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不同结构复杂度下结合集成学习的模型修正方法

林光伟 张熠

林光伟, 张熠. 不同结构复杂度下结合集成学习的模型修正方法[J]. 工程力学, 2022, 39(S): 153-157. doi: 10.6052/j.issn.1000-4750.2021.05.S030
引用本文: 林光伟, 张熠. 不同结构复杂度下结合集成学习的模型修正方法[J]. 工程力学, 2022, 39(S): 153-157. doi: 10.6052/j.issn.1000-4750.2021.05.S030
LIN Guang-wei, ZHANG Yi. EFFICIENT MODEL UPDATING APPROACHES INTEGRATING ENSEMBLE LEARNING METHODS FOR DIFFERENT STRUCTURAL COMPLEXITY[J]. Engineering Mechanics, 2022, 39(S): 153-157. doi: 10.6052/j.issn.1000-4750.2021.05.S030
Citation: LIN Guang-wei, ZHANG Yi. EFFICIENT MODEL UPDATING APPROACHES INTEGRATING ENSEMBLE LEARNING METHODS FOR DIFFERENT STRUCTURAL COMPLEXITY[J]. Engineering Mechanics, 2022, 39(S): 153-157. doi: 10.6052/j.issn.1000-4750.2021.05.S030

不同结构复杂度下结合集成学习的模型修正方法

doi: 10.6052/j.issn.1000-4750.2021.05.S030
基金项目: 国家自然科学基金项目(51908324,52111540161)
详细信息
    作者简介:

    林光伟(1999−),男,宁夏人,博士生,主要从事防灾减灾研究(E-mail: lin-gw19@mails.tsinghua.edu.cn)

    通讯作者:

    张 熠(1987−),男,湖北人,副教授,博士,博导,主要从事防灾减灾研究(E-mail: zhang-yi@tsinghua.edu.cn)

  • 中图分类号: TP181;TU31

EFFICIENT MODEL UPDATING APPROACHES INTEGRATING ENSEMBLE LEARNING METHODS FOR DIFFERENT STRUCTURAL COMPLEXITY

  • 摘要: 模型不确定性不可避免地影响到数值模型分析精度和可靠性,需要找到一种合适的方法,根据实测数据对模型参数值进行修正。该研究采用结合了过渡马尔科夫链蒙特卡罗(TMCMC)方法的贝叶斯模型修正理论对结构模型参数进行修正。采用Kriging法和多项式混沌展开法(PCE)构造代理模型。将该修正方法应用于两个不同结构复杂度的实例,这两个模型分别代表高维线性模型和非线性模型。在两个实例下验证了代理模型的有效性和准确性,讨论了基于代理模型的修正方法在不同结构复杂度下的优缺点。针对代理模型存在的不足,提出了一种代理集成学习框架进行改进。
  • 图  1  不同方法下结构特征的对比

    Figure  1.  Comparison of features in different methods

    图  2  国家体育场有限元模型

    Figure  2.  Finite element model of the National Stadium

    表  1  十层框架中待修正参数的描述

    Table  1.   Description of updated parameters in ten-storey frame

    参数真实值变异系数先验分布区间
    θ11.50.01均匀分布[0,3]
    θ2~θ91.00.01均匀分布[0,3]
    下载: 导出CSV

    表  2  十层框架的待修正参数(括号内为误差百分比)

    Table  2.   Updated parameters in ten-storey frame (% errors in parenthesis)

    参数聚类前聚类后
    解析法Kriging法PCE法解析法Kriging法PCE法
    θ11.92 (28.0)1.68 (12.8)1.97 (38.1)1.60 (6.5)1.48 (2.5)1.55 (3.4)
    θ21.15 (15.0)0.96 (−3.7)1.09 (8.6)0.94 (−5.5)0.93 (6.6)1.07 (6.8)
    θ31.02 (1.9)1.00 (0.1)0.97 (−2.6)1.12 (11.7)0.98 (2.1)0.91 (−8.8)
    θ40.90 (−10.1)1.01 (0.7)1.06 (−5.9)0.93 (−6.7)1.05 (4.3)0.97 (−3.2)
    θ51.04 (3.6)1.05 (4.7)1.06 (6.4)1.01 (1.0)1.04 (4.4)0.97 (−2.7)
    θ61.00 (0.2)1.06 (6.1)1.15 (15.4)0.99 (−0.8)1.01 (1.1)0.89 (−9.6)
    θ70.98 (−2.4)1.02 (2.7)1.11 (10.5)0.99 (−0.8)1.03 (2.6)0.93 (−6.8)
    θ81.03 (3.2)1.06 (5.9)1.22 (22.5)0.94 (−6.4)1.04 (3.8)0.90 (−9.7)
    θ91.00 (−0.3)1.06 (6.2)1.03 (3.0)0.91 (−9.2)1.08 (7.6)1.06 (5.7)
    θ100.96 (−3.8)1.24 (23.5)1.25 (24.5)0.96 (−3.5)1.07 (6.6)1.11 (10.7)
    下载: 导出CSV

    表  3  十层框架中的特征修正结果

    Table  3.   Updated features in ten-storey frame

    参数实测值解析模型Kriging模型PCE模型
    修正值误差/(%)修正值误差/(%)修正值误差/(%)
    f11.581.57−0.21.600.41.590.2
    f24.704.69−0.14.853.34.730.7
    f37.717.781.17.720.27.841.9
    f410.5110.570.610.671.510.762.3
    f513.0813.402.513.352.213.362.2
    f615.3115.722.716.075.015.753.0
    f717.1617.230.317.703.117.713.2
    f818.6218.921.619.253.519.142.8
    f919.6519.760.620.444.020.303.3
    f1020.2420.11−0.720.692.120.401.3
    下载: 导出CSV

    表  4  十层框架中集成前后的修正参数(括号内为误差百分比)

    Table  4.   Updated parameters before and after ensemble in ten-storey frame (% errors in parenthesis)

    待修正参数Kriging模型PCE模型集成模型
    θ11.68 (12.8)1.97 (38.1)1.55 (3.4)
    θ20.96 (−3.7)1.09 (8.6)1.07 (6.8)
    θ31.00 (0.1)0.97 (−2.6)0.91 (−8.8)
    θ41.01 (0.7)1.06 (−5.9)0.97 (−3.2)
    θ51.05 (4.7)1.06 (6.4)0.97 (−2.7)
    θ61.06 (6.1)1.15 (15.4)0.89 (−9.6)
    θ71.02 (2.7)1.11 (10.5)0.93 (−6.8)
    θ81.06 (5.9)1.22 (22.5)0.90 (−9.7)
    θ91.06 (6.2)1.03 (3.0)1.06 (5.7)
    θ101.24 (23.5)1.25 (24.5)1.07 (6.8)
    下载: 导出CSV

    表  5  鸟巢中待修正参数的描述

    Table  5.   Description of updated parameters in the National Stadium

    参数先验分布区间备注真实值
    θ1均匀分布[μ−0.5, μ+0.5]μ ϵ {1.05, 1.30, 1.50, 1.75, 2.00}1.75
    θ2
    下载: 导出CSV

    表  6  鸟巢中待修正参数(括号内为误差百分比)

    Table  6.   Updated parameters in the National Stadium (% errors in parenthesis)

    先验均值μ1.051.301.501.752.00
    参数θ1θ2θ1θ2θ1θ2θ1θ2θ1θ2
    Kriging模型1.89 (8.0)1.80 (2.8)1.85 (5.6)1.83 (4.5)1.85 (5.6)1.81 (3.4)1.83 (4.5)1.82 (4.0)1.93 (11.2)1.94 (10.9)
    PCE模型1.87 (6.8)1.70 (−3.1)1.82 (4.1)1.67 (−4.6)1.85 (5.7)1.66 (−5.1)1.72 (−1.5)1.74 (−0.6)1.94 (11.3)1.72 (−1.6)
    下载: 导出CSV

    表  7  鸟巢中特征修正结果(括号内为误差百分比)

    Table  7.   Updated features in the National Stadium (% errors in parenthesis)

    变量初始值Kriging模型PCE模型集成模型
    f1/Hz1.1181.109 (−0.81)1.113 (−0.45)1.114 (−0.37)
    f2/Hz1.1331.129 (−0.48)1.128 (−0.44)1.129 (−0.35)
    f3/Hz1.2701.271 (0.06)1.265 (−0.37)1.272 (−0.16)
    f4/Hz1.8381.823 (−0.81)1.830 (−0.44)1.829 (−0.49)
    f5/Hz1.9641.948 (−0.79)1.956 (−0.43)1.962 (−0.10)
    下载: 导出CSV

    表  8  鸟巢中集成前后的修正参数(括号内为误差百分比)

    Table  8.   Updated parameters before and after ensemble in the National Stadium (% errors in parenthesis)

    变量Kriging模型PCE模型集成模型
    θ11.83 (4.5)1.72 (−1.5)1.75 (0.4)
    θ21.82 (4.0)1.74 (−0.6)1.74 (−0.6)
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-30
  • 修回日期:  2022-02-22
  • 网络出版日期:  2022-03-11
  • 刊出日期:  2022-06-06

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