Bridge influence line identification based on variational mode decomposition and piecewise polynomial truncated singular value decomposition

doi:10.3785/j.issn.1008-973X.2025.03.003

Journal of ZheJiang University (Engineering Science)

2025, Vol. 59

Issue (3): 460-468 DOI: 10.3785/j.issn.1008-973X.2025.03.003

Bridge influence line identification based on variational mode decomposition and piecewise polynomial truncated singular value decomposition

Guijun WAN1,2(

),Jianan LI3,4,Dongming FENG3,4,*(

)

1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
2. China Overseas Construction Limited, Shenzhen 518055, China
3. Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing 211189, China
4. School of Civil Engineering, Southeast University, Nanjing 211189, China

Download:

HTML

PDF(1873KB) HTML
Export: BibTeX | EndNote (RIS)

Abstract

A method based on the variational mode decomposition (VMD) and the piecewise polynomial truncated singular value decomposition (PPTSVD) was proposed to improve the accuracy of bridge influence line identification. The method applied VMD to decompose bridge displacement into several intrinsic mode functions (IMFs), extracted the quasi-static component of the bridge response by fusing multiple low-order IMFs, and identified the bridge influence line from the quasi-static component using PPTSVD. To validate the accuracy of the proposed method, a numerical simulation model of a three-span continuous beam bridge and a four-axle vehicle was established, simulating different vehicle speeds, road roughness levels, and noise levels, and tested on 500 sets of numerical results. The proposed method was compared with classical methods, and the effects of vehicle speed, road roughness, and noise on the identification results were comprehensively discussed. Furthermore, validation experiments were conducted to test the accuracy and applicability of the proposed method in a laboratory environment. Results showed that the proposed method accurately identified the bridge influence line from bridge responses, with a maximum error of only 1.38%. Compared to traditional methods, the proposed method significantly reduced the interference of vehicle speed, road roughness, and noise on the identification results, enhancing the robustness and accuracy.

Key words： bridge health monitoring bridge dynamic analysis vehicle-bridge interaction system influence line identification variational mode decomposition

Received: 13 January 2024 Published: 10 March 2025

CLC:

U 441

Fund: 东南大学新进教师科研启动经费资助项目（RF1028623149）；中央高校基本科研业务费专项资金资助项目（2242024K40013）.

Corresponding Authors: Dongming FENG E-mail: gjwan@cohl.com;dfeng@seu.edu.cn

	Service
	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Guijun WAN
	Jianan LI
	Dongming FENG

Cite this article:

Guijun WAN,Jianan LI,Dongming FENG. Bridge influence line identification based on variational mode decomposition and piecewise polynomial truncated singular value decomposition. Journal of ZheJiang University (Engineering Science), 2025, 59(3): 460-468.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.03.003 OR https://www.zjujournals.com/eng/Y2025/V59/I3/460

基于变分模态分解和分段多项式截断奇异值分解的桥梁影响线识别

为了提高桥梁影响线的识别精度，提出基于变分模态分解（VMD）和分段多项式截断奇异值分解（PPTSVD）的桥梁影响线识别方法. 该方法应用VMD技术将桥梁位移分解成若干固有模态函数（IMF），通过融合多个低阶IMF提取桥梁响应的准静态成分，利用PPTSVD从准静态成分中识别桥梁影响线. 为了验证所提方法的准确性，建立三跨连续梁桥和四轴车数值仿真模型，模拟不同车速、路面不平度和噪声水平，并针对500组数值仿真结果进行测试. 将所提方法与经典方法进行对比，并全面讨论车速、路面不平度和噪声对识别结果的影响. 进行验证试验，测试实验室环境下所提方法的准确性和适用性. 研究结果表明，所提方法能从桥梁响应中准确识别出桥梁影响线，最大误差仅为1.38%；相比传统方法，所提方法显著减少了车速、路面不平度和噪声对识别结果的干扰，提高了识别的鲁棒性和精度.

关键词： 桥梁健康监测, 桥梁动力分析, 车桥耦合系统, 影响线识别, 变分模态分解

Fig.1 Diagram of vehicle-bridge coupling model

Fig.2 Flow chart of influence line identification

Fig.3 Comparison of intrinsic mode functions of bridge displacement

Fig.4 Analysis of cutoff frequency for variational mode decomposition

Fig.5 Results comparison of different methods for identifying influence line

Fig.6 Comparison of analysis errors of different methods

Fig.7 Error comparison of different pavement levels

Fig.8 Error comparison of speed

Fig.9 Error comparison of SNR

Fig.10 Maximum error identification results (SNR=20)

Fig.11 Influence line identification test instruments

Fig.12 Bridge displacement measurement data

Fig.13 Test results of influence line identification

Tab.1 Influence line identification error


[1]	WU Y S, YANG Y B, YAU J D Three-dimensional analysis of train-rail-bridge interaction problems[J]. Vehicle System Dynamics, 2001, 36 (1): 1- 35 doi: 10.1076/vesd.36.1.1.3567

[2]	贺文宇, 武骥元, 任伟新基于车致桥梁响应和L1正则化的损伤识别研究[J]. 中国公路学报, 2021, 34 (4): 61- 70 HE Wenyu, WU Jiyuan, REN Weixin Bridge damage detection based on the moving-vehicle-induced response and L1 regularization[J]. China Journal of Highway and Transport, 2021, 34 (4): 61- 70 doi: 10.3969/j.issn.1001-7372.2021.04.005

[3]	邓露, 何维, 俞扬, 等公路车-桥耦合振动的理论和应用研究进展[J]. 中国公路学报, 2018, 31 (7): 38- 54 DENG Lu, HE Wei, YU Yang, et al Research progress in theory and applications of highway vehicle-bridge coupling vibration[J]. China Journal of Highway and Transport, 2018, 31 (7): 38- 54 doi: 10.3969/j.issn.1001-7372.2018.07.003

[4]	莫叶, 王佐才, 丁雅杰, 等基于VMD和DBN的非线性结构模型参数识别[J]. 振动与冲击, 2022, 41 (9): 136- 143 MO Ye, WANG Zuocai, DING Yajie, et al Parametric recognition of nonlinear structural model based on VMD and DBN[J]. Journal of Vibration and Shock, 2022, 41 (9): 136- 143

[5]	XIAO X, XU Y L, ZHU Q Multiscale modeling and model updating of a cable-stayed bridge. II: model updating using modal frequencies and influence lines[J]. Journal of Bridge Engineering, 2015, 20 (10): 04014113 doi: 10.1061/(ASCE)BE.1943-5592.0000723

[6]	MOSES F Weigh-in-motion system using instrumented bridges[J]. Transportation Engineering Journal of ASCE, 1979, 105 (3): 233- 249

[7]	SUN Z, SIRINGORINGO D M, FUJINO Y Load-carrying capacity evaluation of girder bridge using moving vehicle[J]. Engineering Structures, 2021, 229: 111645 doi: 10.1016/j.engstruct.2020.111645

[8]	KONG X, ZHANG J, WANG T, et al. Non-contact vehicle weighing method based on tire-road contact model and computer vision techniques[J]. Mechanical Systems and Signal Processing , 2022, 174: 109093.

[9]	OBRIEN E J, QUILLIGAN M J, KAROUMI R Calculating an influence line from direct measurements[J]. Proceedings of the Institution of Civil Engineers-Bridge Engineering, 2006, 159 (1): 31- 34 doi: 10.1680/bren.2006.159.1.31

[10]	IENG S S Bridge influence line estimation for bridge weigh-in-motion system[J]. Journal of Computing in Civil Engineering, 2015, 29 (1): 060140061

[11]	陈志为, 杨维彪, 程棋锋, 等基于正则化与 B 样条曲线的桥梁影响线识别方法[J]. 中国公路学报, 2019, 32 (3): 101- 108 CHEN Zhiwei, YANG Weibiao, CHENG Qifeng, et al Bridge influence line identification method based on regularization and B-spline curves[J]. China Journal of Highway and Transport, 2019, 32 (3): 101- 108

[12]	王宁波, 任伟新, 何立翔基于桥梁动力响应的应变影响线提取[J]. 中南大学学报: 自然科学版, 2014, 45 (12): 4362- 4369 WANG Ningbo, REN Weixin, HE Lixiang Extraction of strain influence line of bridge from dynamic responses[J]. Journal of Central South University: Science and Technology, 2014, 45 (12): 4362- 4369

[13]	YAN W J, YUEN K V A new probabilistic frequency domain approach for influence line extraction from static transmissibility measurements under unknown moving loads[J]. Engineering Structures, 2020, 216: 110625 doi: 10.1016/j.engstruct.2020.110625

[14]	MUSTAFA S, YOSHIDA I, SEKIYA H An investigation of bridge influence line identification using time-domain and frequency-domain methods[J]. Structures, 2021, 33: 2061- 2065 doi: 10.1016/j.istruc.2021.05.082

[15]	KHUC T, CATBAS F N Structural identification using computer vision-based bridge health monitoring[J]. Journal of Structural Engineering, 2018, 144 (2): 1- 13

[16]	周宇, 许成超, 赵青, 等变截面悬链线无铰拱应变影响线的解析解[J]. 计算力学学报, 2022, 39 (5): 551- 556 ZHOU Yu, XU Chengchao, ZHAO Qing, et al Practical analytical expression to strain influence line of varying cross section catenary fixed arch[J]. Chinese Journal of Computational Mechanics, 2022, 39 (5): 551- 556 doi: 10.7511/jslx20210425002

[17]	慕何青, 庞振浩, 王浩, 等结构影响线识别: 反问题可识别性分析与降维贝叶斯不确定性量化[J]. 工程力学, 2023, 40 (1): 51- 62 MU Heqing, PANG Zhenhao, WANG Hao, et al Structural influence line identification: inverse problem identifiability analysis and reduced-dimension Bayesian uncertain quantification[J]. Engineering Mechanics, 2023, 40 (1): 51- 62 doi: 10.6052/j.issn.1000-4750.2021.07.0574

[18]	ZHENG X, YANG D, YI T H, et al Bridge influence line identification based on regularized least-squares QR decomposition method[J]. Journal of Bridge Engineering, 2019, 24 (8): 06019004 doi: 10.1061/(ASCE)BE.1943-5592.0001458

[19]	ZHENG X, YANG D, YI T H, et al Bridge influence line identification from structural dynamic responses induced by a high-speed vehicle[J]. Structural Control and Health Monitoring, 2020, 27 (7): e2544

[20]	DRAGOMIRETSKIY K, ZOSSO D Variational mode decomposition[J]. IEEE Transactions on Signal Processing, 2014, 62 (3): 531- 544 doi: 10.1109/TSP.2013.2288675

[21]	陈震, 魏文杰, 余岭, 等基于PPTSVD的桥梁移动荷载识别[J]. 振动测试与诊断, 2018, 38 (4): 727- 732 CHEN Zhen, WEI Wenjie, YU Ling, et al Identification of dynamic axle loads on bridge based on PPTSVD[J]. Journal of Vibration, Measurement and Diagnosis, 2018, 38 (4): 727- 732

[22]	FROIO D, VERZEROLI L, FERRARI R, et al On the numerical modelization of moving load beam problems by a dedicated parallel computing fem implementation[J]. Archives of Computational Methods in Engineering, 2021, 28 (4): 2253- 2314

[23]	LI J A, FENG D Fatigue life evaluation of bridge stay cables subject to monitoring traffic and considering road roughness[J]. Engineering Structures, 2023, 293: 116572 doi: 10.1016/j.engstruct.2023.116572

[24]	LI J A, FENG D A comparative study of vehicle-bridge interaction dynamics with 2D and 3D vehicle models[J]. Engineering Structures, 2023, 292: 116493 doi: 10.1016/j.engstruct.2023.116493

[25]	ISO. Mechanical vibration-road surface profiles-reporting of measured data: ISO 8608 [S]. Geneva: International Organization for Standardization, 2016.

[1]	Haijun WANG,Tao WANG,Cijun YU. CFRP ultrasonic detection defect identification method based on recursive quantitative analysis[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(8): 1604-1617.

[2]	Man XU,Dongmei ZHANG,Xiang YU,Jiang LI,Yiping WU. Improved GRU landslide displacement prediction model based on multifractal[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(7): 1407-1416.

[3]	Yu ZHOU,Luyi GAN,Shengkui DI,Wenyu HE,Ningbo LI. Bridge model modification experiment based on strain influence line[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(3): 537-546.

[4]	Mao-xia RAN,Qin-yuan HUANG,Xin LIU,Hong SONG,Hao WU. Internal defect detection of arc magnets based on optimized variational mode decomposition[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(11): 2158-2168.

[5]	Ji-jun TONG,Yan-jie BAI,Jian-wei PAN,Jia-feng YANG,Lu-rong JIANG. Ballistocardiogram and respiratory signal separation based on variational mode decomposition[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(10): 2058-2066.

Viewed

Full text

Abstract

Cited

Shared

Discussed