非平稳地震动过程模拟的谱表示-随机函数方法
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摘要
在Priestley演变谱理论的基础上,采用随机函数的思想,建立了一类新的全非平稳过程模拟的谱表示-随机函数方法。在谱表示-随机函数方法中,实现了用2个基本随机变量即可精确表达原随机过程的目的。通过选取基本随机变量的离散代表点集,可以直接由演变功率谱密度函数生成具有给定赋得概率的代表性样本集合。以全非平稳地震动加速度过程的演变功率谱为例,验证了方法的有效性和优越性。最后,结合概率密度演化方法,进行了Duffing振子的随机地震反应分析与抗震可靠度计算。
Based on the Priestley′s evolutionary spectral representation theory and the idea of random function,a hybrid spectral representation and random function approach is presented to simulate non-stationary stochastic processes.This approach uses two basic random variables to capture accurately the second-order statistics of the original stochastic process.Discrete representative points of the two basic random variables are selected,and representative sample functions with assigned probability are generated directly by the evolutionary power spectral density function.By means of the evolutionary power spectral density function of non-stationary ground motion acceleration process,the effectiveness and advantages of this approach are demonstrated.Finally,combining the probability density evolution method,the random dynamic response and reliability of the Duffing oscillator subjected to stochastic ground motions are investigated.
Based on the Priestley′s evolutionary spectral representation theory and the idea of random function,a hybrid spectral representation and random function approach is presented to simulate non-stationary stochastic processes.This approach uses two basic random variables to capture accurately the second-order statistics of the original stochastic process.Discrete representative points of the two basic random variables are selected,and representative sample functions with assigned probability are generated directly by the evolutionary power spectral density function.By means of the evolutionary power spectral density function of non-stationary ground motion acceleration process,the effectiveness and advantages of this approach are demonstrated.Finally,combining the probability density evolution method,the random dynamic response and reliability of the Duffing oscillator subjected to stochastic ground motions are investigated.
引文
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[15]Shinozuka M,Deodatis G.Simulation of stochastic processes by spectral representation[J].Applied Mechanics Review,1991,44(4):191—204.
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[17]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998.
[18]Li J,Chen J B.The number theoretical method in response analysis of nonlinear stochastic structures[J].Computational Mechanics,2007,39(6):693—708.
[19]Peng Y B,Li J.Exceedance probability criterion based stochastic optimal polynomial control of Duffing oscillators[J].International Journal of Non-linear Mechanics,2011,46:457—469.
[20]Li J,Chen J B,Fan W L.The equivalent extreme-value event and evaluation of the structural system reliability[J].Structural Safety,2007,29(2):112—131.
[2]Shinozuka M.Simulation of multivariate and multidimensional random processes[J].Journal of the Acoustical Society of America,1971,49(1):357—368.
[3]Shinozuka M,Jan C M.Digital simulation of random processes and its applications[J].Journal of Sound and Vibration,1972,25(1):111—128.
[4]Chen J B,Sun W L,Li J,et al.Stochastic harmonic function representation of stochastic processes[J].Journal of Applied Mechanics-Transactions of the ASME,2013,80(1):011001.
[5]Chen J B,Li J.Optimal determination of frequencies in the spectral representation of stochastic processes[J].Computational Mechanics,2013,51(5):791—806.
[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—228.Liang Jianwen.Simulation of non-stationary ground motion processes(I)[J].Acta Seismologica Sinica,2005,27(2):213—228.
[7]Liang J W,Chaudhuri S R,Shinozuka M.Simulation of nonstationary stochastic processes by spectral representation[J].Journal of Engineering Mechanics,2007,133(6):616—627.
[8]刘章军,方兴.平稳地震动过程的随机函数-谱表示模拟[J].振动与冲击,2013,32(24):6—10.Liu Zhang-jun,Fang Xing.Simulation of stationary ground motion with random functions and spectral representation[J].Journal of Vibration and Shock,2013,32(24):6—10.
[9]中华人民共和国住房和城乡建设部.GB50011-2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.
[10]Cacciola P,Deodatis G.A method for generating fully non-stationary and spectrum-compatible ground motion vector processes[J].Soil Dynamics and Earthquake Engineering,2011,31:351—360.
[11]Li J,Chen J B.Stochastic Dynamics of Structures[M].Singapore:John Wiley&Sons Pte Ltd,2009.
[12]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 on probability density evolution equations of stochastic dynamical systems[J].Advances in Mechanics,2010,40(2):170—188.
[13]Priestley M B.Evolutionary spectra and nonstationary processes[J].Journal of the Royal Statistical Society:Series B,1965,27:204—237.
[14]Priestley M B.Power spectral analysis of non-stationary random processes[J].Journal of Sound and Vibration,1967,6(1):86—97.
[15]Shinozuka M,Deodatis G.Simulation of stochastic processes by spectral representation[J].Applied Mechanics Review,1991,44(4):191—204.
[16]Deodatis G.Non-stationary stochastic vector processes:seismic ground motion applications[J].Probabilistic Engineering Mechanics,1996,11:149—168.
[17]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998.
[18]Li J,Chen J B.The number theoretical method in response analysis of nonlinear stochastic structures[J].Computational Mechanics,2007,39(6):693—708.
[19]Peng Y B,Li J.Exceedance probability criterion based stochastic optimal polynomial control of Duffing oscillators[J].International Journal of Non-linear Mechanics,2011,46:457—469.
[20]Li J,Chen J B,Fan W L.The equivalent extreme-value event and evaluation of the structural system reliability[J].Structural Safety,2007,29(2):112—131.
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