非平稳地震作用下线性系统的首次穿越
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摘要
在结构动力学系统的可靠性分析中,受随机激励线性系统的首次穿越问题一直是研究热点之一。该文给出了非平稳地震作用下线性系统首次穿越的重要抽样法。应用Gisranov定理变换概率测度,利用设计点构造控制函数,应用到系统的Ito随机微分方程中。通过数值模拟,结果显示了方法的正确性与有效性。与蒙特卡罗模拟方法相比较,样本数量、计算时间都明显减小。
In the reliability analysis of dynamical systems subjected to uncertain excitations,the first passage failure is the most important issue.This paper suggests a procedure for estimating failure probabilities of linear systems subjected to a non-stationary earthquake based on importance sampling technique.By using of Gisranov Theorem,the probability measure of Wiener processes is transformed and a control function is constructed.The simulation results show that the method is correct and effective.The number of samples and the computational time are reduced significantly,compared with direct Monte Carlo simulations.
In the reliability analysis of dynamical systems subjected to uncertain excitations,the first passage failure is the most important issue.This paper suggests a procedure for estimating failure probabilities of linear systems subjected to a non-stationary earthquake based on importance sampling technique.By using of Gisranov Theorem,the probability measure of Wiener processes is transformed and a control function is constructed.The simulation results show that the method is correct and effective.The number of samples and the computational time are reduced significantly,compared with direct Monte Carlo simulations.
引文
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[9]Heonsang Koo,Armen Der Kiureghian,KazuyaFujimura.Design-point excitation for non-linear randomvibrati ons[J].Probabilistic Engineering Mechanics,2005,20:136―147.
[10]Olsen A Ivanova,Naess A.Estimation of failureprobabilities of linear dynamic systems by importancesampling[J].Sadhana,Journal of Engineering Scienceand Indian Academy Science,2006,31(4):1―15.
[11]Olsen A I,Naess A.An importance sampling procedurefor estimating failure probabilities of non-linear dynamicsystems subjected to random noise[J].InternationalJournal of Non-linear Mechanics,2007,42:848―863.
[12]Pradlwarter H J,Schueller G I.Excursion probabilities ofnon-linear systems[J].International Journal ofNon-linear Mechanics,2004,39:1447―1452.
[13]Ogawa J,Tanaka H.Importance sampling for stochasticsystems under stationary noise having a specified powerspectrum[J].Probabilistic Engineering Mechanics,2009,24:537―544.
[14]任丽梅,徐伟,肖玉柱,王文杰.基于重要样本法的结构动力学系统的首次穿越[J].力学学报,2012,44(3):648―652.Ren Limei,Xu Wei,Xiao Yuzhu,Wang Wenjie.Firstexcursion probabilities of dynamical systems byimportance sampling[J].Chinese Journal of Theoreticaland Applied Mechanics,2012,44(3):648―652.(inChinese)
[2]Socha L,Soong T T.Linearization in analysis ofnonlinear stochastic systems[J].Applied MechanicsReviews,1991,44:399―422.
[3]Sharp W D,Allen E J.Numerical solution of firstpassage problems using an approximate ChapmanKolmogorov relation[J].Probabilistic EngineeringMechanics,1998,3(13):233―241.
[4]Wei Li,Wei Xu.First passage problem for strongnonlinear stochastic dynamical system[J].Chaos,Solitons&Fractals,2006,28(2):414―421.
[5]Zhu W Q,Wu Y J.First-passage time of duffingoscillator under combined harmonic and white-noiseexcitations[J].Nonlinear Dynamics,2003,32:291―305.
[6]Newton N J.Variance reduction for simulated diffusions[J].SIAM Journal of Applied Mathematics,1994,54(6):1780―1805.
[7]Macke M,Bucher C.Importance sampling for randomlyexcited dynamical systems[J].Journal of Sound andVibration,2003,268:269―290.
[8]Au S K,Beck J L.First excursion probabilities for linearsystems by very efficient importance sampling[J].Probabilistic Engineering Mechanics,2001(16):193―207.
[9]Heonsang Koo,Armen Der Kiureghian,KazuyaFujimura.Design-point excitation for non-linear randomvibrati ons[J].Probabilistic Engineering Mechanics,2005,20:136―147.
[10]Olsen A Ivanova,Naess A.Estimation of failureprobabilities of linear dynamic systems by importancesampling[J].Sadhana,Journal of Engineering Scienceand Indian Academy Science,2006,31(4):1―15.
[11]Olsen A I,Naess A.An importance sampling procedurefor estimating failure probabilities of non-linear dynamicsystems subjected to random noise[J].InternationalJournal of Non-linear Mechanics,2007,42:848―863.
[12]Pradlwarter H J,Schueller G I.Excursion probabilities ofnon-linear systems[J].International Journal ofNon-linear Mechanics,2004,39:1447―1452.
[13]Ogawa J,Tanaka H.Importance sampling for stochasticsystems under stationary noise having a specified powerspectrum[J].Probabilistic Engineering Mechanics,2009,24:537―544.
[14]任丽梅,徐伟,肖玉柱,王文杰.基于重要样本法的结构动力学系统的首次穿越[J].力学学报,2012,44(3):648―652.Ren Limei,Xu Wei,Xiao Yuzhu,Wang Wenjie.Firstexcursion probabilities of dynamical systems byimportance sampling[J].Chinese Journal of Theoreticaland Applied Mechanics,2012,44(3):648―652.(inChinese)
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