强震地面运动的混沌特性分析
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摘要
引入非线性动力学理论和混沌时间序列分析方法考察强震地面运动加速度时程的非线性特征。首先采用功率谱分析法、主成份分析法和Cao方法定性判断地震动加速度时程具有混沌特性,然后应用混沌时间序列分析方法定量计算了30条地震动加速度时程的三个非线性特征参数。计算表明,这些地震动时程的关联维数为2.0~4.0的分数维,Kolm ogorov熵K2为大于零的有限正值,最大Lyapunov指数在0~1.0之间。结果说明,强震地面运动具有混沌特性,地震动的高度不规则和复杂性是地震过程强非线性的反映。
The nonlinear dynamic theory and the chaotic time series analysis method were adopted to examine the nonlinear characteristics of strong earthquake ground motions in this paper.Based on the power spectrum analysis,principal component analysis,and Cao's method,the acceleration time series of ground motions have been determined qualitatively being of the chaotic property.Then,the chaotic time series analysis method is applied to calculate quantitatively the three nonlinear characteristic parameters of 30 records of ground acceleration.Numerical results show that the correlation dimension of these ground motions is a fractal dimension between 2.0 and 4.0.Their Kolmogorov entropy K2is a finite value larger than zero,and their maximal Lyapunov exponent is in the interval 0-1.0.The result has demonstrated that the strong ground motions possess the chaotic character,and the severe irregularity and complexity of ground motions are the reflection of high nonlinearity of earthquake process.
The nonlinear dynamic theory and the chaotic time series analysis method were adopted to examine the nonlinear characteristics of strong earthquake ground motions in this paper.Based on the power spectrum analysis,principal component analysis,and Cao's method,the acceleration time series of ground motions have been determined qualitatively being of the chaotic property.Then,the chaotic time series analysis method is applied to calculate quantitatively the three nonlinear characteristic parameters of 30 records of ground acceleration.Numerical results show that the correlation dimension of these ground motions is a fractal dimension between 2.0 and 4.0.Their Kolmogorov entropy K2is a finite value larger than zero,and their maximal Lyapunov exponent is in the interval 0-1.0.The result has demonstrated that the strong ground motions possess the chaotic character,and the severe irregularity and complexity of ground motions are the reflection of high nonlinearity of earthquake process.
引文
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[13]Huang J,Turcotte D L.Evidence for chaotic faultinteraction in the seismicity of the San Andreas faultand Nakai trough[J].Nature,1990,348(2):234-236.
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[22]杨迪雄,赵岩,李刚.近断层地震动运动特征对长周期结构动力响应的影响分析[J].防灾减灾工程学报,2007,27(2):133-140.Yang D X,Zhao Y,Li G.Influence analysis ofmotion characteristics of near-fault ground motions onseismic responses of long-period structures[J].Journal of Disaster Prevention and MitigationEngineering,2007,27(2):133-140.
[2]胡聿贤.地震工程学(第二版)[M].北京:地震出版社,2006.Hu Y X.Earthquake Engineering(2ndEdition)[M].Beijing:Seismology Press,2006.
[3]Kantz H,Schreiber T.Nonlinear Time SeriesAnalysis[M].Cambridge:Cambridge UniversityPress,1997.
[4]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2002.LüJ H,Lu J A,Chen S H.Chaotic Time SeriesAnalysis and Application[M].Wuhan:WuhanUniversity Press,2002.
[5]刘秉正,彭建华.非线性动力学[M].北京:高等教育出版社,2004.Liu B Z,Peng J H.Nonlinear Dynamics[M].Beijing:Higher Education Press,2004.
[6]韩敏.混沌时间序列预测理论与方法[M].北京:中国水利水电出版社,2007.Han M.Prediction Theory and Method of ChaoticTime Series[M].Beijing:China Waterpower Press,2007.
[7]Cao L Y.Practical method for determining theminimum embedding dimension of a scalar time series[J].Physica D,1997,110(1-2):43-50.
[8]曾锦光,舒雅琴,钟勇.地震记录的分形和混沌性质[J].石油地球物理勘探,1995,30(6):743-748.Zeng J G,Shu Y Q,Zhong Y.Fractal and chaoticproperty of ground motion recording[J].PetroleumGeophysics Exploration,1995,30(6):743-748.
[9]Turcotte D L.Fractals and Chaos in Geology andGeophysics[M].Cambridge:Cambridge UniversityPress,1997.
[10]朱令人,陈.地震分形[M].北京:地震出版社,2000.Zhu L R,Chen Y.Earthquake Fractal[M].Beijing:Seismology Press,2000.
[11]蒋金泉,秦广鹏,刘传孝.综放沿空巷道围岩系统混沌动力学特性研究[J].岩石力学与工程学报,2006,25(9):1754-1763.Jiang J Q,Qin G P,Liu C X.Chaotic dynamicsfeature of fully-mechanized caving roadwaysurrounding rock system[J].Chinese Journal of RockMechanics and Engineering,2006,25(9):1754-1763.
[12]李强.地震前兆混沌时间序列多尺度分维异常识别研究[J].防灾减灾工程学报,2007,27(2):211-216.Li Q.Research on anomaly identification ofearthquake precursor observation chaotic time serieswith multi-scale fractal dimension method[J].Journal of Disaster Prevention and MitigationEngineering,2007,27(2):211-216.
[13]Huang J,Turcotte D L.Evidence for chaotic faultinteraction in the seismicity of the San Andreas faultand Nakai trough[J].Nature,1990,348(2):234-236.
[14]Carlson J M,Langer J S,Shaw B E.Dynamics ofearthquake faults[J].Reviews of Modern Physics,1994,66(2):657-670.
[15]Vieira M S.Chaos and synchronized chaos in anearthquake model[J].Physical Review Letters,1999,82(1):201-204.
[16]Montagne R,Vasconcelos G R.Complex dynamics ina one-block model for earthquakes[J].Physica A,2004,342(2):178-185.
[17]Grassberger P,Procaccia I.Measuring the stran-geness of strong attractors[J].Physica D,1983,9(3):189-208.
[18]Grassberger P,Procaccia I.Estimation of theKolmogorov entropy from a chaotic signal[J].Physica Review A,1983,28(4):2591-2593.
[19]赵贵兵,石炎福,段文锋,等.从混沌时间序列同时计算关联维和Kolmogorov熵[J].计算物理,1999,16(3):309-315.Zhao G B,Shi Y F,Duan W F,et al.Calculation ofcorrelation dimension and Kolmogorov entropy fromchaotic time series[J].Computational Physics,1999,16(3):309-315.
[20]Rosenstein M T,Collins J J,De luca C J.A practicalmethod for calculating largest Lyapunov exponentsfrom small data sets[J].Physica D,1993,65(1):117-134.
[21]Wang G Q,Zhou X Y,Zhang P Z,et al.Characteristics of amplitude and duration for nearfault strong ground motion from the 1999 Chi-Chi,Taiwan,earthquake[J].Soil Dynamics andEarthquake Engineering,2002,22(1):73-96.
[22]杨迪雄,赵岩,李刚.近断层地震动运动特征对长周期结构动力响应的影响分析[J].防灾减灾工程学报,2007,27(2):133-140.Yang D X,Zhao Y,Li G.Influence analysis ofmotion characteristics of near-fault ground motions onseismic responses of long-period structures[J].Journal of Disaster Prevention and MitigationEngineering,2007,27(2):133-140.
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