EI、Scopus 收录
中文核心期刊
Quick Search Issue Search Advanced Search
Volume 51 Issue 4
Turn off MathJax
Article Contents
Abstract
References
Related Articles
Shi Sheng, Du Dongsheng, Wang Shuguang, Li Weiwei. NON-UNIFORM TIME STEP TVD SCHEME FOR PROBABILITY DENSITY EVOLUTION FUNCTION WITH IMPROVEMENT OF INITIAL CONDITION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1223-1234. DOI: 10.6052/0459-1879-18-446
Citation: Shi Sheng, Du Dongsheng, Wang Shuguang, Li Weiwei. NON-UNIFORM TIME STEP TVD SCHEME FOR PROBABILITY DENSITY EVOLUTION FUNCTION WITH IMPROVEMENT OF INITIAL CONDITION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1223-1234. DOI: 10.6052/0459-1879-18-446
shu

NON-UNIFORM TIME STEP TVD SCHEME FOR PROBABILITY DENSITY EVOLUTION FUNCTION WITH IMPROVEMENT OF INITIAL CONDITION

  • Colleye of Civil Engineering, Nanjing Tech University, Nanjing 211816, China

  • Received Date: December 23, 2018
    Graphical Abstract
    • Abstract
  • Randomness appears widely in practical engineering problems, and nonlinear stochastic response analysis of complex structures is one of the major difficulties. Fortunately, the probability density evolution method proposed in recent years has provided a feasible way to solve this kind of problem. Due to the complexity of practical engineering problems, however, the probability density evolution function is commonly solved by time-consuming numerical methods. Hence, it is crucial to improve the computational efficiency and accuracy of these numerical algorithms. Base on the non-uniform mesh partitioning technique, a new kind of non-uniform time step TVD (total variation diminishing) scheme for probability density evolution function was derived, which improves the computational efficiency by reducing the number of iterations to 43.4%. With the increase of sample duration, the error of estimated mean value remained almost constant, while the error of estimated standard deviation increased accordingly, but the increase rate tended to diminish. The computing time also increased as the sample duration increased, but unusual cases appeared due to the adaptive time step mesh partitioning of the randomly generated samples. In addition, a new kind of initial condition with cosine function form is proposed based on the conventional initial condition with pulse-like function form. The result revealed that the initial condition with pulse-like function form is a special case of the proposed cosine function form initial condition, and the initial condition with cosine function form possesses better accuracy than the initial condition with pulse-like function form when a proper parameter is selected. The improved TVD scheme for probability density evolution equation on non-uniform time step grids with improved initial condition is illustrated with several numerical examples provided in the last section. The work accomplished in this paper is a supplement for the solving method of probability density evolution equation, and provides a basis for engineering application.
    • FullText(HTML)
    • References (1)
  • [1] 朱位秋 . 随机振动. 北京: 科学出版社, 1992
    [1] ( Zhu Weiqiu . Random Vibration. Beijing: Science Press, 1992(in Chinese))
    [2] Housner GW . Characteristics of strong-motion earthquakes. Bulletin of the Seismological Society of America, 1947,37(1):19-31
    [3] Vlachos C, Papakonstantinou KG, Deodatis G . A multi-modal analytical non-stationary spectral model for characterization and stochastic simulation of earthquake ground motions. Soil Dynamics and Earthquake Engineering, 2016,80:177-191
    [4] Muscolino G, Alderucci T . Closed-form solutions for the evolutionary frequency response function of linear systems subjected to separable or non-separable non-stationary stochastic excitations. Probabilistic Engineering Mechanics, 2015,40:75-89
    [5] Wang D, Fan ZL, Hao SW , et al. An evolutionary power spectrum model of fully nonstationary seismic ground motion. Soil Dynamics and Earthquake Engineering, 2018,105:1-10
    [6] 王鼎, 李杰 . 工程地震动的物理随机函数模型. 中国科学:技术科学, 2011,54(3):356-364
    [6] ( Wang Ding, Li Jie . Physical random function model of ground motions for engineering purposes. Science China Tech. Sci., 2011,54(3):356-364(in Chinese))
    [7] Clough R, Penzien J . Dynamics of Structures. New York: McGraw-Hill, 1973
    [8] Chen JB, Rui ZM . Dimension-reduced FPK equation for additive white-noise excited nonlinear structures. Probabilistic Engineering Mechanics, 2018: 53:1-13
    [9] Li J, Jiang ZM . A data-based CR-FPK method for nonlinear structural dynamic systems. Theoretical and Applied Mechanics Letters, 2018(4):231-244
    [10] 阚琳洁, 张建国, 邱继伟 . 柔性机构时变可靠性分析的时变随机响应面法. 振动与冲击, 2019,2:253-258
    [10] ( Kan Linjie, Zhang Jianguo, Qiu Jiwei . Time-varying stochastic response surface method for the time-varying reliability analysis of flexible mechanisms. Journal of Vibration and Shock, 2019,2:253-258(in Chinese))
    [11] Huang XZ, Liu Y, Zhang YM , et al.Reliability analysis of structures using stochastic response surface method and saddlepoint approximation. Structural and Multidisciplinary Optimization, 2017(6):2003-2012
    [12] 刘俊, 陈林聪, 孙建桥 . 随机激励下滞迟系统的稳态响应闭合解. 力学学报, 2017,49(3):685-692
    [12] ( Liu Jun, Cheng Lincong, Sun Jianqiao . The closed-form solution of steady state response of hysteretic system under stochastic excitation. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(3):685-692(in Chinese))
    [13] 李杰, 陈建兵 . 随机结构动力反应分析的概率密度演化方法. 力学学报, 2003,35(4):437-442
    [13] ( Li Jie, Chen Jianbing . Probability density evolution method for analysis of stochastic structural dynamic response. Chinese Journal of Theoretical and Applied Mechanics, 2003,35(4):437-442(in Chinese))
    [14] 李杰, 陈建兵 . 随机动力系统中的概率密度演化方程及其研究进展. 力学进展, 2010,40(2):170-188
    [14] ( Li Jie, Chen Jianbing . Advances in the research on probability density evolution equations of stochastic dynamic systems. Advances in Mechanics, 2010,40(2):170-188(in Chinese))
    [15] 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. 工程力学, 2014,31(4):1-10
    [15] ( Chen Jianbing, Li Jie . Probability density evolution method for stochastic seismic response and reliability of structures. Journal of Engineering Mechanics, 2014,31(4):1-10(in Chinese))
    [16] 李杰, 陈建兵 . 概率密度演化理论的若干研究进展. 应用数学和力学, 2017,38(1):32-43
    [16] ( Li Jie, Chen Jianbing . Some new advances in the probability density evolution method. Applied Mathematics and Mechanics, 2017,38(1):32-43(in Chinese))
    [17] 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
    [17] ( 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))
    [18] 宋鹏彦, 陈建兵, 万增勇 等. 混凝土框架结构随机地震反应概率密度演化分析. 建筑结构学报, 2015,36(11):117-123
    [18] ( Song Pengyan, Chen Jianbing, Wan Zengyong , et al. Probability density evolution analysis of stochastic seismic response of concrete frame structures. Journal of Building Structures, 2015,36(11):117-123(in Chinese))
    [19] 余志武, 何华武, 蒋丽忠 等. 多动力作用下高速铁路轨道-桥梁结构体系动力学及关键技术研究. 土木工程学报, 2017,50(11):1-9
    [19] ( Yu Zhiwu, He Huawu, Jiang Lizhong , et al. Dynamics and key technology research on high-speed railway track-bridge system under multiple dynamic sources. China Civil Engineering Journal, 2017,50(11):1-9(in Chinese))
    [20] 刘章军, 熊敏, 万勇 . 基于概率密度演化的连续刚构桥抗震可靠度. 西南交通大学学报, 2014,49(1):39-44
    [20] ( Liu Zhangjun, Xiong Min, Wan Yong . Seismic reliability analysis of continuous rigid frame bridge using probability density evolution method. Journal of Southwest Jiaotong University, 2014,49(1):39-44(in Chinese))
    [21] 郭弘原, 顾祥林, 周彬彬 等. 基于概率密度演化的锈蚀混凝土梁时变可靠性分析. 建筑结构学报, 2019,40(1):67-73
    [21] ( Guo Hongyuan, Gu Xianglin, Zhou Binbin , et al. Time-dependent reliability analysis for corroded RC beams based on probability density evolution theory. Journal of Building Structures, 2019,40(1):67-73(in Chinese))
    [22] 李杰, 徐军 . 结构随机动力稳定性的定量分析方法. 力学学报, 2016,48(3):702-713
    [22] ( Li Jie, Xu Jun . A quantitative approach to stochastic dynamic stability of structures. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(3):702-713(in Chinese))
    [23] 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. 力学学报, 2016,48(2):413-421
    [23] ( Jiang Zhongming, Li Jie . Analytical solutions of the generalized probability density evolution equation of three classes stochastic systems. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(2):413-421(in Chinese))
    [24] 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. 力学学报, 2006,38(1):134-140
    [24] ( Chen Jianbing, Li Jie . Strategy of selecting points via number theoretical method in probability density evolution analysis of stochastic response of structures. Chinese Journal of Theoretical and Applied Mechanics, 2006,38(1):134-140(in Chinese))
    [25] Li J, Chen JB . The number theoretical method in response analysis of nonlinear stochastic structures. Computational Mechanics, 2007,39(6):693-708
    [26] 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. 振动工程学报, 2006,19(1):1-8
    [26] ( Chen Jianbing, Li Jie . Strategy of selecting points via sphere of contact in probability density evolution method for response analysis of stochastic structures. Journal of Vibration Engineering, 2006,19(1):1-8(in Chinese))
    [27] Chen JB, Li J . Strategy for selecting representative points via tangent spheres in the probability density evolution method. International Journal for Numerical Methods in Engineering, 2008,74(13):1988-2014
    [28] 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
    [28] ( 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))
    [29] Li J, Chen JB . Dynamic response and reliability analysis of structures with uncertain parameters. International Journal for Numerical Methods in Engineering, 2004,62(25):289-315
    [30] Papadopoulos V, Ioannis K . A Galerkin-based formulation of the probability density evolution method for general stochastic finite element systems. Comput Mech, 2015,57(5):701-716
    • Related Articles

  • Related Articles

    [1]Zhang Zhe, Dai Honghua, Feng Haoyang, Wang Xuechuan, Yue Xiaokui. EFFICIENT NUMERICAL METHOD FOR ORBIT DYNAMIC FUNCTIONS WITH INITIAL VALUE AND TWO-POINT BOUNDARY-VALUE CONSTRAINTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(2): 503-516. DOI: 10.6052/0459-1879-21-336
    [2]Qin Zecong, Fang Le. AN IMPROVED METHOD FOR INITIALIZING HOMOGENEOUS ISOTROPIC TURBULENT FLOWS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(6): 1319-1325. DOI: 10.6052/0459-1879-16-180
    [3]Yang Sun, Boying Wu, Guotai Feng. The ausmpw scheme based on adaptive algorithm of interpolating multiwavelets applied to solve euler equations[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(6): 744-751. DOI: 10.6052/0459-1879-2008-6-2007-374
    [4]Lifu Liang, En Luo, Xiaojiu Feng. A variational principle form for initial value problems in analytical mechanics[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(1): 106-111. DOI: 10.6052/0459-1879-2007-1-2006-027
    [5]ORTHOGONALITY CONDITIONS FOR ACTIVE PLATE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(1). DOI: 10.6052/0459-1879-2004-1-2002-392
    [6]REPLY TO DISCUSSION ON“ APPLICATIONS OF A SECONDORDER UPWIND TVD SCHEME TO NONEQUILIBRIUMHYPERSONIC FLOWS AROUND BLUNT-BODY”[J]. Chinese Journal of Theoretical and Applied Mechanics, 1998, 30(6): 757-760. DOI: 10.6052/0459-1879-1998-6-1995-188
    [7]DISCUSSION ON "APPLICATIONS OF A SECOND-ORDERUPWIND TVD SCHEME TO NONEQUILIBRIUM HYPERSONICFLOWS AROUND BLUNT-BODY[J]. Chinese Journal of Theoretical and Applied Mechanics, 1998, 30(6): 754-756. DOI: 10.6052/0459-1879-1998-6-1995-187
    [8]CONSTRUCTION OF AN ADAPTIVE HYBRID FORM OF TVD SCHEMES[J]. Chinese Journal of Theoretical and Applied Mechanics, 1995, 27(6): 647-652. DOI: 10.6052/0459-1879-1995-6-1995-480
    [9]APPLICATIONS OF A SECOND-ORDER UPWIND TVD SCHEME TO NONEQUILIBRIUM HYPERSONIC FLOWS AROUND BLUNT-BODY[J]. Chinese Journal of Theoretical and Applied Mechanics, 1994, 26(2): 139-148. DOI: 10.6052/0459-1879-1994-2-1995-531
    [10]ADAPTIVE OPEN BOUNDARY CONDITION FOR DISPERSIVE WAVES[J]. Chinese Journal of Theoretical and Applied Mechanics, 1993, 25(3): 334-342. DOI: 10.6052/0459-1879-1993-3-1995-649

  • Cited by

    Periodical cited type(5)

    1. 赵一飞，刘浪. 广义概率密度演化方程差分解法的计算精度比较与改进. 南昌大学学报(工科版). 2025(01): 38-43+48 .
    2. 周永峰，李杰. 含多维随机变量的广义概率密度演化方程解析解:以Euler-Bernoulli梁为例. 力学学报. 2024(09): 2659-2668 . 本站查看
    3. 刘纲，唐伟，高凯. 基于概率密度演化的斜拉索多级变幅时变疲劳可靠度分析. 铁道科学与工程学报. 2022(01): 191-197 .
    4. 朱志辉，刘禹兵，高雪萌，周高扬，余志武. 概率密度演化方程差分格式的计算精度及初值条件改进. 工程力学. 2022(11): 13-21 .
    5. 黄斌，贺志赟，张衡. 随机桁架结构几何非线性问题的混合摄动-伽辽金法求解. 力学学报. 2019(05): 1424-1436 . 本站查看

    Other cited types(6)

Catalog

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (1616) PDF downloads (101) Cited by(11)
    Related

    Download Center

    Author Center

    Copyright © Editorial Office of the Chinese Journal of Mechanics   京ICP备05039218号-1

    Address：15 Beishihuan Xi Lu, Haidian District, Beijing, China   China Pos：100190

    Tel：010-62536271

    Email：lxxb@cstam.org.cn

    微信公众号
    RSS

    Supported by: Beijing Renhe Information Technology Co., Ltd.  Baidu Analytics

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return