基于正则化与B样条曲线的桥梁影响线识别方法
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摘要
为了快速评估既有桥梁的安全性,研究了基于多源实测信息快速准确识别桥梁影响线的方法。首先利用桥梁动力响应及车辆移动的实测信息,建立影响线识别的数学模型。在模型中引入Tikhonov正则化方法以解决病态矩阵求解问题,通过设置罚函数项以取得较光滑并贴近真实的影响线。然后通过基函数扩展法重构影响线,将其表示为一系列三次B样条基函数的线性组合,从而将问题从识别众多影响线因子简化为识别少量基函数权重系数。为了验证上述方法的可行性,先在实验室模拟钢制试验小车在钢筋混凝土三跨连续梁模型上移动的过程。基于实测布置于梁底的多测点挠度和应变响应时程以及相应的试验车信息,可识别出不同位置测点的挠度和应变影响线。试验结果表明无论是影响线的总体形状还是局部峰值,识别解与基准解均能较好地吻合。该方法还被进一步应用到一座简支现浇预应力混凝土箱梁桥。该试验通过实测检测车过桥期间的桥梁跨中截面若干测点的动应变、动挠度以及车辆重力、实时位置等信息,准确识别了对应于不同车道的挠度和应变影响线。通过对比桥梁静载实测和影响线虚拟加载结果,发现两者偏差绝对值在5%以内。在一定程度上表明了该影响线识别方法具有较高精度,并具备工程应用的良好潜力。
To evaluate the safety of existing bridges quickly, the bridge influence line(BIL) identification method based on multiple sources of measured information was studied. First, the measured information for the dynamic responses of the bridge and moving vehicle were used to establish a mathematical model for the influence line identification. In the model, the Tikhonov regularization method was used to solve the problem of an ill-conditioned matrix, and the penalty function was established to identify a smooth BIL that would replicate the real BIL faithfully. The influence line was then reconstructed using the basis function extension method, which uses a linear combination of a series of cubic B-spline basis functions for the representation; thus, the identification problem was transformed from solving for many influence line factors into a small number of basis function weight coefficients. To verify the feasibility of the above method, simulations were first conducted for the process where the loaded vehicle made of steel moved on a reinforced concrete three-span continuous beam model. Based on the measured deflection and strain response time history of the beam and the corresponding vehicle information, the deflection and strain influence lines of different measurement points were identified. The experimental results show that both the overall shapes and local peak values of the BILs are in good agreement with the baseline solutions. Furthermore, this method was applied to a simply supported cast-in-situ prestressed concrete box girder bridge. Based on the dynamic strain and deflection responses measured at the mid-span of the beam, as well as the axle weight and real-time position of the moving vehicle, the deflection and strain influence lines were accurately identified for different lanes. By comparing the results of static load testing of the bridge and BIL-based virtual loading, it is found that the deviation of the absolute value is within 5%, which indicates that the influence line identification method has high accuracy and good potential for engineering applications.
To evaluate the safety of existing bridges quickly, the bridge influence line(BIL) identification method based on multiple sources of measured information was studied. First, the measured information for the dynamic responses of the bridge and moving vehicle were used to establish a mathematical model for the influence line identification. In the model, the Tikhonov regularization method was used to solve the problem of an ill-conditioned matrix, and the penalty function was established to identify a smooth BIL that would replicate the real BIL faithfully. The influence line was then reconstructed using the basis function extension method, which uses a linear combination of a series of cubic B-spline basis functions for the representation; thus, the identification problem was transformed from solving for many influence line factors into a small number of basis function weight coefficients. To verify the feasibility of the above method, simulations were first conducted for the process where the loaded vehicle made of steel moved on a reinforced concrete three-span continuous beam model. Based on the measured deflection and strain response time history of the beam and the corresponding vehicle information, the deflection and strain influence lines of different measurement points were identified. The experimental results show that both the overall shapes and local peak values of the BILs are in good agreement with the baseline solutions. Furthermore, this method was applied to a simply supported cast-in-situ prestressed concrete box girder bridge. Based on the dynamic strain and deflection responses measured at the mid-span of the beam, as well as the axle weight and real-time position of the moving vehicle, the deflection and strain influence lines were accurately identified for different lanes. By comparing the results of static load testing of the bridge and BIL-based virtual loading, it is found that the deviation of the absolute value is within 5%, which indicates that the influence line identification method has high accuracy and good potential for engineering applications.
引文
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[9]CHEN Zhi-wei,CAI Qin-lin,LEI Ying,et al.Damage Detection of Long-span Bridges Using Stress Influence Lines Incorporating Control Charts[J].Science China Technological Sciences,2013,57(9):1689-1697.
[10]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.
[11]LENG S S.Bridge Influence Line Estimation for Bridge Weigh-in-motion System[J].Journal of Computing in Civil Engineering,2015,29(1):06014006.
[12]CHEN Zhi-Wei,ZHU Song-ye,XU You-lin,et al.Damage Detection in Long Suspension Bridges Using Stress Influence Lines[J].Journal of Bridge Engineering,2015,20(3):05014013.
[13]SUN Shou-wang,SUN Li-Ming,CHEN Lin.Damage Detection Based on Structural Response Induced by Traffic Load:Methodlogy and Application[J].International Journal of Structural Stability and Dynamics,2015,16(4):1640026.
[14]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 Ning-bo,REN Wei-xin,HE Li-xiang.Extraction of Influence Line of Bridge from Dynamic Responses[J].Journal of Central South University:Science and Technology,2014,45(12):4362-4369.
[15]TIKHONOV A N.Solution of Incorrectly Formulated Problems and the Regularization Method[J].Soviet Mathematics Doklady,1963,5(4):1035-1038.
[16]SCHERZER O.The Use of Morozovs Discrepancy Principle for Tikhonov Regularization for Solving Nonlinear Ill-posed Problems[J].Computing,1993,51(1):45-60.
[17]HANSEN P C.Analysis of Discrete Ill-posed Problems by Means of the L-curve[J].SIAM Review,1992,34(4):561-580.
[18]JUDD K L.Numerical Methods in Economics[M].Cambridge:MIT Press,1998.
[2]李兆霞,王滢,吴佰建,等.桥梁结构劣化与损伤过程的多尺度分析方法及其应用[J].固体力学学报,2010,31(6):731-755.LI Zhao-xia,WANG Ying,WU Bai-jian,et al.Multi-scale Modeling and Analyses on Structural Deterioration and Damage in Long-span Bridges and Its Application[J].Chinese Journal of Solid Mechanics,2010,31(6):731-755.
[3]李亚东.既有桥梁评估方法研究[J].铁道学报,1997,19(3):109-115.LI Ya-dong.Research on Methods for Assessment of Existing Bridges[J].Journal of the China Railway Society,1997,19(3):109-115.
[4]SARAF V,NOWAK A S.Proof Load Testing of Deteriorated Steel Girder Bridges[J].Journal of Structural Engineering,1998,3(2):82-90.
[5]MELCHERS R E.Assessment of Existing StructuresApproaches and Research Needs[J].Journal of Structural Engineering,2001,127(4):406-411.
[6]宗周红,任伟新,郑振飞.既有桥梁承载能力评估方法[J].地震工程与工程振动,2005,25(5):147-152.ZONG Zhou-hong,REN Wei-xin,ZHENG Zhen-fei.Load-carrying Capacity Assessment Methods of Existing Bridges[J].Earthquake Engineering and Engineering Vibration,2005,25(5):147-152.
[7]陈孝珍,朱宏平,陈传尧.基于静载试验的桥梁安全性评价[J].华中科技大学学报:城市科学版,2005,22(3):37-40.CHEN Xiao-zhen,ZHU Hong-ping,CHEN Chuanyao.Bridge Safety Assessment Based on Static Loading Test[J].Journal of Huazhong University of Science and Technology:Urban Science Edition,2005,22(3):37-40.
[8]林贤坤,张令弥,郭勤涛,等.基于模态挠度法的预应力连续箱梁桥状态评估[J].土木工程学报,2010,43(10):83-90.LIN Xian-kun,ZHANG Ling-mi,GUO Qin-tao,et al.Application of Modal Deflection Method for Condition Assessment of Prestressed Concrete Continuous Box-girder Bridges[J].China Civil Engineering Journal,2010,43(10):83-90.
[9]CHEN Zhi-wei,CAI Qin-lin,LEI Ying,et al.Damage Detection of Long-span Bridges Using Stress Influence Lines Incorporating Control Charts[J].Science China Technological Sciences,2013,57(9):1689-1697.
[10]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.
[11]LENG S S.Bridge Influence Line Estimation for Bridge Weigh-in-motion System[J].Journal of Computing in Civil Engineering,2015,29(1):06014006.
[12]CHEN Zhi-Wei,ZHU Song-ye,XU You-lin,et al.Damage Detection in Long Suspension Bridges Using Stress Influence Lines[J].Journal of Bridge Engineering,2015,20(3):05014013.
[13]SUN Shou-wang,SUN Li-Ming,CHEN Lin.Damage Detection Based on Structural Response Induced by Traffic Load:Methodlogy and Application[J].International Journal of Structural Stability and Dynamics,2015,16(4):1640026.
[14]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 Ning-bo,REN Wei-xin,HE Li-xiang.Extraction of Influence Line of Bridge from Dynamic Responses[J].Journal of Central South University:Science and Technology,2014,45(12):4362-4369.
[15]TIKHONOV A N.Solution of Incorrectly Formulated Problems and the Regularization Method[J].Soviet Mathematics Doklady,1963,5(4):1035-1038.
[16]SCHERZER O.The Use of Morozovs Discrepancy Principle for Tikhonov Regularization for Solving Nonlinear Ill-posed Problems[J].Computing,1993,51(1):45-60.
[17]HANSEN P C.Analysis of Discrete Ill-posed Problems by Means of the L-curve[J].SIAM Review,1992,34(4):561-580.
[18]JUDD K L.Numerical Methods in Economics[M].Cambridge:MIT Press,1998.