Stiffness correction of integral joints in steel truss bridges based on RSM-NSGA- Ⅱ

Authors

• Guan Jingyuan, School of Civil Engineering & Transportation , South China University of Technology , Guangzhou , Guangdong 510640 , ChinaFollow
• Chen Hao, School of Civil Engineering & Transportation , South China University of Technology , Guangzhou , Guangdong 510640 , China ;Hainan Nuclear Power Co ., Ltd., Changjiang , Hainan 572700 , China
• Qin Yonggang, China Railway Major Bridge Engineering Group Co ., Ltd., Wuhan , Hubei 430050 , China
• Ma Niujing, School of Civil Engineering & Transportation , South China University of Technology , Guangzhou , Guangdong 510640 , ChinaFollow
• Zhen Xiaoxia, School of Civil Engineering & Transportation , South China University of Technology , Guangzhou , Guangdong 510640 , China

Corresponding Author

马牛静，男，博士，副研究员.E-mail：[email protected]

Abstract

In response to the high precision requirements for alignment control, complex construction procedures, and significant stress variations in steel truss highway-railway bridges, this paper aims to improve the predictive accuracy of finite element models in bridge construction monitoring. The Hongqili highway-railway bridge was used as the engineering background, and a multi-scale numerical model was built using ANSYS. Based on the response surface method (RSM ) and NSGA- Ⅱ method, the joint stiffness of the member-based model was corrected to obtain a rigid-arm model equivalent to the multi-scale model. First, based on the improved AHP-CRITIC combination weighting method, the importance of deflection and stress indices at multiple control points was evaluated, and satisfaction functions for the deflection and stress indices were developed. Second, combinations of correction parameter samples were generated using the BBD experimental design, and iterative calculations of the APDL model were driven by parametric programming. Parameter significance analysis was performed on the resulting samples, and incomplete quadratic polynomial equations were derived through regression. Finally, a bi-objective optimization problem was constructed using the deflection satisfaction function and the stress satisfaction function as objectives, and the NSGA- Ⅱ method was used for multi-objective optimization to obtain the Pareto front. Three representative points were extracted to evaluate the validity of the surrogate model and the effectiveness of the optimization, and the optimal solution with the minimum comprehensive absolute error was obtained. The results demonstrate that the maximum error decreases from 12.1% to 4.6%, the average error of the deflection indices decreases from 9.4% to 1.0%, the average error of the stress indices decreases from 4.2% to 3.0%, and the overall average error decreases from 6.8% to 2.0%. The findings indicate that the proposed correction method can provide a reference for stiffness correction of steel truss bridges.

Publication Date

10-29-2026

DOI

10.14048/j.issn.1671-2579.2026.05.013

First Page

124

Last Page

135

Submission Date

October 2026

Recommended Citation

Jingyuan, Guan; Hao, Chen; Yonggang, Qin; Niujing, Ma; and Xiaoxia, Zhen (2026) "Stiffness correction of integral joints in steel truss bridges based on RSM-NSGA- Ⅱ," Journal of China & Foreign Highway: Vol. 46: Iss. 5, Article 13.
DOI: 10.14048/j.issn.1671-2579.2026.05.013
Available at: https://zwgl1980.csust.edu.cn/journal/vol46/iss5/13

Reference

[1]郑凯锋,冯霄暘,衡俊霖,等.钢桥 2020年度研究进展[J].土木与环境工程学报 (中英文 ),2021,43(增刊 1):53-69.Zheng Kaifeng,Feng Xiaoyang,Heng Junlin,et al.State-of-the-art review of steel bridges in 2020 [J].Journal of Civil and Environmental Engineering,2021,43(S1):53-69.

[2]周绪红,张喜刚,刘界鹏,等.桥梁结构智能设计研究现状及展望 [J].中国公路学报,2025,38(6):1-16.Zhou Xuhong,Zhang Xigang,Liu Jiepeng,et al.State-of-the-art and prospect on intelligent design of bridge structures [J].China Journal of Highway and Transport,2025,38(6):1-16.

[3]王佐才,丁雅杰,戈壁,等.桥梁结构非线性模型修正研究综述 [J].交通运输工程学报,2022,22(2):59-75.Wang Zuocai,Ding Yajie,Ge Bi,et al.Review on nonlinear model updating for bridge structures [J].Journal of Traffic and Transportation Engineering,2022,22(2):59-75.

[4]郝常顺,刘保东,孙武鹏,等.大跨度铁路桥梁健康监测技术研究与应用综述 [J].铁道科学与工程学报,2025,22(4):1662 -1685.Hao Changshun,Liu Baodong,Sun Wupeng,et al.Review on research and application of health monitoring technology for long-span railway bridges [J].Journal of Railway Science and Engineering,2025,22(4):1662 -1685.

[5]Jaishi B,Ren W X.Finite element model updating based on eigenvalue and strain energy residuals using multiobjective optimisation technique [J].Mechanical Systems and Signal Processing,2007,21(5):2295 -2317.

[6]Fang S E,Perera R.Damage identification by response surface based model updating using D-optimal design [J].Mechanical Systems and Signal Processing,2011,25(2):717-733.

[7]于祥敏,刘进,张围,等.钢桁梁斜拉桥结构设计和工程应用研究 [J].桥梁建设,2025,55(5):121-129.Yu Xiangmin,Liu Jin,Zhang Wei,et al.Structural design and engineering application of steel truss cable-stayed bridge [J].Bridge Construction,2025,55(5):121-129.

[8]颜东煌,陈常松.带刚臂空间梁单元及其在斜拉桥计算中的应用 [J].湖南大学学报,1999,26(2):72.Yan Donghuang,Chen Changsong.Space beam element with stiffarm and its application in cable stayed bridges [J].Journal of Hunan University Natural Sciences,1999,26(2):72.

[9]黄永辉,王荣辉,饶瑞.考虑整体节点刚域影响的钢桁梁桥空间受力计算分析 [J].中国铁道科学,2012,33(5):8-14.Huang Yonghui,Wang Ronghui,Rao Rui.The calculation and analysis of the spatial mechanical behavior for steel truss bridge considering the effect of integral joint rigid zone [J].China Railway Science,2012,33(5):8-14.

[10]盛兴旺,郑纬奇,戴劲.考虑整体节点刚域模拟影响的钢桁梁力学效应分析 [J].桥梁建设,2016,46(6):78-82.Sheng Xingwang,Zheng Weiqi,Dai Jin.Analysis of mechanical effect of steel truss girder considering influences of rigid zone simulation of integral joints [J].Bridge Construction,2016,46(6):78-82.

[11]刘高成,刘建,董创文,等.参照多尺度模型的钢桁梁节点刚域优化 [J].中外公路,2024,44(5):173-182.Liu Gaocheng,Liu Jian,Dong Chuangwen,et al.Rigid domain optimization of steel truss joint with reference to multi-scale model [J].Journal of China & Foreign Highway,2024,44(5):173-182.

[12]冯霄暘,马芹纲,宋德洲,等.公路组合桥面钢桁梁桥整体式节点计算对比 [J].科学技术与工程,2021,21(15):6454 -6462.Feng Xiaoyang,Ma Qingang,Song Dezhou,et al.Comparison of calculation of integral joints of highway steel truss bridge with composite deck [J].Science Technology and Engineering,2021,21(15):6454 -6462.

[13]谷利雄,陈浩,吴玉贤,等.基于误差函数的钢桁梁顶推施工线形控制研究 [J].世界桥梁,2025,53（6）:99-106.Gu Lixiong,Chen Hao,Wu Yuxian,et al.Error function based geometry control of steel truss superstructure installed by incremental launching method [J].World Bridges,2025,53(6):99-106.

[14]杨咏昕,陈艾荣,项海帆.桥梁结构动力特性分析中节点刚 性 区 问 题 的 处 理 [J].土 木 工 程 学 报,2001,34(1):14-18.Yang Yongxin,Chen Airong,Xiang Haifan.Problems of nodal rigid zone in modeling bridge structures for dynamic analysis [J].China Civil Engineering Journal,2001,34(1):14-18.

[15]朱志辉,张鹏,赵婷婷,等.考虑节点刚域影响的钢 ‒混组合桁架梁桥行车动力响应分析 [J].湖南大学学报 (自然科学版 ),2018,45(5):19-28.Zhu Zhihui,Zhang Peng,Zhao Tingting,et al.Driving dynamic response analysis of a steel-concrete composite trussed girder bridge considering the effect of nodal rigid zone [J].Journal of Hunan University (Natural Sciences ),2018,45(5):19-28.

[16]宗周红,褚福鹏,牛杰.基于响应面模型修正的桥梁结构损伤识别方法 [J].土木工程学报,2013,46(2):115-122.Zong Zhouhong,Chu Fupeng,Niu Jie.Damage Identification methods of bridge structures using response surface based on finite element model updating [J].China Civil Engineering Journal,2013,46(2):115-122.

[17]关维溢,段璐琦.基于响应面法的 UHPC-NC 连续箱梁桥优化设计 [J].中外公路,2023,43(3):76-82.Guan Weiyi,Duan Luqi.Optimization design of UHPC-NC continuous box girder bridge based on response surface method [J].Journal of China & Foreign Highway,2023,43(3):76-82.

[18]王晓光,党李涛,马明.基于振动频率的响应面模型修正稳健估计法 [J].公路交通科技,2022,39(2):77-84.Wang Xiaoguang,Dang Litao,Ma Ming.A robust estimation method for response surface model updating based on vibration frequency [J].Journal of Highway and Transportation Research and Development,2022,39(2):77-84.

[19]Wang C W,Ansari F,Wu B,et al.LSTM approach for condition assessment of suspension bridges based on time-series deflection and temperature data [J].Advances in Structural Engineering,2022,25(16):3450 -3463.

[20]Xia Z Y,Li A Q,Li J H,et al.Model updating of an existing bridge with high-dimensional variables using modified particle swarm optimization and ambient excitation data [J].Measurement,2020,159:107754.

[21]王凌波,郭欣军,赵鹏,等.基于响应面的上加劲双层钢桁梁桥多目标优化算法 [J].交通运输工程学报,2025,25(2):252-269.Wang Lingbo,Guo Xinjun,Zhao Peng,et al.Multi-objective optimization algorithm for upper stiffened double-deck steel truss girder bridge based on response surface [J].Journal of Traffic and Transportation Engineering,2025,25(2):252-269.

[22]王祺顺,何维,吴欣,等.基于 RBFNN-ISSA 的特大跨径悬索桥有限元模型修正 [J].振动与冲击,2024,43(7):155-167.Wang Qishun,He Wei,Wu Xin,et al.Finite element model correction of super long-span suspension bridge based on RBFNN-ISSA [J].Journal of Vibration and Shock,2024,43(7):155-167.

[23]Hu Z,Rao R,Chen H,et al.Calculation parameter correction of steel truss nodal plate based on machine learning theory [J].Advances in Mechanical Engineering,2025,17(2):16878132251319384.

[24]储胡照,吉军立,董婷婷,等.平列式公铁两用钢桁梁桥疲劳损伤及寿命研究 [J].振动、测试与诊断,2024,44(5):979-986,1041 -1042.Chu Huzhao,Ji Junli,Dong Tingting,et al.Fatigue damage and life of steel truss joints in parallel-type combined highway and railway bridge [J].Journal of Vibration,Measurement & Diagnosis,2024,44(5):979-986,1041 -1042.

[25]商淑杰,姜磊,岳秀鹏,等.钢桁梁全焊整体节点应力集中系数研究 [J].公路交通科技,2023,40(10):137-152.Shang Shujie,Jiang Lei,Yue Xiupeng,et al.Study on stress concentration factor of full-welded integral joint in steel truss bridge [J].Journal of Highway and Transportation Research and Development,2023,40(10):137-152.

[26]赵汗青,简方梁,淡丹辉,等.大跨连续钢桁梁桥健康监测系统设计及应用 [J].世界桥梁,2024,52（6）:56-63.Zhao Hanqing,Jian Fangliang,Dan Danhui,et al.Design and application of health monitoring system for long-span continuous steel truss bridge [J].World Bridges,2024,52(6):56-63.

[27]施洲,赵旭泼,刘振标,等.公铁合建斜拉桥钢桁 ‒混凝土板组合梁受力特性 [J].铁道科学与工程学报,2024,21(7):2778-2789.Shi Zhou,Zhao Xupo,Liu Zhenbiao,et al.Mechanical characteristics of steel truss-concrete slab composite girder of a railway-cum-road cable-stayed bridge [J].Journal of Railway Science and Engineering,2024,21(7):2778 -2789.

[28]喻伟,杨娜,李珏.基于 AHP-DEMATEL 的公路养护决策与计划实施后评估方法 [J].中外公路,2024,44(5):277-283.Yu Wei,Yang Na,Li Jue.Post-evaluation method for decision-making and implementation of highway maintenance projects based on AHP-DEMATEL [J].Journal of China & Foreign Highway,2024,44(5):277-283.

[29]王敏,邹婕,王惠琳,等.基于改进的 AHP-CRITIC-MARCOS 配电网设备风险评估方法 [J].电力系统保护与控制,2023,51(3):164-172.Wang Min,Zou Jie,Wang Huilin,et al.Improved AHP-CRITIC-MARCOS-based risk assessment method for distribution network equipment [J].Power System Protection and Control,2023,51(3):164-172.[30]靳春玲,安祥,贡力,等.基于 G2-CRITIC-UMT 模型的铁路隧道低碳施工评价研究 [J].铁道标准设计,2025,69(1):139-146.Jin Chunling,An Xiang,Gong Li,et al.Research on low-carbon construction evaluation of railway tunnels based on G 2-CRITIC-UMT model [J].Railway Standard Design,2025,69(1):139-146.

[31]赵书强,汤善发.基于改进层次分析法、CRITIC法与逼近理想解排序法的输电网规划方案综合评价 [J].电力自动化设备,2019,39(3):143-148,162.Zhao Shuqiang,Tang Shanfa.Comprehensive evaluation of transmission network planning scheme based on improved analytic hierarchy process,CRITIC method and TOPSIS [J].Electric Power Automation Equipment,2019,39(3):143-148,162.

[32]冯青松,王龙,孙魁,等.基于 NSGA- Ⅱ遗传算法的市域快线无砟轨道结构多目标优化 [J].铁道标准设计,2025,69(1):15-21.Feng Qingsong,Wang Long,Sun Kui,et al.Multi-objective optimization of ballastless track of urban express line based on NSGA- Ⅱ genetic algorithm [J].Railway Standard Design,2025,69(1):15-21.