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基于多项式混沌展开的结构动力特性高阶统计矩计算

万华平 邰永敢 钟剑 任伟新

万华平, 邰永敢, 钟剑, 任伟新. 基于多项式混沌展开的结构动力特性高阶统计矩计算[J]. 应用数学和力学, 2018, 39(12): 1331-1342. doi: 10.21656/1000-0887.390165
引用本文: 万华平, 邰永敢, 钟剑, 任伟新. 基于多项式混沌展开的结构动力特性高阶统计矩计算[J]. 应用数学和力学, 2018, 39(12): 1331-1342. doi: 10.21656/1000-0887.390165
WAN Huaping, TAI Yonggan, ZHONG Jian, REN Weixin. Computation of High-Order Moments of Structural Dynamic Characteristics Based on Polynomial Chaos Expansion[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1331-1342. doi: 10.21656/1000-0887.390165
Citation: WAN Huaping, TAI Yonggan, ZHONG Jian, REN Weixin. Computation of High-Order Moments of Structural Dynamic Characteristics Based on Polynomial Chaos Expansion[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1331-1342. doi: 10.21656/1000-0887.390165

基于多项式混沌展开的结构动力特性高阶统计矩计算

doi: 10.21656/1000-0887.390165
基金项目: 国家自然科学基金(51878235;51508144);香江学者计划(XJ2016039);中国博士后科学基金(2015M581981);安徽省自然科学基金(1608085QE118)
详细信息
    作者简介:

    万华平(1986—),男,副教授(E-mail: huaping.wan@hftu.edu.cn);任伟新(1960—),男,教授,博士生导师(通讯作者. E-mail: renwx@hfut.edu.cn).

  • 中图分类号: O324

Computation of High-Order Moments of Structural Dynamic Characteristics Based on Polynomial Chaos Expansion

Funds: The National Natural Science Foundation of China(51878235; 51508144);China Postdoctoral Science Foundation(2015M581981)
  • 摘要: 结构参数的不确定性会导致其动力特性的不确定性, 量化动力特性的不确定性能为结构动力设计分析提供准确的动力信息.统计矩是表征结构动力特性不确定性非常重要的统计量, 比如均值和方差.传统的MonteCarlo(蒙特卡洛)模拟方法需要大量次数的模型运算来保证结果的收敛, 其用于复杂结构的动力特性统计矩计算因耗时太高而使用受限.该文采用多项式混沌展开替代模型来取代计算花费高的有限元模型, 然后在替代模型框架下快速有效地计算结构动力特性的统计矩.该方法在建立替代模型之初只需要少量次数有限元分析, 后续的统计矩计算无需有限元模型, 因此从根本上解决了动力特性统计矩计算花费高的难题.该文的多项式混沌展开方法适用于参数服从任意概率分布, 能够有效地计算高阶统计矩, 为量化结构动力特性不确定性提供更多统计矩信息.最后通过平铝板算例验证了此方法的有效性.
  • [1] 万华平, 任伟新, 颜王吉. 桥梁结构动力特性不确定性的全局灵敏度分析的解析方法[J]. 振动工程学报, 2016,29(3): 429-435.(WAN Huaping, REN Weixin, YAN Wangji. Analytical global sensitivity analysis for uncertainty in structural dynamic properties of bridges[J]. Journal of Vibration Engineering,2016,29(3): 429-435.(in Chinese))
    [2] 万华平, 任伟新, 钟剑. 桥梁结构固有频率不确定性量化的高斯过程模型方法[J]. 中国科学: 技术科学, 2016,46(9): 919-925.(WAN Huaping, REN Weixin, ZHONG Jian. Gaussian process model-based approach for uncertainty quantification of natural frequencies of bridge[J]. Scientia Sinica: Technologica,2016,46(9): 919-925.(in Chinese))
    [3] SHINOZUKA M, ASTILL C J. Random eigenvalue problems in structural analysis[J]. AIAA Journal,1972,10(4): 456-462.
    [4] SZEKELY G S, SCHUELLER G I. Computational procedure for a fast calculation of eigenvectors and eigenvalues of structures with random properties[J]. Computer Methods in Applied Mechanics and Engineering,2001,191(8/10): 799-816.
    [5] WAN H P, MAO Z, TODD M D, et al. Analytical uncertainty quantification for modal frequencies with structural parameter uncertainty using a Gaussian process metamodel[J]. Engineering Structures,2014,75: 577-589.
    [6] 陈塑寰, 张宗芬. 结构固有频率的统计特性[J]. 振动工程学报, 1991,4(1): 90-95.(CHEN Shuhuan, ZHANG Zongfen. Statistics of structural natural frequeneies[J]. Journal of Vibration Engineering,1991,4(1): 90-95.(in Chinese))
    [7] 刘春华, 秦权. 桥梁结构固有频率的统计特征[J]. 中国公路学报, 1997,10(4): 50-55.(LIU Chunhua, QIN Quan. Statistics of natural frequencies for bridge structures[J]. China Journal of Highway and Transport,1997,10(4): 50-55.(in Chinese))
    [8] ADHIKARI S, FRISWELL M I. Random matrix eigenvalue problems in structural dynamics[J]. International Journal for Numerical Methods in Engineering,2007,69(3): 562-591.
    [9] QIU Z P, WANG X J, FRISWELL M I. Eigenvalue bounds of structures with uncertain-but-bounded parameters[J]. Journal of Sound and Vibration,2005,282(1/2): 297-312.
    [10] MODARES M, MULLEN R, MUHANNA R. Natural frequencies of a structure with bounded uncertainty[J]. Journal of Engineering Mechanics,2006,132(12): 1363-1371.
    [11] MOENS D, VANDEPITTE D. Interval sensitivity theory and its application to frequency response envelope analysis of uncertain structures[J]. Computer Methods in Applied Mechanics and Engineering,2007,196(21/24): 2486-2496.
    [12] WANG C, GAO W, SONG C M, et al. Stochastic interval analysis of natural frequency and mode shape of structures with uncertainties[J]. Journal of Sound and Vibration,2014,333(9): 2483-2503.
    [13] GAUTSCHI W. Orthogonal Polynomials: Computation and Approximation [M]. Oxford: Oxford University Press, 2004.
    [14] WAN H P, REN W X, TODD M D. An efficient metamodeling approach for uncertainty quantification of complex systems with arbitrary parameter probability distributions[J]. International Journal for Numerical Methods in Engineering,2017,109(5): 739-760.
    [15] WAN H P, REN W X. Parameter selection in finite-element-model updating by global sensitivity analysis using Gaussian process metamodel[J]. Journal of Structural Engineering,2015,141(6): 04014164.
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出版历程
  • 收稿日期:  2018-06-13
  • 修回日期:  2018-10-16
  • 刊出日期:  2018-12-01

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