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

概率密度演化理论的若干研究进展

李杰 陈建兵

李杰, 陈建兵. 概率密度演化理论的若干研究进展[J]. 应用数学和力学, 2017, 38(1): 32-43. doi: 10.21656/1000-0887.370336
引用本文: 李杰, 陈建兵. 概率密度演化理论的若干研究进展[J]. 应用数学和力学, 2017, 38(1): 32-43. doi: 10.21656/1000-0887.370336
LI Jie, CHEN Jian-bing. Some New Advances in the Probability Density Evolution Method[J]. Applied Mathematics and Mechanics, 2017, 38(1): 32-43. doi: 10.21656/1000-0887.370336
Citation: LI Jie, CHEN Jian-bing. Some New Advances in the Probability Density Evolution Method[J]. Applied Mathematics and Mechanics, 2017, 38(1): 32-43. doi: 10.21656/1000-0887.370336

概率密度演化理论的若干研究进展

doi: 10.21656/1000-0887.370336
基金项目: 国家自然科学基金(51538010;11672209)
详细信息
    作者简介:

    李杰(1957—),男,教授,博士,博士生导师(通讯作者. E-mail: lijie@tongji.edu.cn).

  • 中图分类号: O324

Some New Advances in the Probability Density Evolution Method

Funds: The National Natural Science Foundation of China(51538010;11672209)
  • 摘要: 介绍了随机动力系统中概率密度演化理论的基本方程与求解方法〖CX4〗.〖CX〗在此基础上,论述了广义概率密度演化方程求解的若干新进展,包括群演化方程及其求解、概率空间剖分的理性准则、点集加密技术与信息拓展方法等.
  • [1] Crandall S H. Random Vibration [M]. Cambridge: MIT Press, 1958.
    [2] Shinozuka M. Monte Carlo solution of structural dynamics[J]. Computers & Structures,1972,2(5/6): 855-874.
    [3] Liu W K, Bestefield G, Belytschko T. Transient probabilistic systems[J]. Computer Methods in Applied Mechanics and Engineering,1988,67(1): 27-54.
    [4] Kleiber M, Hien T D. The Stochastic Finite Element Method: Basic Perturbation Technique and Computer Implementation [M]. John Wiley & Sons, 1992.
    [5] Ghanem R, Spanos P D. Stochastic Finite Elements: A Spectral Approach [M]. Berlin: Springer-Verlag, 1991.
    [6] 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 Systems—Analysis and Modeling [M]. Beijing: Science Press, 1996.(in Chinese))
    [7] ZHU Wei-qiu, HUANG Zhi-long. Lyapunov exponents and stochastic stability of quasi-integrable-Hamiltonian systems[J]. ASME Journal of Applied Mechanics,1999,66(1): 211-217.
    [8] 朱位秋. 非线性随机动力学与控制[M]. 北京: 科学出版社, 2003.(ZHU Wei-qiu. Nonlinear Stochastic Dynamics and Control [M]. Beijing: Science Press, 2003.(in Chinese))
    [9] ZHU Wei-qiu. Nonlinear stochastic dynamics and control in Hamiltonian formulation[J].Applied Mechanics Reviews,2006,59(4): 230-248.
    [10] Fang T, Leng X L, Song C Q. Chebyshev polynomial approximation for dynamical response problems of random system[J]. Journal of Sound and Vibration,2003,266(1): 198-206.
    [11] XIU Dong-bin. Fast numerical methods for stochastic computations: a review[J]. Communications in Computational Physics,2009,5(2/4): 242-272.
    [12] Housner G W. Characteristics of strong-motion earthquakes[J]. Bulletin of the Seismological Society of America,1947,37(1): 19-31.
    [13] Kanai K. Semi-empirical formula for the seismic characteristics of the ground[J]. Bull Earthquake Research Institute, University of Tokyo,1957,35(2): 309-325.
    [14] Tajimi H. A statistical method of determining the maximum response of a building structure during an earthquake[C]// Proc Second World Conf on Earthq Eng.Vol11. Tokyo, Japan, 1960.
    [15] 胡聿贤, 周锡元. 地震力统计理论的评介[C]//刘恢先, 编. 地震工程研究报告集(第一集). 北京: 科学出版社, 1962: 21-32.(HU YU-xian, ZHOU Xi-yuan. A review on statistical theory for seismic forces[C]//LIU Hui-xian, ed. Collected Research Reports on Earthquake Engineering(Volume One).Beijing: Science Press, 1962: 21-32.(in Chinese))
    [16] Clough R W, Penzien J. Dynamics of Structures [M]. 2nd ed. McGraw-Hill College, 1973.
    [17] Davenport A G. The spectrum of horizontal gustiness near the ground in high winds[J]. Quarterly Journal of the Royal Meteorological Society,1961,87(372): 194-211.
    [18] Hasselmann K, Barnett T P, Bouws E, et al. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP)[J]. Erga nzungsheft Deut Hydr Zeit,1973,12: 1-95.
    [19] Wen Y K. Method for random vibration of hysteretic systems[J]. Journal of the Engineering Mechanics Division,1976,102(2): 249-263.
    [20] Roberts J B, Spanos P D. Random Vibration and Statistical Linearization [M]. Chichester: John Wiley & Sons Ltd, 1990.
    [21] Lutes L D, Sarkani S. Random Vibrations: Analysis of Structural and Mechanical Systems[M]. Amsterdam: Elsevier, 2004.
    [22] Goller B, Pradlwarter H J, Schueller G I. Reliability assessment in structural dynamics[J]. Journal of Sound and Vibration,2013,332(10): 2488-2499.
    [23] 李杰, 陈建兵. 随机结构非线性动力响应的概率密度演化分析[J]. 力学学报, 2003,35(6): 716-722.(LI Jie, CHEN Jian-bing. The probability density evolution method for analysis of dynamic nonlinear response of stochastic structures[J]. Acta Mechanica Sinica,2003,35(6): 716-722.(in Chinese))
    [24] LI Jie, CHEN Jian-bing. Stochastic Dynamics of Structures [M]. Singapore: John Wiley & Sons, 2009.
    [25] LI Jie, CHEN Jian-bing, FAN Wen-liang. The equivalent extreme-value event and evaluation of the structural system reliability[J]. Structural Safety,2007,29(2): 112-131.
    [26] LI Jie, PENG Yong-bo, CHEN Jian-bing. A physical approach to structural stochastic optimal controls[J]. Probabilistic Engineering Mechanics,2010,25(1): 127-141.
    [27] Vanmarcke E. Random Fields [M]. 2nd ed. Singapore: World Scientific, 2010.
    [28] LI Jie, YAN Qi, CHEN Jian-bing. Stochastic modeling of engineering dynamic excitations for stochastic dynamics of structures[J]. Probabilistic Engineering Mechanics,2012,27(1): 19-28.
    [29] LIU Zhang-jun, LIU Wei, PENG Yong-bo. Random function based spectral representation of stationary and non-stationary stochastic processes[J]. Probabilistic Engineering Mechanics,2016,45: 115-126.
    [30] CHEN Jian-bing, SUN Wei-ling, LI Jie, et al. Stochastic harmonic function representation of stochastic processes[J]. Journal of Applied Mechanics,2013,80(1): 011001-1-011001-11.
    [31] 李杰, 吴建营, 陈建兵. 混凝土随机损伤力学[M]. 北京: 科学出版社, 2014.(LI Jie, WU Jian-ying, CHEN Jian-bing. Stochastic Damage Mechanics of Concrete Structures [M]. Beijing: Science Press, 2014.(in Chinese))
    [32] LI Jie, CHEN Jian-bing. The principle of preservation of probability and the generalized density evolution equation[J]. Structural Safety,2008,30(1): 65-77.
    [33] LI Jie, CHEN Jian-bing, SUN Wei-ling, et al. Advances of the probability density evolution method for nonlinear stochastic systems[J]. Probabilistic Engineering Mechanics,2012,28: 132-142.
    [34] 蒋仲铭, 李杰. 三类随机系统广义概率密度演化方程的解析解[J]. 力学学报, 2016,48(2): 1-9.(JIANG Zhong-ming, LI Jie. Analytical solutions of the generalized probability density evolution equation of three classes stochastic systems[J]. Chinese Journal of Theoretical and Applied Mechanics,2016,48(2): 1-9.(in Chinese))
    [35] LI Jie, CHEN Jian-bing. Dynamic response and reliability analysis of structures with uncertain parameters[J]. International Journal for Numerical Methods in Engineering,2005,62(2): 289-315.
    [36] Papadopoulos V, Kalogeris I. A Galerkin-based formulation of the probability density evolution method for general stochastic finite element systems[J]. Computational Mechanics,2016,57(5): 701-716.
    [37] XU Jun, CHEN Jian-bing, LI Jie. Probability density evolution analysis of engineering structures via cubature points[J]. Computational Mechanics,2012,50(1): 135-156.
    [38] CHEN Jian-bing, Ghanem R, LI Jie. Partition of the probability-assigned space in probability density evolution analysis of nonlinear stochastic structures[J]. Probabilistic Engineering Mechanics,2009,24(1): 27-42.
    [39] LI Jie, TAO Wei-feng. A first order assemble evolution method for solving GDEE[C]// Proceedings of the 〖STBX〗1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering.Crete, Greece, 2015: 891-897.
    [40] Papoulis A, Pillai S U. Probability, Random Variables and Stochastic Processes [M]. 4th ed. Boston: McGraw-Hill, 2002.
    [41] 华罗庚, 王元. 数论在近似分析中的应用[M]. 北京: 科学出版社, 1978.(HUA Luo-geng, WANG Yuan. Applications of Number Theory to Numerical Analysis [M]. Beijing: Science Press, 1978.(in Chinese))
    [42] Niederreiter H. Random Number Generation and Quasi-Monte Carlo Methods [M]. Philadelphia: Society for Industrial and Applied Mathematics, 1992.
    [43] CHEN Jian-bing, ZHANG Sheng-han. Improving point selection in cubature by a new discrepancy[J]. SIAM Journal on Scientific Computing,2013,35(5): A2121-A2149.
    [44] CHEN Jian-bing, YANG Jun-yi, LI Jie. A GF-discrepancy for point selection in stochastic seismic response analysis of structures with uncertain parameters[J]. Structural Safety,2016,59: 20-31.
    [45] CHEN Jian-bing, SONG Peng-yan. A generalized L2-discrepancy for cubature and uncertainty quantification of nonlinear structures[J]. Science China: Technological Sciences,2016,59(6): 941-952.
    [46] CHEN Jian-bing, SONG Peng-yan, REN Xiao-dan. Stochastic dynamic response analysis of nonlinear structures with general nonuniform random parameters by minimizing GL2-discrepancy[J]. International Journal for Multiscale Computational Engineering,2016,14(3): 215-235.
    [47] XU Jun, WANG Ding, DANG Chao. A marginal fractional moments based strategy for points selection in seismic response analysis of nonlinear structures with uncertain parameters[J]. Journal of Sound and Vibration,2017,387: 226-238.
    [48] 李杰, 孙伟玲. 广义概率密度演化方程的再生核质点加密算法[J]. 计算力学学报, 2016,33(4): 543-549.(LI Jie, SUN Wei-ling. The refined algorithm of generalized density evolution equation based on reproducing kernel particle method[J]. Chinese Journal of Computational Mechanics,2016,33(4): 543-549.(in Chinese))
    [49] JIANG Zhong-ming, LI Jie. A new reliability method combining Kriging and probability density evolution method[J]. International Journal of Structural Stability and Dynamics.
    [50] LI Jie, TAO Wei-feng. Application of SVM in ensemble evolution method of stochastic structural analysis[C]//5th International Symposium on Reliability Engineering and Risk Management.Seoul, Korea, 2016.
  • 加载中
计量
  • 文章访问数:  723
  • HTML全文浏览量:  28
  • PDF下载量:  2032
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-11-04
  • 刊出日期:  2017-01-15

目录

    /

    返回文章
    返回