非平稳随机激励下系统首次穿越概率的近似解法

何军

非平稳随机激励下系统首次穿越概率的近似解法

何军

上海交通大学船建学院土木工程系,上海 200240

基金项目: 国家自然科学基金资助项目(50478017)

详细信息

作者简介:
何军(1968- ),男,河北人,副教授,博士(Tel:+86-21-34206697;Fax:+86-21-34206698;E-mail:junhe@sjtu.edu.cn).

中图分类号: O29
计量
- 文章访问数: 2801
- HTML全文浏览量: 132
- PDF下载量: 674
- 被引次数: 0
出版历程
- 收稿日期: 2008-05-06
- 修回日期: 2008-12-05
- 刊出日期: 2009-02-15

Approximation for the First Passage Probability of Systems Under Nonstationary Random Excitation

HE Jun

Department of Civil Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, P. R. China

摘要

摘要: 提出了非平稳Gauss白噪声激励下线性系统条件首次穿越概率的近似解析解．该近似解基于VanMarcke 近似，但是，因为引进了随机过程和界限水平的标准化，VanMarcke 公式中的期望衰减率可由响应的二阶统计矩获得，而不需要知道响应的相关函数或谱密度函数．给出了非平稳激励下线性系统响应的显式二阶统计矩．调制白噪声激励下单自由度线性系统的首次穿越概率分析说明了该方法的精度、效率和应用过程．
- 首次穿越概率 /
- D类界限 /
- 衰减率 /
- 非平稳激励 /
- 包络线过程
Abstract: An approximate method is presented for obtaining analytical solutions for the conditional fast passage piubability of systems under modulated white noise excitation, the method is based on VanMarcke's approximation, however, because the normalization of the response was introduced, the expected decay rates can be evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the response of considered stnrcrures. Explicit solutions for the second-moment statistics of the response were given. The accuracy, efficiency and usage of the proposed method were demonstrated by the fast passage analysis of single-degree-of freedom (SDOF) linear systems under two special types of modulated white noise excitations.
- first passage probability /
- D-type barrier /
- decay rate /
- nonstationary excitation /
- envelope Process

HTML全文

参考文献(22)

[1]	Wen Y K, Chen H C. System reliability under time varying loads: Ⅰ[J].Internat J Engng Mech ASCE,1989,115(4): 808-823. doi: 10.1061/(ASCE)0733-9399(1989)115:4(808)
[2]	Beck A T, Melchers R E. On the ensemble crossing rate approach to time variant reliability analysis of uncertain structures[J].Internat J Probab Engng Mech,2004,19(1): 9-19. doi: 10.1016/j.probengmech.2003.11.018
[3]	Polidori D C, Beck J L, Papadimitriou C. New approximations for reliability integrals[J].Internat J Engng Mech ASCE,1999,125(4)：466-475. doi: 10.1061/(ASCE)0733-9399(1999)125:4(466)
[4]	Bayer V, Bucher C. Importance sampling for the first passage problems of nonlinear structures[J].Internat J Probab Engng Mech,1999，14(1): 27-32. doi: 10.1016/S0266-8920(98)00014-9
[5]	Au S K, Beck J L. First excursion probability for linear system by very efficient important sampling[J].Internat J Probab Engng Mech,2001,16(2)：193-207. doi: 10.1016/S0266-8920(01)00002-9
[6]	Roberts J B. First-passage probability for randomly excited systems: diffusion methods[J].Internat J Probab Engng Mech,1986,1(1): 66-81. doi: 10.1016/0266-8920(86)90029-9
[7]	Proppe C, Pradlwarter H J, Schuёller G I. Equivalent linearization and Monte Carlo simulation in stochastic dynamics[J].Internat J Probab Engng Mech,2003, 18(1)：1-15. doi: 10.1016/S0266-8920(02)00037-1
[8]	Zhu W Q, Deng M L, Huang Z L. First-passage failure of quasi-integrable Hamiltonian systems[J].Internat J Appl Mech ASME,2002,69(2)：274-282. doi: 10.1115/1.1460912
[9]	Coleman J J. Reliability of aircraft structures in resisting change failure[J]. Internat J Operations Reserch, 1959,7(4): 639-645.
[10]	VanMarcke E H. On the distribution of the first-passage time for normal stationary random process[J].Internat J Appl Mech ASME,1975,42(2): 215-220. doi: 10.1115/1.3423521
[11]	Lutes L D, Chen Y T, Tzuang S H. First-passage approximations for simple oscillators[J].Internat J Engng Mech Div ASCE,1980,106(EM6): 1111-1124.
[12]	Madsen P H, Krenk S. An integral equation method for the first-passage prolem in random vibration[J].Internat J Appl Mech ASME,1983,51(3): 674-679.
[13]	Langley R S. A first passage approximation for normal stationary random processes[J]. J Sound Vibration,1988,122(2): 261-275. doi: 10.1016/S0022-460X(88)80353-5
[14]	Engelund S, Rackwitz R, Lange C. Approximations of first-passage times for differentiable processes based on high-order threshold crossings[J].Internat J Probab Engng Mech,1995,10(1): 53-60. doi: 10.1016/0266-8920(94)00008-9
[15]	Naess A, Karlsen H C. Numerical calculation of the level crossing rate of second order stochastic Volterra systems[J].Internat J Probab Engng Mech,2004，19(2): 155-160. doi: 10.1016/j.probengmech.2003.11.012
[16]	何军. 非Gauss随机特性下的结构首次失效时间研究[J].应用数学和力学，2007,28(11): 1325-1332.
[17]	Song J, Kiureghian A D. Joint first-passage probability and reliability of systems under stochastic excitation[J].Internat J Engng Mech ASCE,2006,132(1): 65-77. doi: 10.1061/(ASCE)0733-9399(2006)132:1(65)
[18]	Iwan W D, Hou Z K. Explicit solutions for the response of simple systems subjected to nonstationary random excitation[J].Internat J Struct Saf,1989,6(2/4):77-86. doi: 10.1016/0167-4730(89)90011-8
[19]	Michaelov G, Sarkani S, Lutes L D. Spectral characteristic of nonstationary random processes response of a simple oscillator[J].Internat J Struct Saf,1999,21(2): 245-267. doi: 10.1016/S0167-4730(99)00019-3
[20]	Rice S O. Mathematical analysis of random noise[J].Bell System Technical Journal,1944,2: 282-332.[Re-published In: N Wax，Ed.Selected Papers on Noise and Stochastic Processes. [C]. New York: Dover, 1954].
[21]	Langley R S. On various definitions of the envelope of a random process[J].J Sound Vibration,1986,105(3): 503-512. doi: 10.1016/0022-460X(86)90175-6
[22]	Krenk S, Madsen H O, Madsen P H. Stationary and transient response envelopes[J]. Internat J Engng Mech ASCE,1983,109(1): 263-278. doi: 10.1061/(ASCE)0733-9399(1983)109:1(263)

施引文献

资源附件(0)

访问统计

计量

文章访问数: 2801
HTML全文浏览量: 132
PDF下载量: 674
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

非平稳随机激励下系统首次穿越概率的近似解法

作者简介:
何军(1968- ),男,河北人,副教授,博士(Tel:+86-21-34206697;Fax:+86-21-34206698;E-mail:junhe@sjtu.edu.cn).

计量

Approximation for the First Passage Probability of Systems Under Nonstationary Random Excitation

计量

目录

留言板

非平稳随机激励下系统首次穿越概率的近似解法

作者简介: 何军(1968- ),男,河北人,副教授,博士(Tel:+86-21-34206697;Fax:+86-21-34206698;E-mail:junhe@sjtu.edu.cn).

计量

出版历程

Approximation for the First Passage Probability of Systems Under Nonstationary Random Excitation

计量

出版历程

目录

作者简介:
何军(1968- ),男,河北人,副教授,博士(Tel:+86-21-34206697;Fax:+86-21-34206698;E-mail:junhe@sjtu.edu.cn).