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基于改进加权响应面的结构可靠度计算方法

吴洁 张建国 游令非 叶楠

吴洁, 张建国, 游令非, 等 . 基于改进加权响应面的结构可靠度计算方法[J]. 北京航空航天大学学报, 2021, 47(8): 1638-1645. doi: 10.13700/j.bh.1001-5965.2020.0251
引用本文: 吴洁, 张建国, 游令非, 等 . 基于改进加权响应面的结构可靠度计算方法[J]. 北京航空航天大学学报, 2021, 47(8): 1638-1645. doi: 10.13700/j.bh.1001-5965.2020.0251
WU Jie, ZHANG Jianguo, YOU Lingfei, et al. Structural reliability calculation method based on improved weighted response surface[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(8): 1638-1645. doi: 10.13700/j.bh.1001-5965.2020.0251(in Chinese)
Citation: WU Jie, ZHANG Jianguo, YOU Lingfei, et al. Structural reliability calculation method based on improved weighted response surface[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(8): 1638-1645. doi: 10.13700/j.bh.1001-5965.2020.0251(in Chinese)

基于改进加权响应面的结构可靠度计算方法

doi: 10.13700/j.bh.1001-5965.2020.0251
基金项目: 

国家自然科学基金 51675026

详细信息
    通讯作者:

    张建国. E-mail: zjg@buaa.edu.cn

  • 中图分类号: TB114.3

Structural reliability calculation method based on improved weighted response surface

Funds: 

National Natural Science Foundation of China 51675026

More Information
  • 摘要:

    在结构可靠度分析中,响应面法由于具有良好的适用性和可操作性,是目前广泛使用的基于代理模型的分析方法。针对响应面法的计算效率和精度难以平衡兼顾等难点问题,提出一种基于改进加权响应面的结构可靠度计算方法。首先,在迭代过程中,同时考虑样本点与验算点距离、极限状态函数值、联合概率密度函数值3个权重因子对样本点进行赋权,采用加权回归并重复利用已有样本点更新不含交叉项的二次多项式响应面函数。其次,在迭代收敛后,选取已有样本点中权重较大的样本点加权拟合含有交叉项的二次多项式响应面函数。最后,结合数值算例和工程案例,通过与传统抽样方法和其他响应面法进行对比,验证了改进加权响应面法的可行性。结果表明所提方法具有较高效率的同时也保证了精度。

     

  • 图 1  非线性加权响应面法流程[22]

    Figure 1.  Flowchart of weighted nonlinear response surface method[22]

    图 2  改进加权响应面法流程

    Figure 2.  Flowchart of improved weighted response surface method

    图 3  算例1求解过程

    Figure 3.  Solving process of Example 1

    图 4  带有集中力的悬臂梁

    Figure 4.  A cantilever beam with concentrated force

    图 5  算例2求解过程

    Figure 5.  Solving process of Example 2

    图 6  十杆桁架结构

    Figure 6.  Ten-bar truss structure

    图 7  十杆桁架ANSYS仿真结果

    Figure 7.  ANSYS simulation results of ten-bar truss

    图 8  算例3求解过程

    Figure 8.  Solving process of Example 3

    表  1  算例1计算结果比较

    Table  1.   Comparison of calculation results of Example 1

    方法 失效概率 误差/% 结构分析次数 计算时间/s
    蒙特卡罗法 0.003 622 0 10 000 000
    经典响应面法 0.003 369 6.985 09 30 0.061
    线性加权响应面法 0.003 362 7.178 36 20 0.023
    单加权响应面法 0.003 366 7.067 92 20 0.026
    双加权响应面法 0.003 393 6.322 37 20 0.034
    改进加权响应面法 0.003 689 1.849 81 15 0.048
    下载: 导出CSV

    表  2  算例2计算结果比较

    Table  2.   Comparison of calculation results of Example 2

    方法 失效概率 误差/% 结构分析次数 计算时间/s
    蒙特卡罗法 0.005 959 0 10 000 000
    经典响应面法 0.005 691 4.497 40 56 0.026
    线性加权响应面法 0.005 691 4.497 40 28 0.021
    单加权响应面法 0.005 689 4.530 96 49 0.031
    双加权响应面法 0.005 861 1.644 57 21 0.030
    改进加权响应面法 0.005 967 0.134 25 21 0.052
    下载: 导出CSV

    表  3  算例3计算结果比较

    Table  3.   Comparison of calculation results of Example 3

    方法 失效概率 误差/% 结构分析次数
    蒙特卡罗法[23] 0.844 20 0 100 000
    经典响应面法 0.836 41 0.922 77 196
    线性加权响应面法 0.879 58 4.199 10 21
    单加权响应面法 0.838 17 0.714 29 28
    双加权响应面法 0.836 32 0.933 43 49
    改进加权响应面法 0.848 89 0.555 56 21
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-06-11
  • 录用日期:  2020-08-07
  • 刊出日期:  2021-08-20

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