考虑初始条件影响的移动荷载识别稀疏正则化方法
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摘要
利用桥梁实测响应反演桥面移动荷载是桥梁工程的研究热点之一。但既有移动荷载正则化识别方法没有考虑未知初始条件的影响。针对此问题,基于稀疏正则化技术提出了一种新的移动荷载识别方法。首先分别采用冗余字典与模态空间描述移动荷载与初始条件,计算各个荷载与初始条件分量引起的响应,归一化构造用于表达响应的像字典。然后利用像字典对响应进行稀疏分解,其结果即可用于估算未知移动荷载。最后采用数值仿真算例评价所提方法的可行性与有效性,并通过实验室搭建的车-桥系统模型对新方法进行实验验证。研究结果表明:未知初始条件下,所提方法能有效地识别移动荷载。
Moving force identification(MFI)from measured responses of bridges is a hot topic in bridge engineering.Current regularization-based MFI methods do not consider any influences from unknown initial conditions.In this study,a novel method is proposed for solving the MFI problem under unknown initial conditions based on sparse regularization.Firstly,the redundant dictionary and modal space are used for expressing moving forces and initial conditions,respectively.Responses induced by each component of moving forces and initial conditions are calculated and used for forming an image dictionary via normalization.The measured responses are decomposed by the image dictionary and then the decomposed results are used for estimating the moving forces.Finally,numerical simulations are used for assessing the accuracy and feasibility of the proposed method.A vehicle-bridge system model is then designed and fabricated in laboratory.A series of responses of a beam bridge subjected to moving vehicles are measured and used to verify the proposed method.The results show that the proposed method can identify the moving forces under unknown initial conditions.
Moving force identification(MFI)from measured responses of bridges is a hot topic in bridge engineering.Current regularization-based MFI methods do not consider any influences from unknown initial conditions.In this study,a novel method is proposed for solving the MFI problem under unknown initial conditions based on sparse regularization.Firstly,the redundant dictionary and modal space are used for expressing moving forces and initial conditions,respectively.Responses induced by each component of moving forces and initial conditions are calculated and used for forming an image dictionary via normalization.The measured responses are decomposed by the image dictionary and then the decomposed results are used for estimating the moving forces.Finally,numerical simulations are used for assessing the accuracy and feasibility of the proposed method.A vehicle-bridge system model is then designed and fabricated in laboratory.A series of responses of a beam bridge subjected to moving vehicles are measured and used to verify the proposed method.The results show that the proposed method can identify the moving forces under unknown initial conditions.
引文
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[16]Yu Y,Cai C S,Deng L.State-of-the-art review on bridge weigh-in-motion technology[J].Advances in Structural Engineering,2016,19(9):1—17.
[17]Qiao B,Zhang X,Wang C,et al.Sparse regularization for force identification using dictionaries[J].Journal of Sound and Vibration,2016,368:71—86.
[18]Pan C D,Yu L,Liu H L,et al.Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization[J].Mechanical Systems&Signal Processing,2018,98:32—49.
[19]Beck A,Teboulle M.A Fast Iterative Shrinkage Thresholding Algorithm for Linear Inverse Problems[J].Siam Journal on Imaging Sciences,2009,2(1):183—202.
[2] Zhu X Q,Law S S.Recent developments in inverse problems of vehicle-bridge interaction dynamics[J].Journal of Civil Structural Health Monitoring,2016,6(1):107—128.
[3] Yu L,Chan T H T.Recent research on identification of moving loads on bridges[J].Journal of Sound and Vibration,2007,305(1-2):3—21.
[4] Law S S,Chan T H T,Zhu Q X,et al.Regularization in moving force identification[J].Journal of Engineering Mechanics,2001,127(2):136—148.
[5] Zhu X Q,Law S S. Moving loads identification through regularization[J].Journal of Engineering Mechanics,2002,128(128),989—1000.
[6] Sun H,Feng D,Liu Y,et al.Statistical regularization for identification of structural parameters and external loadings using state space models[J].Computer-Aided Civil and Infrastructure Engineering,2015,30(11):843—858.
[7] Feng D,Sun H,Feng M Q.Simultaneous identification of bridge structural parameters and vehicle loads[J].Computers&Structures,2015,157:76—88.
[8]陈震,余岭.基于截断GSVD方法的桥梁移动荷载识别[J].振动与冲击,2014,33(10):97—100.CHEN Zhen,YU Ling.Identification of dynamic axle loads on bridge based on truncated generalized singular value decomposition[J].Journal of Vibration and Shock,2014,33(10):97—100.
[9] Bao Y Q,Li H,Chen Z C,et al.Sparse l1optimization-based identification approach for the distribution of moving heavy vehicle loads on cable-stayed bridges[J].Structural Control&Health Monitoring,2016,23(1):144—155.
[10]Pan C D,Yu L,Liu H L.Identification of moving vehicle forces on bridge structures via moving average Tikhonov regularization[J].Smart Materials&Structures,2017,26:085041.
[11]钱长照,陈昌萍.利用弯矩影响线的移动荷载识别方法[J].动力学与控制学报,2016,14(2):182—185.QIAN Changzhao,CHEN Changping. Method for moving force identification using bending moment influence line[J].Journal of Dynamics and Control,2016,14(2):182—185.
[12]王宁波,任伟新,李苗.基于影响线的桥梁移动荷载识别[J].振动与冲击,2013,32(3):129—133.WANG Ning-bo,REN Wei-xin,LI Miao. Moving loads identification of bridge based on influence line[J].Journal of Vibration and Shock,2013,32(3):129—133.
[13]王蕾,侯吉林,欧进萍.基于荷载形函数的大跨桥梁结构移动荷载识别[J].计算力学学报,2012,29(02):153—158.WANG Lei,HOU Ji-lin,OU Jin-ping.Moving force identification based on load shape function for a longspan bridge structure[J].Chinese Journal of Computational Mechanics,2012,29(02):153—158.
[14]尤琼,史治宇,罗绍湘.基于小波有限元的移动荷载识别[J].振动工程学报,2010,23(2):188—193.YOU Qiong,SHI Zhi-yu,LAW Siu Seong.Moving force identification based on wavelet finite element method[J].Journal of Vibration Engineering,2010,23(2):188—193.
[15]修建权,尤琼,史治宇.基于小波有限元法的连续梁移动荷载识别[J].振动与冲击,2012,31(6):141—144.XIU Jian-quan,YOU Qiong,SHI Zhi-yu. Moving force identification on continuous bridges with wavelet finite element method[J].Journal of Vibration and Shock,2012,31(6):141—144.
[16]Yu Y,Cai C S,Deng L.State-of-the-art review on bridge weigh-in-motion technology[J].Advances in Structural Engineering,2016,19(9):1—17.
[17]Qiao B,Zhang X,Wang C,et al.Sparse regularization for force identification using dictionaries[J].Journal of Sound and Vibration,2016,368:71—86.
[18]Pan C D,Yu L,Liu H L,et al.Moving force identification based on redundant concatenated dictionary and weighted l1-norm regularization[J].Mechanical Systems&Signal Processing,2018,98:32—49.
[19]Beck A,Teboulle M.A Fast Iterative Shrinkage Thresholding Algorithm for Linear Inverse Problems[J].Siam Journal on Imaging Sciences,2009,2(1):183—202.