概率密度演化理论的若干研究进展

李杰; 陈建兵

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

李杰,
陈建兵

同济大学土木工程学院;土木工程防灾国家重点实验室(同济大学),上海 200092

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
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出版历程
- 收稿日期: 2016-11-04
- 刊出日期: 2017-01-15

Some New Advances in the Probability Density Evolution Method

College of Civil Engineering, Tongji University;State Key Laboratory of Disaster Reduction in Civil Engineering(Tongji University), Shanghai 200092, P.R.China

Funds: The National Natural Science Foundation of China(51538010;11672209）

摘要

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.
- 随机动力系统 /
- 概率密度演化理论 /
- 群演化 /
- GF偏差 /
- 点集加密
Abstract: The governing equation and solving algorithm of the probability density evolution method for stochastic dynamical systems were outlined. On this basis, some new advances in the solution of the generalized density evolution equation were discussed, including the ensemble evolution equation and its solution, the rational criterion for partitioning of the probability space, the densification technique of point set and the information reconstruction, etc.
- stochastic dynamical system /
- probability density evolution method /
- ensemble evolution /
- GF discrepancy /
- point set densification

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参考文献(50)

[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.