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基于基因表达式编程的FRP约束混凝土极限轴向应变预测

邓楚兵 薛新华

邓楚兵, 薛新华. 基于基因表达式编程的FRP约束混凝土极限轴向应变预测[J]. 复合材料学报, 2022, 39(0): 1-11
引用本文: 邓楚兵, 薛新华. 基于基因表达式编程的FRP约束混凝土极限轴向应变预测[J]. 复合材料学报, 2022, 39(0): 1-11
Chubing DENG, Xinhua XUE. Prediction of ultimate axial strain of FRP-confined concrete based on gene expression programming[J]. Acta Materiae Compositae Sinica.
Citation: Chubing DENG, Xinhua XUE. Prediction of ultimate axial strain of FRP-confined concrete based on gene expression programming[J]. Acta Materiae Compositae Sinica.

基于基因表达式编程的FRP约束混凝土极限轴向应变预测

详细信息
    通讯作者:

    薛新华,博士,教授,博士生导师,研究方向为岩土工程 E-mail: xuexinhua@scu.edu.cn

  • 中图分类号: TU37

Prediction of ultimate axial strain of FRP-confined concrete based on gene expression programming

  • 摘要: 纤维增强树脂复合材料(FRP)以其质量轻、强度高、耐腐蚀和施工方便等优势被广泛应用于混凝土结构性能提升和受损构件加固中。FRP约束混凝土的极限条件是选择FRP种类、选择FRP厚度及确定包裹层数等必须要考虑的因素,现有极限应力模型的预测结果能够较好的反映真实情况,而现有极限轴向应变模型的预测精度偏低,故本文对极限轴向应变进行了研究。由于影响FRP约束混凝土极限轴向应变的因素较多,许多研究人员提出的模型在输入参数的选择上存在较大差异,故本文在通过基因表达式编程建立极限轴向应变模型的同时还探讨了不同输入形式对模型预测精度的影响。采用决定系数及平均绝对误差等五种统计指标对模型预测结果进行评价,并将其与现有模型进行对比分析。研究结果表明:原始数据和新数据组合的输入形式对应的模型具有最高的预测精度,因此在模型输入参数的选择上不能仅考虑原始数据或者新数据;与其他研究人员所提模型相比,本文所提模型预测精度更高,其决定系数为0.893,平均绝对误差等指标均在0.35以下。

     

  • 图  1  GEP语言示意图

    Figure  1.  Diagram of GEP language

    图  2  FRP约束混凝土极限轴向应变模型最优参数确定

    Figure  2.  Determination of optimal parameters of ultimate axial strain model of FRP-confined concrete

    图  3  不同输入形式下的FRP约束混凝土极限轴向应变模型的预测结果与试验结果对比

    Figure  3.  Comparison between experimental and prediction results of ultimate axial strain models of FRP-confined concrete under different input forms

    图  4  GEP模型的表达式树

    Figure  4.  Expression trees of GEP model

    图  5  FRP约束混凝土GEP模型的参数敏感性分析结果

    Figure  5.  Parameter sensitivity analysis results of GEP model for FRP-confined concrete

    表  1  FRP约束混凝土的极限轴向应变模型

    Table  1.   Ultimate axial strain models of FRP-confined concrete

    Model and yearUltimate axial strain
    Ahmad et al [23]
    (2020)
    ${\varepsilon _{ { {{\rm{cu}}} } } } = (1.85 + 7.46\rho _{ {\varepsilon } }^{ { {1} }{ {.171} } }\rho _{ {k} }^{ { {0} }{ {.71} } }){\varepsilon _{ { {{\rm{co}}} } } }$
    Yu and Teng [24]
    (2011)
    ${\varepsilon _{ { {{\rm{cu}}} } } } = 0.0033 + 0.6{\left( \dfrac{ { {E_l} } }{ {f_{ { {co} } }^{ {'} } } }\right)^{0.8} }{({\varepsilon _{ { {{\rm{h}},{\rm{rup}}} } } })^{1.45} }$
    Benzaid et al [25]
    (2010)
    ${\varepsilon _{ { {{\rm{cu}}} } } } = 2{\varepsilon _{ { {{\rm{co}}} } } } + 7.6\dfrac{ { {f_l} } }{ {f_{ { {{\rm{co}}} } }^{ {'} } } }{\varepsilon _{ { {{\rm{co}}} } } }$
    Teng et al [26]
    (2009)
    ${\varepsilon _{ { {{\rm{cu}}} } } } = 1.75{\varepsilon _{ { {{\rm{co}}} } } } + 6.5{\varepsilon _{ { {{\rm{co}}} } } }\rho _{ {\varepsilon } }^{ { {1} }{ {.45} } }\rho _{ {{\rm{k}}} }^{ { {0} }{ {.8} } }$
    Al-Tersawy et al [27] (2007) ${\varepsilon _{ { {{\rm{cu}}} } } } = 2{\varepsilon _{ { {{\rm{co}}} } } } + 8.16{\left( \dfrac{ { {f_l} } }{ {f_{ { {{\rm{co}}} } }^{ {'} } } }\right)^{0.34} }{\varepsilon _{ { {{\rm{co}}} } } }$
    Ilki et al [28]
    (2004)
    ${\varepsilon _{ { {{\rm{cu}}} } } } = {\varepsilon _{ { {{\rm{co}}} } } } + 20{\left( \frac{ { {f_l} } }{ {f_{ { {{\rm{co}}} } }^{ {'} } } }\right)^{0.5} }{\varepsilon _{ { {{\rm{co}}} } } }$
    Xiao and Wu [29]
    (2000)
    ${\varepsilon _{ { { {\rm{cu} } } } } } = \dfrac{ { {\varepsilon _{ { { {\rm{h} },{\rm{rup} } } } } } - 0.0005} }{ {7{ {\left( \dfrac{ { {E_l} } }{ {f_{ { {{\rm{co}}} } }^{ {'} } } }\right)}^{ - 0.8} } } }$
    Samaan et al [30]
    (1998)
    ${\varepsilon _{ { {{\rm{cu}}} } } } = \dfrac{ {f_{ { {{\rm{cc}}} } }^{ {'} } - 0.872f_{ { {{\rm{co}}} } }^{ {'} } - 0.371{f_l} - 6.258} }{ {245.61f{ {_{ { {{\rm{co}}} } }^{ {'} } }^{0.2} } + 1.3456\dfrac{ { {E_{ { {{\rm{FRP}}} } } }T} }{D} } }$
    Mander et al [31]
    (1988)
    ${\varepsilon _{ { {{\rm{cu}}} } } } = \left( 1 + 5\left( \dfrac{ {f_{ { {{\rm{cc}}} } }^{ {'} } } }{ {f_{ { {co} } }^{ {'} } } } - 1\right)\right){\varepsilon _{ { {{\rm{co}}} } } }$
    Notes:$f_{ { {{\rm{cc}}} } }'$—Peak strength of FRP-confined concrete; $ {\varepsilon _{{{cu}}}} $—Ultimate axial strain of FRP-confined concrete; $f_{ { {{\rm{co}}} } }^{ {'} }$—Peak strength of unconfined concrete; ${\varepsilon _{ { {{\rm{co}}} } } }$—Peak strain of unconfined concrete; $D$—Diameter of the concrete core; $H$—Height of the concrete core; ${E_{ {{\rm{c}}} } }$—Elastic modulus of the concrete core;$T$—Total thickness of the FRP jacket; ${E_{ { {{\rm{FRP}}} } } }$—Elastic modulus of the FRP jacket; $ {\varepsilon _{{{h,rup}}}} $—Hoop rapture strain of the FRP jacket; $ {f_l} $—Confining stress; ${\rho _{ {{\rm{k}}} } }$—Stiffness ratio;$ {\rho _{{\varepsilon }}} $ —Strain ratio; See Table 2 for variable units.
    下载: 导出CSV

    表  2  FRP约束普通混凝土圆柱体试验数据的统计参数

    Table  2.   Statistical parameters of test data of FRP-confined normal concrete cylinder

    ParameterMinMaxMedianAverageStandard
    deviation
    $D$/mm100200152146.08017.816
    $H$/mm200788305314.10694.341
    $f_{ { {{\rm{co}}} } }^{ {'} }$/MPa26.255.24240.5777.100
    ${\varepsilon _{ { {{\rm{co}}} } } }$/%0.160.420.2390.2490.047
    ${E_c}$/GPa24.2135.1429.7729.6922.731
    $T$/mm0.115.210.4950.7940.882
    ${E_{ { {{\rm{FRP}}} } } }$/GPa13.6629.6105154.604113.36
    ${\varepsilon _{ { {{\rm{h}},{\rm{rup}}} } } }$/%0.193.091.081.2080.504
    ${\rho _{ {{\rm{k}}} } }$2.55538.1149.32410.6837.153
    $ {\rho _{{\varepsilon }}} $0.0100.3690.0496.4305.659
    $ {f_l} $/MPa0.90513.4354.3334.9222.154
    ${\varepsilon _{ { {{\rm{cu}}} } } }$/%0.45.551.611.8301.005
    下载: 导出CSV

    表  3  FRP约束普通混凝土圆柱体试验数据的皮尔逊相关性分析结果

    Table  3.   Results of Pearson correlation analysis of test data of FRP-confined normal concrete cylinder

    $ {\rho _{{k}}} $$ {\rho _{{\varepsilon }}} $$ {f_l} $$ {\varepsilon _{{{cu}}}} $
    $D$−0.223**−0.064−0.017−0.121
    $H$−0.041−0.131−0.108−0.127
    $f_{ { {{\rm{co}}} } }^{ {'} }$−0.211**0.0390.136−0.029
    ${\varepsilon _{ { {{\rm{co}}} } } }$−0.163*−0.181*−0.180*0.236**
    ${E_c}$−0.198**0.0890.151−0.003
    $T$0.161*0.356**0.553**0.297**
    ${E_{ { {{\rm{FRP}}} } } }$0.509**−0.544**−0.031−0.165*
    ${\varepsilon _{ { {{\rm{h}},{\rm{rup}}} } } }$−0.395**0.926**0.0860.377**
    ${\rho _{ {{\rm{k}}} } }$1−0.334**0.669**0.379**
    $ {\rho _{{\varepsilon }}} $−0.334*10.165*0.301**
    $ {f_l} $0.669**0.165*10.653**
    ${\varepsilon _{ { {{\rm{cu}}} } } }$0.379**0.301*0.653**1
    Notes: **. Correlation is significant at the 0.01 level (2-tailed).
    *. Correlation is significant at the 0.05 level (2-tailed).
    下载: 导出CSV

    表  4  FRP约束混凝土极限轴向应变模型的参数设置

    Table  4.   Parameters setting of ultimate axial strain model of FRP-confined concrete

    Parameter typesSettingParameter typesSetting
    Population
    size
    50Gene transposition rate0.3
    Head
    length
    12Gene recombination rate0.3
    Gene
    Number
    3One-point recombination rate0.4
    Chromosome length45Two-point recombination rate0.4
    Connection functionaddition (+)IS transposition rate0.3
    Mutation
    rate
    0.044RIS transposition rate0.3
    下载: 导出CSV

    表  5  FRP约束混凝土极限轴向应变模型的输入形式

    Table  5.   Input informs of ultimate axial strain model of FRP-confined concrete

    NoModelUltimate axial strain$ {\varepsilon _{{{cu}}}} $
    1A${\varepsilon _{ { {{\rm{cu}}} } } } = {f_1}(D,H,f_{ { {{\rm{co}}} } }^{ {'} },{\varepsilon _{ { {{\rm{co}}} } } },{E_{ {{\rm{c}}} } },T,{E_{ { {{\rm{FRP}}} } } },{\varepsilon _{ { {{\rm{h}},{\rm{rup}}} } } })$
    2B${\varepsilon _{ { {{\rm{cu}}} } } } = {f_2}({f_l},{\rho _{ {\varepsilon } } },{\rho _{ {{\rm{k}}} } })$
    3C${\varepsilon _{ { {{\rm{cu}}} } } } = {f_3}({\varepsilon _{ { {{\rm{co}}} } } },{\rho _{ {\varepsilon } } },{\rho _{ {{\rm{k}}} } })$
    4D${\varepsilon _{ { {{\rm{cu}}} } } } = {f_4}(f_{ { {{\rm{co}}} } }^{ {'} },{\varepsilon _{ { {{\rm{co}}} } } },{f_l})$
    5E${\varepsilon _{ { {{\rm{cu}}} } } } = {f_5}({\varepsilon _{ { {{\rm{co}}} } } },T,{E_{ { {{\rm{FRP}}} } } },{\varepsilon _{ { {{\rm{h}},{\rm{rup}}} } } },{f_l},{\rho _{ {\varepsilon } } },{\rho _{ {{\rm{k}}} } })$
    下载: 导出CSV

    表  6  不同输入形式下的FRP约束混凝土极限轴向应变模型的预测结果

    Table  6.   Prediction results of ultimate axial strain models of FRP-confined concrete under different input forms

    Model$ {R^{\text{2}}} $MAERRSERMSEMAPE
    Model A 0.487 0.414 0.721 0.682 0.257
    Model B 0.561 0.533 0.841 0.796 0.299
    Model C 0.893 0.228 0.334 0.316 0.160
    Model D 0.705 0.362 0.543 0.514 0.260
    Model E 0.740 0.543 0.762 0.721 0.353
    Notes: R2—Determination coefficient; MAE—Mean absolute error; RRSE—Relative square root error; RMSE—Root mean square error; MAPE—Mean absolute percentage error.
    下载: 导出CSV

    表  7  FRP约束混凝土GEP模型的参数重要性分析结果

    Table  7.   Parameter importance analysis results of GEP model for FRP-confined concrete

    ModelParameter$ {R^{{2}}} $Conclusion

    GEP
    Without${\varepsilon _{ { {{\rm{co}}} } } }$ 0.496
    ${\rho _{ {{\rm{k}}} } } > {\rho _{ {\varepsilon } } } > {\varepsilon _{ { {{\rm{co}}} } } }$
    Without${\rho _{ {{\rm{k}}} } }$ 0.112
    Without$ {\rho _{{\varepsilon }}} $ 0.397
    Without${\varepsilon _{ { {{\rm{co}}} } } }$ 0.522
    Teng et al [26] Without${\rho _{ {{\rm{k}}} } }$ 0.118 ${\rho _{ {{\rm{k}}} } } > {\rho _{ {\varepsilon } } } > {\varepsilon _{ { {{\rm{co}}} } } }$
    Without$ {\rho _{{\varepsilon }}} $ 0.245
    下载: 导出CSV

    表  8  各FRP约束混凝土极限轴向应变模型的预测结果

    Table  8.   Prediction results of ultimate axial strain models of FRP-confined concrete

    Model$ {R^{\text{2}}} $MAERRSERMSEMAPE
    GEP 0.893 0.228 0.334 0.316 0.160
    Ahmad et al [23] 0.743 0.327 0.524 0.496 0.206
    Yu and Teng [24] 0.611 0.394 0.721 0.683 0.199
    Benzaid et al [25] 0.664 0.814 1.129 1.068 0.410
    Teng et al [26] 0.701 0.357 0.563 0.533 0.208
    Al-Tersawy et al [27] 0.550 0.513 0.767 0.726 0.348
    Ilki et al [28] 0.682 0.881 1.029 0.974 0.671
    Xiao and Wu [29] 0.572 0.412 0.742 0.702 0.213
    Samaan et al [30] 0.478 1.713 2.061 1.950 0.971
    Mander et al [31] 0.681 0.379 0.544 0.613 0.204
    下载: 导出CSV
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  • 收稿日期:  2021-11-22
  • 录用日期:  2022-01-15
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