EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一类Markov过程的最大绝对值过程概率密度求解的新方法

陈建兵 律梦泽

陈建兵, 律梦泽. 一类Markov过程的最大绝对值过程概率密度求解的新方法[J]. 力学学报, 2019, 51(5): 1437-1447. doi: 10.6052/0459-1879-19-104
引用本文: 陈建兵, 律梦泽. 一类Markov过程的最大绝对值过程概率密度求解的新方法[J]. 力学学报, 2019, 51(5): 1437-1447. doi: 10.6052/0459-1879-19-104
Chen Jianbing, Lü Mengze. A NEW METHOD FOR THE PROBABILITY DENSITY OF MAXIMUM ABSOLUTE VALUE OF A MARKOV PROCESS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1437-1447. doi: 10.6052/0459-1879-19-104
Citation: Chen Jianbing, Lü Mengze. A NEW METHOD FOR THE PROBABILITY DENSITY OF MAXIMUM ABSOLUTE VALUE OF A MARKOV PROCESS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1437-1447. doi: 10.6052/0459-1879-19-104

一类Markov过程的最大绝对值过程概率密度求解的新方法

doi: 10.6052/0459-1879-19-104
基金项目: 1)国家杰出青年科学基金;国家自然科学基金(11672209);国家自然科学基金(11761131014);国家自然科学基金(51538010);科技部国家重点实验室基金资助项目(SLDRCE19-B-23)
详细信息
    通讯作者:

    陈建兵

  • 中图分类号: U260.17

A NEW METHOD FOR THE PROBABILITY DENSITY OF MAXIMUM ABSOLUTE VALUE OF A MARKOV PROCESS

  • 摘要: 随机过程或随机系统响应的最大绝对值概率分布往往是科学与工程中关心的重要挑战性问题.本文从理论与数值上进行了Markov过程的时变最大绝对值过程及其概率分布研究.文中,通过引入扩展状态向量,构造了最大绝对值$\!$-$\!$-$\!$状态量联合向量过程,由此将不具有Markov性的最大值过程转化为具有Markov性的向量随机过程.在此基础上,通过最大绝对值$\!$-$\!$-$\!$状态量之间的关系,建立了联合向量过程的转移概率密度函数.进而,结合Chapman-Kolmogorov方程和路径积分方法,提出了最大绝对值概率密度函数求解的数值方法.由此,可以得到Markov过程最大绝对值过程的时变概率密度函数,可进一步用于结构动力可靠度分析等.通过数值算例,验证了本文所提方法的有效性. 该方法有望推广到更一般随机系统的极值分布估计之中.

     

  • [1] Arrechi FT . Transition Phenomena in Nonlinear Optics. Berlin: Springer, 1981
    [2] Bras RL . Hydrology: An Introduction to Hydrological Science. Reading: Addison-Wesley, 1990
    [3] 胡岗 . 随机力与非线性系统. 上海: 上海科技教育出版社, 1994
    [3] ( Hu Gang. Stochastic Forces and Nonlinear Systems. Shanghai: Shanghai Scientific and Technological Education Publishing House, 1994 (in Chinese))
    [4] ?ksendal B. Stochastic Differential Equations. 5th Ed. Berlin: Springer-Verlag, 1998
    [5] Hull JC. Option , Futures, Other Derivatives. 4th Ed. Upper Saddle River: Prentice-Hall, 2000
    [6] Li J, Chen JB . Stochastic Dynamics of Structure. Singapore: John Wiley & Sons (Asia) Pte Ltd, 2009
    [7] 苏成, 徐瑞 . 非平稳随机激励下结构体系动力可靠度时域解法. 力学学报, 2010,42(3):512-520
    [7] ( Su Cheng, Xu Rui . Time-domain method for dynamic reliability of structural systems subjected to non-stationary random excitations. Chinese Journal of Theoretical and Applied Mechanics, 2010,42(3):512-520 (in Chinese))
    [8] Fisher RA, Tippett LHC . Limiting forms of the frequency distribution of the largest and smallest member of a sample. Mathematical Proceedings of the Cambridge Philosophical Society, 1928,24(2):180-190
    [9] Gumbel EJ. Statistics of Extremes. New York: Columbia University Press, 1958
    [10] Coles S . An Introduction to Statistical Modeling of Extreme Values. Springer, 2001
    [11] Powell A . On the fatigue failure of structures due to vibration excited by random pressure fields. The Journal of the Acoustical Society of America, 1958,30(2):1130-1135
    [12] Dudley RM. Real Analysis and Probability. Cambridge: The Press Syndicate of the University of Cambridge, 1989
    [13] Klebaner FC. Introduction to Stochastic Calculus with Application. 2nd Ed. London: Imperial College Press, 2005
    [14] Redner S. A Guide to First-Passage Processes. Cambridge: Cambridge University Press, 2001
    [15] 陈建兵, 李杰 . 非线性随机结构动力可靠度的密度演化方法. 力学学报, 2004,36(2):196-201
    [15] ( Chen Jianbing, Li Jie . The probability density evolution method for dynamic reliability assessment of nonlinear stochastic structures. Chinese Journal of Theoretical and Applied Mechanics, 2004,36(2):196-201 (in Chinese))
    [16] Monili A, Talkner P, Katul GG , et al. First passage time statistics of Brownian motion with purely time dependent drift and diffusion. Physica A - Statistical Mechanics & Its Applications, 2011,390:1841-1852
    [17] Kou S, Zhong H . First-passage times of two-dimensional Brownian motion. Advanced Applied Probability, 2016,48:1045-1060
    [18] Li J, Chen JB . The principle of preservation of probability and the generalized density evolution equation. Structural Safety, 2008,30:65-77
    [19] 陈建兵, 张圣涵 . 非均布随机参数结构非线性响应的概率密度演化. 力学学报, 2014,46(1):136-144
    [19] ( Chen Jianbing, Zhang Shenghan . Probability density evolution analysis of nonlinear response of structures with non-uniform random parameters. Chinese Journal of Theoretical and Applied Mechanics, 2014,46(1):136-144 (in Chinese))
    [20] Chen JB, Li J . The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters. Structural Safety, 2007,29:77-93
    [21] Mannella R, Palleschi V . Fast and precise algorithm for computer simulation of stochastic differential equations. Physical Review A, 1989,40(6):3381-3386
    [22] Honeycutt RL . Stochastic Runge-Kutta algorithms. I. White noise. Physical Review A, 1992,45(2):600-603
    [23] Honeycutt RL . Stochastic Runge-Kutta algorithms. II. Colored noise. Physical Review A, 1992,45(2):604-610
    [24] Higham DJ . An algorithmic introduction to numerical simulation of stochastic differential equations. Society for Industrial and Applied Mathematics, 2001,43(3):525-546
    [25] 朱位秋. 随机振动. 北京:科学出版社, 1992
    [25] ( Zhu Weiqiu. Random Vibration. Beijing: Science Press, 2003)
    [26] Gardiner CW . Handbook of Stochastic Methods for Physics. 2nd Ed. Berlin: Springer-Verlag, 1985
    [27] 徐伟 . 非线性随机动力学的若干数值方法及应用. 北京: 科学出版社, 2013
    [27] ( Xu Wei. Numerical Analysis Methods for Stochastic Dynamical System. Beijing: Science Press, 2013 (in Chinese))
    [28] Risken H . The Fokker-Planck Equation. 2nd Ed. Berlin: Springer-Verlag, 1989
    [29] Chen JB, Lyu MZ . A new approach for the time-variant probability density function of the maximum value of a Markov process. Journal of Computational Physics, 2019 ( under review)
    [30] Lyu MZ, Chen JB, Pirrotta A . A novel method based on augmented Markov vector process for the time-variant extreme value distribution of stochastic dynamical systems enforced by Poisson white noise. Communications in Nonlinear Science and Numerical Simulation, 2019 ( accepted)
    [31] Er GK . Exponential closure method for some randomly excited non-linear systems. International Journal of Non-Linear Mechanics, 2000,35:69-78
    [32] 朱位秋 . 非线性随机动力学与控制---Hamilton理论体系框架. 北京: 科学出版社, 2003
    [32] ( Zhu Weiqiu. Nonlinear Stochastic Dynamics and Control---Hamiltonian Formulation. Beijing: Science Press, 2003 (in Chinese))
    [33] Chen JB, Yuan SR . Dimension Reduction of the FPK Equation via an Equivalence of Probability Flux for Additively Excited Systems. Journal of Engineering Mechanics, 2014,140(11):04014088
    [34] Chen JB, Rui ZM . Dimension-reduced FPK equation for additive white-noise excited nonlinear structures. Probabilistic Engineering Mechanics, 2018,53:1-13
    [35] 芮珍梅, 陈建兵 . 加性非平稳激励下结构速度响应的FPK方程降维. 力学学报, 2019,51(3):922-931
    [35] ( Rui Zhenmei, Chen Jianbing . Dimension reduction of FPK equation for velocity response analysis of structures subjected to additive nonstationary excitations. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(3):922-931 (in Chinese))
  • 加载中
计量
  • 文章访问数:  1090
  • HTML全文浏览量:  116
  • PDF下载量:  108
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-04-25
  • 刊出日期:  2019-09-18

目录

    /

    返回文章
    返回