利用正交Hilbert谱模拟非平稳随机地震动
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摘要
基于样本记录正交HHT变换的Hilbert谱提出了非平稳随机地震动过程的模拟方法。利用正交EMD法对IMF分量进行处理,克服了传统EMD分解存在能量泄漏的缺点,使正交HHT法可以精确分析非平稳信号的时频特性。在此基础上,把样本的Hilbert谱均值作为地震动随机过程的目标Hilbert谱,引入随机相位角来进行非平稳随机地震动过程的仿真,并且给出了随机过程的统计特性函数。通过对2个地震动记录的模拟,验证了模拟的地震动样本,能完全反映原记录强度和频率的非平稳特性,在时频分布上和原记录非常接近,具有相同的统计特征,并且模拟样本之间也具有良好的离散性。
A new method is proposed for the simulation of nonstationary stochastic earthquake ground motion based on orthogonal Hilbert-Huang transform(OHHT) spectra of its sample observations.Orthogonal EMD method is introduced to treat with IMF.OHHT avoids leakage of energy compared with conventional HHT,and it can be used for analysis of nonstationary signal.The average of the Hilbert spectra over the samples is defined as the Hilbert spectrum of the earthquake motion process and used as the target in the simulation of the process.Random Phase is also introduced to simulate nonstationary earthquake.The statistic characteristics function of stochastic process is given in the paper.Simulations of two earthquake ground motion are carried out.The results show that the samples can accurately reflect amplitude and frequency nonstationary of records.Samples and record of same earthquake ground motion process have same statistic characteristics.
A new method is proposed for the simulation of nonstationary stochastic earthquake ground motion based on orthogonal Hilbert-Huang transform(OHHT) spectra of its sample observations.Orthogonal EMD method is introduced to treat with IMF.OHHT avoids leakage of energy compared with conventional HHT,and it can be used for analysis of nonstationary signal.The average of the Hilbert spectra over the samples is defined as the Hilbert spectrum of the earthquake motion process and used as the target in the simulation of the process.Random Phase is also introduced to simulate nonstationary earthquake.The statistic characteristics function of stochastic process is given in the paper.Simulations of two earthquake ground motion are carried out.The results show that the samples can accurately reflect amplitude and frequency nonstationary of records.Samples and record of same earthquake ground motion process have same statistic characteristics.
引文
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[13]楼梦麟,黄天立.正交化经验模式分解方法[J].同济大学学报:自然科学版,2007,35(3):293-298.LOU Menglin,HUANG Tianli.Orthogonal empiricalmode decomposition[J].Journal of Tongji University:Natural Science Edition,2007,35(3):293-298.
[14]Husid R L.Analisis de terremotos:analisis general[J].Revista del ID1EM,1969,8(1):21-42.
[2]吴再光,林皋,韩国城.水平成层地基非平稳随机地震反应分析[J].土木工程学报,1992,25(3):60-67.WU Zaiguang,LIN Gao,HAN Guocheng.Nonstarionary stochastic seismic response analysis ofhorizontal layered foundations[J].China CivilEngineering Journal,1992,25(3):60-67
[3]Spanosa P D,Giaralish A,Politis N P.Time-frequencyrepresentation of earthquake accelerograms and inelasticstructural response records using the adaptive chirpletdecom position and empirical mode decomposition[J].Soil Dynamics and Earthquake Engineering,2007,27(6):675-689.
[4]Peng Yongbo,Li Jie.Investigation on starting-time ofphase evolution and simulation of earthquake groundmotions[J].Journal of Earthquake Engineering andEngineering Vibration,2011,31(4):158-166.
[5]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.CAO Hui,LAI Ming,BAI Shaoliang.Study on thesimulation of earthquake ground motions based onwavelet transform[J].China Civil Engineering Journal,2002,35(4):40-46.
[6]梁建文.非平稳地震动过程模拟方法(Ⅰ)[J].地震学报,2005,27(2):213-224.LIANG Jianwen.Simulation of non-stationary groundmotion processes(Ⅰ)[J].Acta Seismologica Sinica,2005,27(2):213-224.
[7]樊剑,袁涌,曾志和.基于谐小波变换的地震波非平稳随机模型建立[J].华中科技大学学报:自然科学版,2010,38(4):118-120.FAN Jian,YUAN Yong,ZENG Zhihe.Establishmentof nonstationary stochastic model of earthquake recordusing harmonic wavelet transforms[J].Journal of Hua-zhong University of Science and Technology:NaturalScience Edition:2010,38(4):118-120.
[8]He J.An efficient numerical method for estimating reli-abilities of linear structures under fully nonstationaryearthquake[J].Structural Safety,2010,32(3):200-208.
[9]Cacciola P.A stochastic approach for generating spectrumcompatible fully nonstationsry earthquakes[J].Computer&Structures,2010,88(15/16):889-901.
[10]Abbas A M,Manohar C S.Reliability-based vertornonstationary random critical earthquake excitations forparametrically excited systems[J].Structral Safety,2007,29(1):32-48.
[11]Takewaki I.Critical envelope functions for non-station-ary random earthquake input[J].Computer&Struc-tures,2004,82(20/21):1671-1683.
[12]Huang N E,Shen Z,Long S R,et al.The empiricalmode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis[J].TheRoyal Society,1998,454:903-995.
[13]楼梦麟,黄天立.正交化经验模式分解方法[J].同济大学学报:自然科学版,2007,35(3):293-298.LOU Menglin,HUANG Tianli.Orthogonal empiricalmode decomposition[J].Journal of Tongji University:Natural Science Edition,2007,35(3):293-298.
[14]Husid R L.Analisis de terremotos:analisis general[J].Revista del ID1EM,1969,8(1):21-42.
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