MEI Zhen, GUO Zi-xiong, HUANG Qun-xian, LIU Yang. Effects of the Number of Representative Points on the Analysis Accuracy of the Probability Density Evolution Method[J]. Applied Mathematics and Mechanics, 2016, 37(1): 97-106. doi: 10.3879/j.issn.1000-0887.2016.01.008
Citation: MEI Zhen, GUO Zi-xiong, HUANG Qun-xian, LIU Yang. Effects of the Number of Representative Points on the Analysis Accuracy of the Probability Density Evolution Method[J]. Applied Mathematics and Mechanics, 2016, 37(1): 97-106. doi: 10.3879/j.issn.1000-0887.2016.01.008

Effects of the Number of Representative Points on the Analysis Accuracy of the Probability Density Evolution Method

doi: 10.3879/j.issn.1000-0887.2016.01.008
Funds:  The National Natural Science Foundation of China(51208219)
  • Received Date: 2015-09-06
  • Rev Recd Date: 2015-11-13
  • Publish Date: 2016-01-16
  • 3 sets of random ground motions with different-size samples were generated based on a physical stochastic ground motion model and a strategy of selecting points via sphere of contact. Then the stochastic response analysis of a model structure subjected to the generated ground motions was carried out with the probability density evolution method (PDEM). Through comparison of the results from the stochastic seismic response analysis, the effects of the number of representative points on the analysis accuracy of the PDEM were investigated. Numerical results show that a relatively small number of representative points selected under the strategy of sphere of contact yield fairly accurate results of the 1st- and 2nd-order statistical characteristics of structural responses. At the same time, it is pointed out that a small sample size may lead to a certain analytical errors of the response probability distribution at each time point. Therefore, the number of representative points in the PDEM should be reasonably determined according to the number of random variables of the related stochastic dynamic system, the method of selecting representative points and the expected calculation accuracy.
  • loading
  • [1]
    林家浩, 张亚辉. 随机振动的虚拟激励法[M]. 北京: 科学出版社, 2004.(LIN Jia-hao, ZHANG Ya-hui. Pseudo-Excitation Method for Random Vibration [M]. Beijing: Science Press, 2004.(in Chinese))
    [2]
    Lutes L D, Sarkani S. Random Vibrations: Analysis of Structural and Mechanical Systems[M]. Amsterdam: Elsevier, 2004.
    [3]
    朱位秋. 非线性随机动力学与控制——Hamilton理论体系框架[M]. 北京: 科学出版社, 2003.(ZHU Wei-qiu. Nonlinear Stochastic Dynamics and Control—Hamilton Theoretical Framework[M]. Beijing: Science Press, 2003.(in Chinese))
    [4]
    李杰, 陈建兵. 随机结构反应的概率密度演化分析[J]. 同济大学学报(自然科学版), 2003,31(12): 1387-1391.(LI Jie, CHEN Jian-bing. Probability density evolution of stochastic structural responses[J]. Journal of Tongji University(Natural Science),2003,31(12): 1387-1391.(in Chinese))
    [5]
    Li J, Chen J B. Probability density evolution method for dynamic response analysis of structures with uncertain parameters[J].Computational Mechanics,2004,34(5): 400-409.
    [6]
    Li J, Chen J B.Stochastic Dynamics of Structures [M]. Singapore: John Wiley & Sons, 2009.
    [7]
    陈建兵, 李杰. 结构随机地震反应与可靠度的概率密度演化分析研究进展[J]. 工程力学, 2014,31(4): 1-10.(CHEN Jian-bing, LI Jie. Probability density evolution method for stochastic seismic response and reliability of structures[J]. Engineering Mechanics,2014,31(4): 1-10.(in Chinese))
    [8]
    LI Jie, CHEN Jian-bing. The dimension-reduction strategy via mapping for probability density evolution analysis of nonlinear stochastic systems[J]. Probabilistic Engineering Mechanics,2006,21(4): 442-453.
    [9]
    陈建兵, 李杰. 结构随机响应概率密度演化分析的数论选点法[J]. 力学学报, 2006,38(1): 134-140.(CHEN Jian-bing, LI Jie. Strategy of selecting points via number theoretical method in probability density evolution analysis of stochastic response of structures[J]. Chinese Journal of Theoretical and Applied Mechanics,2006,38(1): 134-140.(in Chinese))
    [10]
    LI Jie, CHEN Jian-bing. The number theoretical method in response analysis of nonlinear stochastic structures[J]. Computational Mechanics,2007,39(6): 693-708.
    [11]
    陈建兵, 李杰. 随机结构反应概率密度演化分析的切球选点法[J]. 振动工程学报, 2006,19(1): 1-8.(CHEN Jian-bing, LI Jie. Strategy of selecting points via sphere of contact in probability density evolution method for response analysis of stochastic structures[J]. Journal of Vibration Engineering,2006,19(1): 1-8.(in Chinese))
    [12]
    CHEN Jian-bing, LI Jie. Strategy for selecting representative points via tangent spheres in the probability density evolution method[J].International Journal for Numerical Methods in Engineering,2008,74(13): 1988-2014.
    [13]
    李杰, 徐军, 陈建兵. 概率密度演化理论的拟对称点法[J]. 武汉理工大学学报, 2010,32(9): 1-5.(LI Jie, XU Jun, CHEN Jian-bing. The use of quasi-symmetric point method in probability density evolution theory[J]. Journal of Wuhan University of Technology,2010,32(9): 1-5.(in Chinese))
    [14]
    李杰, 艾晓秋. 基于物理的随机地震动模型研究[J]. 地震工程与工程振动, 2006,26(5): 21-26.(LI Jie, AI Xiao-qiu. Study on random model of earthquake ground motion based on physical process[J].Earthquake Engineering and Engineering Vibration,2006,26(5): 21-26.(in Chinese))
    [15]
    艾晓秋, 李杰. 基于随机Fourier谱的地震动合成研究[J]. 地震工程与工程振动, 2009,29(2): 7-12.(AI Xiao-qiu, LI Jie. Synthesis method of non-stationary ground motion based on random Fourier spectra[J].Earthquake Engineering and Engineering Vibration,2009,29(2): 7-12.(in Chinese))
    [16]
    李杰, 李国强. 地震工程学导论[M]. 北京: 地震出版社, 1992.(LI Jie, LI Guo-qiang. Introduction to Earthquake Engineering [M]. Beijing: Seismological Press, 1992.(in Chinese))
    [17]
    钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994,34(2): 131-136.(ZHONG Wan-xie. On precise time-integration method for structural dynamics[J]. Journal of Dalian University of Technology,1994,34(2): 131-136.(in Chinese))
    [18]
    LI Jie, MEI Zhen, CHEN Jian-bing, PENG Yong-bo. Experimental investigations of stochastic control of randomly base-excited structures[J]. Advances in Structural Engineering,2012,15(11): 1963-1975.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1116) PDF downloads(500) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return