随机地震动的概率密度演化
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摘要
利用广义概率密度演化方程,研究了随机地震动加速度时程的时变概率密度分布。利用集集地震实测地震动记录建模,识别给出了Ⅱ类场地随机地震动物理模型的基本参数及其分布。引入空间伸缩变换和Voronoi准则,发展了多维概率空间剖分的实用算法,对比分析了随机地震动模型与真实地震动的概率密度函数。结果表明:随机地震动物理模型可以客观反映真实地震动加速度时程的精细概率结构。
The time-varying probability density distribution of stochastic seismic ground motion acceleration time history was researched using generalized probability density evolution equation.Authors established a model by using actual acceleration records from Chi-Chi earthquake and identified basic parameters and their distributions in physical model of stochastic seismic ground motion from actual observation records in site class Ⅱ.Further,using the expansion-contraction transformation and Voronoi norm,authors developed a practical algorithm which realized the division of multi-dimension probability space.The probability density function of stochastic seismic ground motion model and actual acceleration records were compared and analyzed.The results show that the physical model of stochastic seismic ground motion can objectively reflect refined probability characteristic of actual seismic acceleration processes.
The time-varying probability density distribution of stochastic seismic ground motion acceleration time history was researched using generalized probability density evolution equation.Authors established a model by using actual acceleration records from Chi-Chi earthquake and identified basic parameters and their distributions in physical model of stochastic seismic ground motion from actual observation records in site class Ⅱ.Further,using the expansion-contraction transformation and Voronoi norm,authors developed a practical algorithm which realized the division of multi-dimension probability space.The probability density function of stochastic seismic ground motion model and actual acceleration records were compared and analyzed.The results show that the physical model of stochastic seismic ground motion can objectively reflect refined probability characteristic of actual seismic acceleration processes.
引文
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[2]安自辉,李杰.地震动随机函数模型研究(Ⅰ)——模型建立[J].地震工程与工程振动,2009,29(5):36-45.AN Zi-hui,LI Jie.Research on Random FunctionModel of Strong Ground Motion(Ⅰ):Model Con-structing[J].Journal of Earthquake Engineering andEngineering Vibration,2009,29(5):36-45.
[3]安自辉,李杰.地震动随机函数模型研究(Ⅱ)——参数统计与模型验证[J].地震工程与工程振动,2009,29(6):40-47.AN Zi-hui,LI Jie.Research on Random FunctionModel of Strong Ground Motion(Ⅱ):ParametricStatistic and Model Certification[J].Journal of Earth-quake Engineering and Engineering Vibration,2009,29(6):40-47.
[4]王鼎,李杰.工程地震动的物理随机函数模型[J].中国科学:技术科学,2011,41(3):356-364.WANG Ding,LI Jie.Physical Random Function Mod-el of Ground Motions for Engineering Purposes[J].Scientia Sinica Techologica,2011,41(3):356-364.
[5]王鼎,李杰.工程场地地震动随机场的物理模型[J].中国科学:技术科学,2012,42(7):798-807.WANG Ding,LI Jie.A Random Physical Model ofSeismic Ground Motion Field on Local EngineeringSite[J].Scientia Sinica Techologica,2012,42(7):798-807.
[6]LI Jie,CHEN Jian-bing.Stochastic Dynamics of Struc-tures[M].Singapore:John Wiley&Sons,2009.
[7]李杰,陈建兵.随机动力系统中的概率密度演化方程及其研究进展[J].力学进展,2010,40(2):170-188.LI Jie,CHEN Jian-bing.Advances in the Research onProbability Density Evolution Equations of StochasticDynamical Systems[J].Advances in Mechanics,2010,40(2):170-188.
[8]李杰,陈建兵.随机结构动力反应分析的概率密度演化方法[J].力学学报,2003,35(4):437-442.LI Jie,CHEN Jian-bing.Probability Density EvolutionMethod for Analysis of Stochastic Structural DynamicResponse[J].Acta Mechanica Sinica,2003,35(4):437-442.
[9]WONG H L,TRIFUNAC M D.Generation of Artifi-cial Strong Motion Accelerograms[J].Earthquake En-gingeering and Structural Dynamics,1979,7(6):509-527.
[10]DZIEWONSKI A M,ANDERSON D L.PreliminaryReference Earth Model[J].Physics of the Earth andPlanetary Interiors,1981,25:297-356.
[11]郭锋,吴东明,许国富,等.中外抗震设计规范场地分类对应关系[J].土木工程与管理学报,2011,28(2):63-66.GUO Feng,WU Dong-ming,XU Guo-fu,et al.SiteClassification Corresponding Relationship BetweenChinese and the Overseas Seismic Design Codes[J].Journal of Civil Engineering and Management,2011,28(2):63-66.
[12]陈建兵,李杰.结构随机响应概率密度演化分析的数论选点法[J].力学学报,2006,38(1):134-140.CHEN Jian-bing.LI Jie.Strategy of Selecting Pointsvia Number Theoretical Method in Probability Densi-ty Evolution Analysis of Stochastic Response ofStructures[J].Chinese Journal of Theoretical and Ap-plied Mechanics,2006,38(1):134-140.
[13]华罗庚,王元.数论在近似分析中的应用[M].北京:科学出版社,1978.HUA Luo-geng,WANG Yuan.Applications of Num-ber Theory to Numerical Analysis[M].Beijing:Sci-ence Press,1978.
[14]方开泰,王元.数论方法在统计中的应用[M].北京:科学出版社,1996.FANG Kai-tai,WANG Yuan.Number-theoreticMethods in Statistics[M].Beijing:Science Press,1996.
[15]廖振鹏.工程波动理论导论[M].北京:科学出版社,2002.LIAO Zhen-peng.Introduction to Wave Motion Theo-ries for Engineering[J].Beijing:Science Press,2002.
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