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基于MLS-SVM的结构整体可靠度与全局灵敏度分析

吕大刚 李功博 宋彦

吕大刚, 李功博, 宋彦. 基于MLS-SVM的结构整体可靠度与全局灵敏度分析[J]. 工程力学, 2022, 39(S): 92-100. doi: 10.6052/j.issn.1000-4750.2021.05.S015
引用本文: 吕大刚, 李功博, 宋彦. 基于MLS-SVM的结构整体可靠度与全局灵敏度分析[J]. 工程力学, 2022, 39(S): 92-100. doi: 10.6052/j.issn.1000-4750.2021.05.S015
LÜ Da-gang, LI Gong-bo, SONG Yan. ANALYSIS OF GLOBAL RELIABILITY AND SENSITIVITY OF STRUCTURES BASED ON MLS-SVM[J]. Engineering Mechanics, 2022, 39(S): 92-100. doi: 10.6052/j.issn.1000-4750.2021.05.S015
Citation: LÜ Da-gang, LI Gong-bo, SONG Yan. ANALYSIS OF GLOBAL RELIABILITY AND SENSITIVITY OF STRUCTURES BASED ON MLS-SVM[J]. Engineering Mechanics, 2022, 39(S): 92-100. doi: 10.6052/j.issn.1000-4750.2021.05.S015

基于MLS-SVM的结构整体可靠度与全局灵敏度分析

doi: 10.6052/j.issn.1000-4750.2021.05.S015
基金项目: 国家重点研发计划项目(2021YFB2600500);国家自然科学基金面上项目(52078176)
详细信息
    作者简介:

    李功博(1990−),男,黑龙江人,硕士,主要从事结构可靠度分析研究(E-mail: kamarjonely@163.com)

    宋 彦(1990−),男,辽宁人,博士生,主要从事结构可靠度和不确定性量化研究(E-mail: 7129792@163.com)

    通讯作者:

    吕大刚(1970−),男,黑龙江人,教授,博士,主要从事结构可靠度、工程风险分析、地震工程等研究(E-mail: ludagang@hit.edu.cn)

  • 中图分类号: TU311.2

ANALYSIS OF GLOBAL RELIABILITY AND SENSITIVITY OF STRUCTURES BASED ON MLS-SVM

  • 摘要: 作为一种有效的代理模型,支持向量机(SVM)以统计学习中的结构风险最小化原则为基本原理,在具有隐式极限状态函数的结构可靠度分析中得到了广泛的应用。然而,传统的支持向量机在核函数的选择、全局基本变量空间建模、计算效率等方面还存在许多不足。针对这些不足,该文提出一种新的基于移动最小二乘(MLS)技术的支持向量机模型(MLS-SVM),可以在全局基本变量空间中具备自适应能力。该文将MLS-SVM应用于复杂结构的整体可靠度和全局灵敏度分析,并将该模型与基于再生核函数的支持向量机(RPK-SVM)及基于最小二乘的支持向量机(LS-SVM)进行比较分析,结果表明:该文提出的模型相较其他两种模型具有更高的精度和计算效率。
  • 图  1  F3各结构可靠度指标随变异系数的变化

    Figure  1.  Changes of structural reliability indexes with variation coefficient on F3 structure

    2  RC框架结构全局灵敏度指标

    2.  Global sensitivity index of RC frame structure

    表  1  结构不确定性因素

    Table  1.   Structural uncertainty factors

    不确定性来源随机变量平均值变异系数相关性系数分布类型
    C30 混凝土 ${X_1}( { {f_{\rm c0,core} } })$ 28.99 N/mm2 0.20 0.3 对数正态
    ${X_2}( { {f_{\rm cu,core} } } )$ 17.91 N/mm2 0.20 0.3
    ${X_3}( { {\varepsilon _{\rm c0,core} } } )$ 0.0023 0.20 0.3
    ${X_4}( { {\varepsilon _{\rm cu,core} } } )$ 0.0143 0.20 0.3
    ${X_5}( { {f_{\rm c0,cover }} } )$ 25.57 N/mm2 0.20 0.3
    ${X_6}( { {\varepsilon _{\rm cu,cover} } } )$ 0.0040 0.20 0.3
    C35 混凝土 ${X_1}( { {f_{\rm c0,core} } })$ 32.57 N/mm2 0.20 0.3 对数正态
    ${X_2}( { {f_{\rm cu,core} } } )$ 20.76 N/mm2 0.20 0.3
    ${X_3}( { {\varepsilon _{\rm c0,core} } } )$ 0.0022 0.20 0.3
    ${X_4}( { {\varepsilon _{\rm cu,core} } })$ 0.0124 0.20 0.3
    ${X_5}( { {f_{\rm c0,cover} } } )$ 29.76 N/mm2 0.20 0.3
    ${X_6}( { {\varepsilon _{\rm cu,cover} } })$ 0.0040 0.20 0.3
    HRB335 钢筋/(N/mm2) ${X_7}( { {f_{\rm y} }})$ 378 0.10 0.4 对数正态
    ${X_8}( { {E_0} } )$ 200000 0.05 0.4
    恒荷载/kN/m3) ${X_9}( \gamma )$ 26.50 0.10 正态
    活荷载/(kN/m) ${X_{10} }( q )$ 0.98 0.45 Gamma
    下载: 导出CSV

    表  2  总水平地震作用及统计信息

    Table  2.   General earthquake level and statistical information

    结构类型标准值平均值变异系数分布类型
    F3487.67548.010.3极值Ⅰ型
    F6506.85665.81
    F9613.28727.79
    下载: 导出CSV

    表  3  考虑水平地震作用变异性的结构整体可靠度指标

    Table  3.   The global reliability index of the structure considering the variability of horizontal earthquake action

    可靠度指标变异系数
    0.20.40.60.81.0
    Kriging F3 0.7527 0.5154 0.4190 0.3327 0.3021
    F6 0.5225 0.4227 0.4061 0.3166 0.2434
    F9 0.6417 0.4609 0.3825 0.2883 0.2848
    SVR(RBF) F3 0.8141 0.5747 0.4228 0.4106 0.3758
    F6 0.5569 0.4689 0.4154 0.3311 0.2502
    F9 0.6888 0.5200 0.4346 0.4003 0.3876
    SVR(RPK) F3 0.7910 0.5666 0.4507 0.4105 0.3569
    F6 0.5576 0.4552 0.4150 0.3276 0.2582
    F9 0.8343 0.6302 0.5390 0.5301 0.5111
    MLS-SVM F3 0.7501 0.5135 0.4278 0.3540 0.2970
    F6 0.5429 0.4420 0.4007 0.3205 0.2460
    F9 0.6125 0.4564 0.35686 0.31469 0.2881
    FORM F3 0.7763 0.5037 0.4048 0.3644 0.3144
    F6 0.5145 0.4529 0.3933 0.3042 0.2400
    F9 0.6571 0.4755 0.4029 0.3221 0.2753
    下载: 导出CSV

    表  4  结构全局灵敏度指标

    Table  4.   Structural global sensitivity index

    随机变量变量编号$ {S_i} $(F3)${{S}_i^{\rm T}}$(F3)$ {S_i} $(F6)${{S}_i^{\rm T}}$(F6)${S_i}$(F9)${{S}_i^{\rm T}}$(F9)
    $钢筋屈服强度{f_{\rm y}}$ 1 0.648700 0.667500 0.693500 0.70350 0.713100 0.72000
    $约束混凝土极限应力{f_{\rm cu,core} }$ 2 0.003650 0.004840 0.005238 0.00374 0.000380 0.00420
    $无约束混凝土峰值应力{f_{\rm c0,cover} }$ 3 0.005449 0.008500 0.008173 0.00880 0.005750 0.04576
    $约束混凝土峰值应变{\varepsilon _{\rm c0,core} }$ 4 0.002653 0.004345 0.003200 0.00536 0.002490 0.00560
    $约束混凝土极限应变 {\varepsilon _{\rm cu,core} }$ 5 0.005102 0.007121 0.004279 0.00580 0.003600 0.00739
    $无约束混凝土极限应变{\varepsilon _{\rm cu,cover} }$ 6 0.000040 0.001440 0.000154 0.00238 0.000319 0.00291
    $约束混凝土峰值应力 {f_{\rm c0,core} }$ 7 0.243000 0.253400 0.230700 0.24000 0.254000 0.27400
    钢筋弹性模量E0 8 0.000259 0.002295 0.000058 0.00191 0.000390 0.00241
    混凝土容重γ 9 0.042550 0.042950 0.045540 0.04286 0.023080 0.01529
    楼面活荷载q 10 0.000008 0.003500 0.000136 0.00245 0.000030 0.00259
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-28
  • 修回日期:  2022-03-06
  • 网络出版日期:  2022-03-19
  • 刊出日期:  2022-06-06

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