EI、Scopus 收录
中文核心期刊

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

小样本数据下圆柱薄壳初始缺陷不确定性量化的极大熵方法

李建宇 杨坤 王博 张丽丽

李建宇, 杨坤, 王博, 张丽丽. 小样本数据下圆柱薄壳初始缺陷不确定性量化的极大熵方法. 力学学报, 2023, 55(4): 1028-1038 doi: 10.6052/0459-1879-22-556
引用本文: 李建宇, 杨坤, 王博, 张丽丽. 小样本数据下圆柱薄壳初始缺陷不确定性量化的极大熵方法. 力学学报, 2023, 55(4): 1028-1038 doi: 10.6052/0459-1879-22-556
Li Jianyu, Yang Kun, Wang Bo, Zhang Lili. A maximum entropy approach for uncertainty quantification of initial geometric imperfections of thin-walled cylindrical shells with limited data. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 1028-1038 doi: 10.6052/0459-1879-22-556
Citation: Li Jianyu, Yang Kun, Wang Bo, Zhang Lili. A maximum entropy approach for uncertainty quantification of initial geometric imperfections of thin-walled cylindrical shells with limited data. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(4): 1028-1038 doi: 10.6052/0459-1879-22-556

小样本数据下圆柱薄壳初始缺陷不确定性量化的极大熵方法

doi: 10.6052/0459-1879-22-556
基金项目: 国家自然科学基金(11772228), 工业装备结构分析国家重点实验室开放课题(GZ21103)和天津市教委科研计划(2022ZD013)资助项目
详细信息
    通讯作者:

    李建宇, 副教授, 主要研究方向为计算力学. E-mail: lijianyu@tust.edu.cn.cn

  • 中图分类号: O302

A MAXIMUM ENTROPY APPROACH FOR UNCERTAINTY QUANTIFICATION OF INITIAL GEOMETRIC IMPERFECTIONS OF THIN-WALLED CYLINDRICAL SHELLS WITH LIMITED DATA

  • 摘要: 具有不确定性特征的初始缺陷被认为是导致薄壳结构实际临界载荷值与理论解不相符并呈现分散特征的主要原因. 对实际薄壳结构初始缺陷的建模至少需要考虑两个方面的不确定性量化, 一是对缺陷分布形式和幅值等固有随机性的量化, 二是对小样本量和不准确测量所导致缺陷统计量的不确定性的量化. 本文在利用随机场的Karhunen-Loeve展开法对薄壳初始几何缺陷建模的基础上, 提出一种基于极大熵原理的缺陷建模方法. 首先, 采用极大熵分布来估计Karhunen-Loeve随机变量的概率密度函数, 以适应不能使用高斯随机场进行缺陷随机场建模的情况. 随后, 通过将经典的等式约束极大熵模型扩展为区间约束极大熵模型, 实现对实际工程中仅能获得少量薄壳结构几何缺陷样本数据所导致的认知不确定性的量化. 最后, 将所提方法用于对国际缺陷数据库的A-Shell进行缺陷建模和临界载荷预测. 研究表明, 所提基于区间约束极大熵原理的随机场建模方法在能够有效表征实测数据高阶矩信息的同时, 还具备量化小样本数据导致的认知不确定性的能力, 并且高斯随机场模型和基于等式约束极大熵原理的随机场模型是本文所提建模方法的两种特殊情况.

     

  • 图  1  圆柱薄壳结构示意图

    Figure  1.  Illustration of thin-walled cylindrical shell

    图  2  区间约束极大熵分布与等式约束极大熵分布的熵值比较

    Figure  2.  Comparison of entropy values between interval constrained maximum entropy distribution and equation constrained maximum entropy distribution

    图  3  不同样本量条件下区间约束极大熵分布与等式约束极大熵分布的比较

    Figure  3.  Comparison of the interval constrained maximum entropy distribution and equation constrained maximum entropy distribution estimated from sample data with different size

    图  4  缺陷轴压圆柱薄壳结构随机屈曲分析流程图

    Figure  4.  Flow chart of stochastic buckling analysis for axial compressive thin-walled cylindrical shell with geometrical imperfection

    图  5  轴向压缩圆筒壳示意图

    Figure  5.  Illustration of the axially compressed cylinder shell

    图  6  A-shell样本缺陷示意图

    Figure  6.  Initial geometrical imperfections of A-shell

    图  7  缺陷随机场的样本统计协方差矩阵

    Figure  7.  Covariance matrix of imperfection random field

    图  8  Karhunen-Loeve随机变量ξ(i)(i = 1,2,3,4,5,6)的概率密度函数估计结果

    Figure  8.  PDF estimation of Karhunen-Loeve random variables ξ(i)(i = 1,2,3,4,5,6)

    图  9  轴压薄壁圆柱筒的轴压力与轴压位移曲线

    Figure  9.  Reaction force-displacement curve of axial compressive thin-walled cylindrical shell

    图  10  屈曲载荷频数图

    Figure  10.  Statistical frequency of the buckling loads

    表  1  模型参数

    Table  1.   Model parameters

    Radius R/mmHeight H/mmThickness t/mmYoung's modulus E/MPaPoisson's ratio νDensity ρ/(mg·mm−3)
    101.60202.290.116 01044100.32
    下载: 导出CSV

    表  2  含缺陷薄壁圆柱壳轴压极限载荷无量纲因子αc的统计均值和变异系数

    Table  2.   Mean and coefficient of variation of the cylindrical shell limit load

    Random field modelNumber of samplesMeanCoefficient of variation
    Gaussian random field1000.90410.0169
    equation constrained maximum
    entropy random field
    1000.90170.0145
    interval constrained maximum
    entropy random field
    1000.90170.0153
    test sample70.89730.0175
    下载: 导出CSV

    表  3  结构临界载荷KDF估计值

    Table  3.   KDF of the cylindrical shell limit load

    Reliability0.9990.990.95
    Gaussian random field0.85690.86470.8803
    interval constrained maximum
    entropy random field
    0.86470.86980.8835
    equation constrained maximum
    entropy random field
    0.87070.87560.8872
    下载: 导出CSV
  • [1] Wagner HNR, Hühne C, Elishakoff I. Probabilistic and deterministic lower-bound design benchmarks for cylindrical shells under axial compression. Thin-Walled Structures, 2020, 146: 179-200
    [2] 王俊奎, 仝立勇. 关于圆筒壳稳定性中的初始缺陷. 力学进展, 1988, 18(2): 215-221 (Wang Junkui, Tong Liyong. On initial imperfections in stability of circular cylindrical shells. Advances in Mechanics, 1988, 18(2): 215-221 (in Chinese)
    [3] 陈志平, 焦鹏, 马赫等. 基于初始缺陷敏感性的轴压薄壁圆柱壳屈曲分析研究进展. 机械工程学报, 2021, 57(22): 114-129 (Chen Zhiping, Jiao Peng, Ma He, et al. Advances in buckling analysis of axial compression loaded thin-walled cylindrical shells based on Iinitial imperfection sensitivity. Journal of Mechanical Engineering, 2021, 57(22): 114-129 (in Chinese) doi: 10.3901/JME.2021.22.114
    [4] 乔丕忠, 王艳丽, 陆林军. 圆柱壳稳定性问题的研究进展. 力学季刊, 2018, 39(2): 223-236 (Qiao Pizhong, Wang Yanli, Lu Linjun. Advances in stability study of cylindrical shells. Chinese Quarterly of Mechanics, 2018, 39(2): 223-236 (in Chinese) doi: 10.15959/j.cnki.0254-0053.2018.02.001
    [5] 王博, 郝鹏, 田阔. 加筋薄壳结构分析与优化设计研究进展. 计算力学学报, 2019, 36(1): 1-12 (Wang Bo, Hao Peng, Tian Kuo. Recent advances in structural analysis and optimization of stiffened shells. Chinese Journal of Computational Mechanics, 2019, 36(1): 1-12 (in Chinese) doi: 10.7511/jslx20180615002
    [6] Anonymous. Eurocode 3: Design of steel structures. European Committee for Standardisation, ENV, 1993-1-6
    [7] Hühne C, Rolfe R, Breitbach E, et al. Robust design of composite cylindrical shells under axial compression-simulation and validation. Thin-Walled Structure, 2008, 46: 947-962 doi: 10.1016/j.tws.2008.01.043
    [8] Wang B, Hao P, Li G, et al. Determination of realistic worst imperfection for cylindrical shells using surrogate model. Structural and Multidisciplinary Optimization, 2013, 48: 777-794 doi: 10.1007/s00158-013-0922-9
    [9] Arbocz J, Starnes Jr J. Future directions and challenges in shell stability analysis. Thin-Walled Structure, 2002, 40: 729-754 doi: 10.1016/S0263-8231(02)00024-1
    [10] Bolotin V, Akademii Nauk SSSR. Statistical methods in the non-linear theory of elastic shells. Otdelenie Tekhnicheskykh Nauk, 1958, 3: 33-41 (in Russian) (English Translation: NASA TTF-85, 1962: 1-16)
    [11] Budiansky B, Hutchinson JW. A survey of some buckling problems. AIAA Journal, 1966, 4(9): 1505-1510 doi: 10.2514/3.3727
    [12] Zhang DL, Chen ZP, Li Y, et al. Lower-bound axial buckling load prediction for isotropic cylindrical shells using probabilistic random perturbation load approach. Thin-Walled Structures, 2020, 155: 106925
    [13] Elishakoff I. Resolution of the 20th Century Conundrum in Elastic Stability. World Scientific Publishing Co. Pte. Ltd., 2014
    [14] Arbocz J, Abramovich H. The initial imperfection databank at the Delft University of Technology, Part 1. Technical Report LR-290, Department of Aerospace Engineering, Delft University of Technology, 1979
    [15] Benedikt K, Raimund R, Christian H, et al. Probabilistic design of axially compressed composite cylinders with geometric and loading imperfections. International Journal Of Structural Stability And Dynamics, 2010, 10: 623-644 doi: 10.1142/S0219455410003658
    [16] Wang B, Du KF, Hao P, et al. Experimental validation of cylindrical shells under axial compression for improved knockdown factors. International Journal of Solids and Structures, 2019, 164: 37-51 doi: 10.1016/j.ijsolstr.2019.01.001
    [17] Arbocz J, Hol JMAM. Collapse of axially compressed cylindrical shells with random imperfections. Thin-walled Structure, 1995, 23: 131-158 doi: 10.1016/0263-8231(95)00009-3
    [18] Schenk CA, Schuëller GI. Buckling analysis of cylindrical shells with random geometrical imperfections. International Journal of Non-Linear Mechanics, 2003, 38: 1119-1132 doi: 10.1016/S0020-7462(02)00057-4
    [19] Craig KJ, Roux WJ. On the investigation of shell buckling due to random geometrical imperfections implemented using Karhunen–Loève expansions. International Journal for Numerical Methods in Engineering, 2008, 73: 1715-1726 doi: 10.1002/nme.2141
    [20] Benedikt K, Milena M, Raimund R. Sample size dependent probabilistic design of axially compressed cylindrical shells. Thin-Walled Structure, 2014, 74: 222-231 doi: 10.1016/j.tws.2013.10.003
    [21] Yang H, Feng SJ, Hao P, et al. Uncertainty quantification for initial geometric imperfections of cylindrical shells: A novel bi-stage random field parameter estimation method. Aerospace Science and Technology, 2022, 124: 107554 doi: 10.1016/j.ast.2022.107554
    [22] Gray A, Wimbush A, De Angelis M, et al. From inference to design: A comprehensive framework for uncertainty quantification in engineering with limited information. Mechanical Systems and Signal Processing, 2022, 165: 108210 doi: 10.1016/j.ymssp.2021.108210
    [23] Fina M, Weber P, Wagner W. Polymorphic uncertainty modeling for the simulation of geometric imperfections in probabilistic design of cylindrical shells. Structural Safety, 2020, 82: 101894
    [24] Feng SJ, Duan YH, Yao CY, et al. A Gaussian process-driven worst realistic imperfection method for cylindrical shells by limited data. Thin-Walled Structure, 2022, 181: 110130 doi: 10.1016/j.tws.2022.110130
    [25] 李建宇, 魏凯杰. 考虑周长约束的圆柱薄壳初始几何缺陷随机场建模方法. 计算力学学报, 2020, 37: 722-728 (Li Jianyu, Wei Kaijie. Modeling initial geometrical imperfections of thin cylindrical shells by random field with perimeter constraints. Chinese Journal of Computational Mechanics, 2020, 37: 722-728 (in Chinese) doi: 10.7511/jslx20200216001
    [26] 李建宇, 佘昌忠, 张丽丽. 薄壁圆筒壳初始几何缺陷不确定性量化的极大熵方法. 计算力学学报, 2022, 39: 443-449 (Li Jianyu, She Changzhong, Zhang Lili. A maximum entropy approach for uncertainty quantification of initial geometric imperfections of thin-walled cylindrical shell. Chinese Journal of Computational Mechanics, 2022, 39: 443-449 (in Chinese) doi: 10.7511/jslx20210209001
    [27] Ghanem RG, Doostan A. On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data. Journal of Computational Physics, 2006, 217(1): 63-81 doi: 10.1016/j.jcp.2006.01.037
    [28] Zhang RJ, Dai HZh. Stochastic analysis of structures under limited observations using kernel density estimation and arbitrary polynomial chaos expansion. Computer Methods in Applied Mechanics and Engineering Part A, 2023, 403: 115689 doi: 10.1016/j.cma.2022.115689
    [29] 李仲民. 基于不完整概率信息的随机场重构方法. [硕士论文]. 哈尔滨: 哈尔滨工业大学, 2021

    Li Zhongmin. The recovery of random fields based on incomplete probabilistic information. [Master Thesis]. Harbin: Harbin Institute of Technology, 2021 (in Chinese)
    [30] Soize C. Uncertainty Quantification: An Accelerated Course with Advanced Applications in Computational Engineering. Springer, 2017
    [31] Murphy KP. Machine Learning: A Probabilistic Perspective. The MIT Press, 2012
    [32] Mihara, Y, Kobayashi T, Fujii F, et al. Postbuckling analyses of elastic cylindrical shells under axial compression. Transactions of the Japan Society of Mechanical Engineers Series A, 2011, 77: 582-589
  • 加载中
图(10) / 表(3)
计量
  • 文章访问数:  283
  • HTML全文浏览量:  91
  • PDF下载量:  69
  • 被引次数: 0
出版历程
  • 收稿日期:  2022-11-24
  • 录用日期:  2023-03-07
  • 网络出版日期:  2023-03-08
  • 刊出日期:  2023-04-18

目录

    /

    返回文章
    返回