studies show that the sum of squares,the normalized power spectrum,and the time-domain envelope function are three essential physical statistics of ground motion based on power spectrum model.
引文
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[10]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.(Xu Guodong,Zhou Xiyuan,Dong Di,et al.,Acase study on the super-randomness of strong groundmotion[J].Journal of Earthquake Engineering andEngineering Vibration,2005,25(2):1-9.(inChinese))
[11]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.(Xu Guodong,Zhou Xiyuan,YanWeiming,et al.Synthesis of manmade ground motionconsidering the super-randomness[J].Journal ofEarthquake Engineering and Engineering Vibration,2005,25(4):11-17.(in Chinese))
[12]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.(Xu Guodong,Zhou Xiyuan,YanWeiming.Some notes on the super-randomness ofstrong ground motion[J].Journal of EarthquakeEngineering and Engineering Vibration,2007,27(1):7-15.(in Chinese))
[13]徐国栋,史培军,周锡元.基于目标功率谱和包线的地震动合成[J].地震工程与工程振动,2010,30(2):1-9.(Xu Guodong,Shi Peijun,Zhou Xiyuan.Artificial ground motion based on target power spectraand envelope[J].Journal of Earthquake Engineeringand Engineering Vibration,2010,30(2):1-9.(inChinese))
[14]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.(Xu Guodong,Shi Peijun,Zhou Xiyuan.Artificial ground motion based on target response spectraand envelope[J].Journal of Earthquake Engineeringand Engineering Vibration,2010,30(1):1-7.(inChinese))
[2]Kanai K.Semi-empirical formula for the seismiccharacteristics of ground motion[C]//Bulletin ofEarthquake Research Institute.Tokyo:TokyoUniversity:1957:306-325.
[3]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[R]//地震工程研究报告集第一集.北京:科学出版社,1962:33-50.
[4]Clough R W,Penzien J.Dynamics of structures[M].New York:McGraw-Hill,1993:16-27.
[5]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.(Ou Jinping,Niu Ditao,Du Xiuli.Random earthquake ground motion model and itsparameter determination used in aseismic design[J].Journal of Earthquake Engineering and EngineeringVibration,1991,11(3):45-54.(in Chinese))
[6]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.(Du Xiuli,Hu Xiao,Chen Houqun.Random process simulation ofstrong ground motion[J].Acta Seismologica Sinica,1994,17(1):103-109.(in Chinese))
[7]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.(Huo Junrong,Hu Yuxian,Feng Qimin.Study on envelope function of acceleration time history[J].Journal of Earthquake Engineering andEngineering Vibration,1991,11(1):1-12.(inChinese))
[8]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.(Jin Xing,Liao Zhenpeng.Theoretical research on intensityenvelope function of strong ground motion[J].ActaSeismologica Sinica,1994,16(4):519-525.(inChinese))
[9]Wang Guo-Quan,Zhou Xi-Yuan,Ma Zong-Jin,et al.A preliminary study on the randomness of responsespectra of the 1999 Chi-Chi,Taiwan Earthquake[J].Bulletin of the Seismological Society of America,2001,91(5):1358-1369.
[10]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.(Xu Guodong,Zhou Xiyuan,Dong Di,et al.,Acase study on the super-randomness of strong groundmotion[J].Journal of Earthquake Engineering andEngineering Vibration,2005,25(2):1-9.(inChinese))
[11]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.(Xu Guodong,Zhou Xiyuan,YanWeiming,et al.Synthesis of manmade ground motionconsidering the super-randomness[J].Journal ofEarthquake Engineering and Engineering Vibration,2005,25(4):11-17.(in Chinese))
[12]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.(Xu Guodong,Zhou Xiyuan,YanWeiming.Some notes on the super-randomness ofstrong ground motion[J].Journal of EarthquakeEngineering and Engineering Vibration,2007,27(1):7-15.(in Chinese))
[13]徐国栋,史培军,周锡元.基于目标功率谱和包线的地震动合成[J].地震工程与工程振动,2010,30(2):1-9.(Xu Guodong,Shi Peijun,Zhou Xiyuan.Artificial ground motion based on target power spectraand envelope[J].Journal of Earthquake Engineeringand Engineering Vibration,2010,30(2):1-9.(inChinese))
[14]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.(Xu Guodong,Shi Peijun,Zhou Xiyuan.Artificial ground motion based on target response spectraand envelope[J].Journal of Earthquake Engineeringand Engineering Vibration,2010,30(1):1-7.(inChinese))
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