地震动随机过程的正交展开
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摘要
介绍了随机过程Karhunen-Loeve分解的基本原理,指出了其在随机过程展开中所具有的优势与局限性.针对Karhunen-Loeve分解在求解特征问题中存在的困难,采用Hartley正交基作为展开函数,发展了一类基于Hartley正交基的随机过程展开方法.考虑到直接对地震动加速度随机过程实施正交展开,很难达到以较少展开项数反映原随机过程的目的.为此,提出了从地震动位移过程的正交展开出发,引入一类能量等效原理,获得了地震动加速度随机过程的正交展开式,进而将地震动随机过程展开为由10个独立随机变量所调制的确定性函数的线性组合形式.
The paper first introduces the basic principle of Karhunen-Loeve decomposition for stochastic processes,and outlines the essential properties of the decomposition.A method based on the Hartley orthogonal bases is proposed to decompose stochastic processes.It is proposed to directly carry out the orthogonal expansion of the seismic displacement to capture main probbilistic characteristics of the seismic ground motion with only a few terms of the series.Based on the principle of energy equivalence,the expanding expression of seismic acceleration process is achieved.The seismic process is expanded into a linear combination of deterministic functions modulated by 10 uncorrelated random variables.
The paper first introduces the basic principle of Karhunen-Loeve decomposition for stochastic processes,and outlines the essential properties of the decomposition.A method based on the Hartley orthogonal bases is proposed to decompose stochastic processes.It is proposed to directly carry out the orthogonal expansion of the seismic displacement to capture main probbilistic characteristics of the seismic ground motion with only a few terms of the series.Based on the principle of energy equivalence,the expanding expression of seismic acceleration process is achieved.The seismic process is expanded into a linear combination of deterministic functions modulated by 10 uncorrelated random variables.
引文
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[17]欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,1991,11(3):45.OU Jinping,NIU Ditao,DU Xiuli.Random earthquake groundmotion model and its parameter determination used in aseismicdesign[J].Earthquake Engineering and Engineering Vibration,1991,11(3):45.
[18]刘章军.工程随机动力作用的正交展开理论及其应用研究[D].上海:同济大学建筑工程系,2007.LIU Zhangjun.Orthogonal expansion method of engineeringstochastic dynamic loads and its application[D].Shanghai:TongjiUniversity.Department of Building Engineering,2007.
[2]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004.LIN Jiahao,ZHANG Yahui.Pseudo-excitation method of randomvibration[M].Beijing:Science Press,2004.
[3]李杰.生命线工程抗震——基础理论与应用[M].北京:科学出版社,2005.LI Jie.Lifeline earthquake engineering——basic theory and itsapplications[M].Beijing:Science Press,2005.
[4]李杰.随机结构系统——分析与建模[M].北京:科学出版社,1996.LI Jie.Stochastic structural system——analysis and modeling[M].Beijing:Science Press,1996.
[5]Gutierrez R,Ruiz J C,Valderrama M J.On the numerical expan-sion of a second order stochastic process[J].Applied StochasticModels and Data Analysis,1992,(8):67.
[6]Huang S P,Quek S T,Phoon K K.Convergence study of thetruncated Karhunen-Loeve expansion for simulation of stochasticprocesses[J].International Journal for Numerical Methods inEngineering,2001,52:1029.
[7]Phoon K K,Huang S P,Quek S T.Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme[J].Probabilistic Engineering Mechanics,2002,17:293.
[8]Phoon K K,Huang H W,Quek S T.Comparison betweenKarhunen-Loeve and wavelet expansion for simulation of Gaus-sian processes[J].Computers and Structures,2004,82:985.
[9]Phoon K K,Huang S P,Quek S T.Simulation of second-orderprocesses using Karhunen-Loeve expansion[J].Computers andStructures,2002,80:1049.
[10]Grigoriu M.Evaluation of Karhunen-Loeve,spectral,and sam-pling representations for stochastic processes[J].Journal of En-gineering Mechanics,2006,132(2):179.
[11]李杰,刘章军.基于标准正交基的随机过程展开法[J].同济大学学报:自然科学版,2006,34(10):1279.LI Jie,LIU Zhangjun.Expansion method of stochastic processesbased on normalized orthogonal bases[J].Journal of Tongji Uni-versity:Natural Science,2006,34(10):1279.
[12]Spanos P D,Ghanem R.Stochastic finite element expansion forrandom media[J].Journal of Engineering Mechanics,1989,115(5):1035.
[13]Field Jr R V,Grigoriu M.On the accuracy of the polynomialchaos approximation[J].Probabilistic Engineering Mechanics,2004,19:65.
[14]Rodriguez G.Analysis and simulation of wave records throughfast Hartley transform[J].Ocean Engineering,2003,30:2255.
[15]Bracewell R N.The Hartley Transform[M].New York:OxfordUniversity Press,1986.
[16]杜修力,陈厚群.地震动随机模拟及其参数确定方法[J].地震工程与工程振动,1994,14(4):1.DU Xiuli,CHEN Houqun.Random simulation and its parameterdetermination method of earthquake ground motion[J].Earth-quake Engineering and Engineering Vibration,1994,14(4):1.
[17]欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,1991,11(3):45.OU Jinping,NIU Ditao,DU Xiuli.Random earthquake groundmotion model and its parameter determination used in aseismicdesign[J].Earthquake Engineering and Engineering Vibration,1991,11(3):45.
[18]刘章军.工程随机动力作用的正交展开理论及其应用研究[D].上海:同济大学建筑工程系,2007.LIU Zhangjun.Orthogonal expansion method of engineeringstochastic dynamic loads and its application[D].Shanghai:TongjiUniversity.Department of Building Engineering,2007.
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