基于集成学习的FRP加固混凝土梁抗弯承载力预测研究

张书颖; 陈适之; 韩万水; 吴刚

doi:10.6052/j.issn.1000-4750.2021.06.0422

基于集成学习的FRP加固混凝土梁抗弯承载力预测研究

doi: 10.6052/j.issn.1000-4750.2021.06.0422

张书颖^1,,
陈适之^1, ,,
韩万水^1,,
吴刚^2,

1.
长安大学公路学院，西安 710064
2.
东南大学土木工程学院，南京 210096

基金项目: 国家重点研发计划项目(2019YFB1600702)；国家自然科学基金青年科学基金项目(52008027)；陕西省自然基金青年项目(2021JQ-269)；中央高校基本科研业务费优秀博士毕业生项目(300102211304)

详细信息

作者简介:
张书颖(1994−)，女，陕西人，博士生，主要从事桥梁管养研究(E-mail: zhang.sy@chd.edu.cn)

韩万水(1977−)，男，河南人，教授，博士，博导，主要从事车桥耦合桥梁评估研究(E-mail: hws@gl.chd.edu.cn)

吴　刚(1976−)，男，浙江人，教授，博士，博导，主要从事智慧桥梁研究(E-mail: g.wu@seu.edu.cn)

通讯作者:
陈适之(1993−)，男，陕西人，讲师，博士，主要从事桥梁健康监测研究 (E-mail: szchen@chd.edu.cn)

中图分类号: U444
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- 被引次数: 0
出版历程
- 收稿日期: 2021-06-03
- 修回日期: 2021-08-19
- 网络出版日期: 2021-08-27
- 刊出日期: 2022-08-01

STUDY ON PREDICTION OF FRP STRENGTHENED REINFORCED CONCRETE BEAM’S MOMENT BEARING CAPACITY BASED ON ENSEMBLE LEARNING ALGORITHM

1.
Highway School, Chang'an University, Xi’an 710064, China
2.
School of Civil Engineering, Southeast University, Nanjing 210096, China

摘要

摘要: 为解决当前纤维增强复合材料(FRP)加固钢筋混凝土梁抗弯承载力预测中模型不统一、计算繁琐、精度有限等问题，建立了统一化的抗弯承载力预测模型。根据既有文献收集外贴式、端锚式和嵌入式3种FRP典型加固方式加固钢筋混凝土梁试验数据，确定影响加固梁承载力的关键因素，通过XGBoost(极限梯度提升树)算法训练回归各影响因素与加固后梁抗弯承载力间的非线性映射关系，得到统一化的FRP加固钢筋混凝土梁抗弯承载力预测模型。随后在测试样本集上对该模型的预测精度进行了验证，与基于支持向量回归(SVR)和人工神经网络(ANN)两种代表性机器学习算法得到的预测模型进行了横向对比，并分析了不同加固方式下的预测精度。研究结果表明：该文得到的基于XGBoost的抗弯承载力预测模型拟合优度R²=0.9417，可见整体精度较高，有良好的性能；相比基于传统机器学习算法SVR和ANN建立的预测模型，基于集成学习算法XGBoost的拟合优度分别提升了8.00%及6.70%，均方根误差减少了33.94%和30.72%，平均绝对误差减少了32.38%和30.51%，表明基于XGBoost的模型精度更高，远优于SVR和ANN；基于XGBoost的模型在外贴式、端锚式和嵌入式加固方式下拟合优度分别达到0.9472、0.9631和0.9278，可见预测精度均表现优良，精度相当，说明该模型可以统一考虑三种不同加固方式；通过分析输入参数的特征重要性，说明了该模型的合理性。研究成果可为实际桥梁工程中FRP加固设计应用提供参考。
- 桥梁工程 /
- 承载力预测 /
- 集成学习 /
- FRP加固 /
- 钢筋混凝土梁
Abstract: A unified moment bearing capacity prediction model is established in order to solve the issues of various models, difficult calculations, and limited accuracy in predicting the moment bearing capacity of reinforced concrete beams strengthened with fiber reinforced polymer (FRP) materials. By collecting the experimental data associated with three typical FRP strengthening types including externally bonded, end anchorage and near-surface mounted FRP from the existing literature, the key factors which affect the bearing capacity of the reinforced beam are determined, and XGBoost (eXtreme Gradient Boosting) algorithm is trained to obtain regressionally the nonlinear relationship between the influencing factors and the moment bearing capacity of the reinforced beam calculated with a unified FRP strengthened reinforced concrete beam moment bearing capacity prediction model. The prediction accuracy of the model is verified through the testing sample set. It is compared with the prediction models based on two representative machine learning algorithms: support vector regression (SVR) and artificial neural network (ANN). The prediction accuracy under different strengthening types is also analyzed. The results illustrate that the R² of the XGBoost-based moment bearing capacity prediction model reaches 0.9417, indicating that the overall accuracy is high. Compared with the prediction model based on SVR and ANN, the R² of the model based on the ensemble learning algorithm XGBoost is increased by 8.00% and 6.70%, the root mean square error is reduced by 33.94% and 30.72%, and the mean absolute error is reduced by 32.38% and 30.51%. It shows that the XGBoost based model has higher accuracy, which is far better than SVR and ANN based model. The R² of the XGBoost based model reaches 0.9472, 0.9631, and 0.9278, respectively under the externally bonded, end anchorage and near-surface mounted strengthening types. It can be seen that the prediction accuracy is relatively good, and the accuracy is at the same level indicating that this model can uniformly considers three different strengthening types. By analyzing the feature importance of the input parameters, the rationality of the model is explained. The research outcome could provide references for the design and application of actual bridge strengthening with FRP.
- bridge engineering /
- prediction of bearing capacity /
- ensemble learning /
- FRP strengthened /
- reinforced concrete beam

HTML全文

图 1 FRP加固RC梁示意图

Figure 1. RC beams strengthened with FRP

下载: 全尺寸图片幻灯片

图 2 FRP加固后承载力与输入参数关系

Figure 2. Variation of the bearing capacity with the input parameters after FRP strengthened

下载: 全尺寸图片幻灯片

图 3 基于XGBoost的承载力预测模型建立流程

Figure 3. Flowchart of developing a XGBoost-based bearing capacity prediction model

下载: 全尺寸图片幻灯片

图 4 网格搜索中SVR和ANN算法的验证结果

Figure 4. Validation results of SVR and ANN under grid search

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图 5 不同模型拟合结果

Figure 5. Fitted result graphs of different models

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图 6 不同加固方式拟合结果

Figure 6. Fitted result graphs of different strengthening methods

下载: 全尺寸图片幻灯片

图 7 基于XGBoost的预测模型中参数的特征重要性

Figure 7. Feature importance of the parameters in the XGBoost based prediction model

下载: 全尺寸图片幻灯片

表 1 FRP加固样本集参数统计特征

Table 1. Statistical characteristics of FRP strengthened sample parameters

	参数	最大值	最小值	中位数	均值	标准差
输入	f_c/MPa	63.47	17.50	39.50	39.24	11.83
	f_y/MPa	608.00	242.20	413.70	418.05	69.33
	f_f/MPa	4510.00	512.00	2100.00	2268.84	1099.42
	E_fr/GPa	299.40	22.00	116.00	136.31	75.15
	r_s/(%)	2.45	0.35	0.66	0.76	0.45
	r_f/(%)	0.93	0.02	0.09	0.16	0.17
	b/mm	200.00	100.00	150.00	156.27	33.38
	h/mm	400.00	180.00	280.00	270.13	46.20
输出	M/(kN·m)	141.00	6.78	40.8	42.67	24.34

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表 2 XGBoost参数

Table 2. Parameters of XGBoost

参数	调节范围	取值	意义
α	[0, 1]	0.2	学习率
s	[0, ∞]	10	树的棵树
D	[0, ∞]	2	树的最大深度
W	[0, ∞]	0	最小叶子节点权重和
γ	[0, ∞]	0.001	节点分裂的最小损失函数下降值

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表 3 不同模型评估指标

Table 3. Evaluation of different models

基础算法	拟合优度 R²	均方根误差 RMSE/(kN·m)	平均绝对误差 MAE/(kN·m)
XGBoost	0.9417	5.9692	4.2076
SVR	0.8664	9.0366	6.2228
ANN	0.8786	8.6163	6.0549

下载: 导出CSV

表 4 不同加固方式评估指标

Table 4. Evaluation of different strengthening methods

加固方式	拟合优度 R²	均方根误差 RMSE/(kN·m)	平均绝对误差 MAE/(kN·m)
外贴式	0.9472	4.2144	3.2194
端锚式	0.9631	3.2522	2.7482
嵌入式	0.9278	9.0925	6.3868

下载: 导出CSV

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