基于实数编码遗传算法的桥梁有限元模型修正方法
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摘要
为克服传统桥梁有限元模型修正迭代优化过程中存在的局部收敛和提高模型修正精度,提出了联合实数编码遗传算法与静动力实测数据的有限元模型修正方法;引入四边形等参元理论和牛顿迭代法编制宏命令,实现有限元模型中车辆荷载的快速自动加载;基于结构有限元模型静动力特性构造目标函数,以实数编码遗传算法为优化策略,采用MATLAB平台建立了有限元模型修正框架;通过对一个简支框架结构的数值模拟,对比了所提出优化方法与其他方法的收敛效率和修正结果,以验证所提出方法的有效性;采用拉丁超立方体抽样分析了有限元模型参数变化对桥梁动力响应的影响,以确定待修正参数,并采用所提方法修正了一座改建的空心板桥梁的实体有限元模型。分析结果表明:零阶算法和一阶算法对参数的敏感性和修正范围依赖大,选用敏感性较小的参数或者参数修正范围大于50%将会导致错误的修正结果;实数编码遗传算法对初始输入不敏感,可避免局部收敛的情况;采用灵敏度分析得到的主要待修正参数有空心板弹性模量、现浇层弹性模量以及支座横桥向和顺桥向的约束刚度;修正后的空心板弹性模量增幅约为19.13%,现浇层弹性模量增幅约为16.00%,横向约束刚度增幅约为46.21%,纵向约束刚度增幅约为72.72%,修正后的有限元模型的静动力特性与实测响应吻合良好,各测点静力响应误差均小于4%,动力响应误差小于3%。
To overcome the local convergence and improve the corrective accuracy in the modified iterative optimization process of traditional finite element model, an updating method was proposed by combining the real coded genetic algorithm(RCGA) and measured data of static and dynamic characteristics. The quadrilateral isoparametric element theory and Newton iteration method were used to compile the macro command to realize the fast automatic loading of vehicle loads in the FEM. The objective function was constructed by the static and dynamic characteristics of the finite element model of the structure, the RCGA was taken as the optimization strategy, and the modification frame of the model was established by the MATLAB platform. Through the numerical simulation of a frame structure, the convergence efficiencies and updating results of the proposed optimization method and other methods were compared to verify the effectiveness of the proposed method. To determine the modified parameters, the Latin hypercube sampling method was used to analyze the parametric influence of finite element model on the dynamic responses of the bridge, and the proposed method was applied to modify the solid finite element model of a reconstructed hollow slab bridge. Analysis result shows that the zero order algorithm and the first order algorithm are depended on the sensibilities and correction ranges of the parameters. When the parameters have less sensitivities or the correction ranges are greater than 50%, the correction result of the model is erroneous. The RCGA is insensitive to the initial inputs, so the local convergence can be avoided. The main parameters to be corrected by the sensitivity analysis are the elastic modulus of hollow slab, the elastic modulus of cast-in-situ layer and the longitudinal and transversal restraint stiffnesses of the supports. After correction, the elastic modulus of hollow slab increases by about 19.13%, the elastic modulus of cast-in-situ layer increases by about 16.00%, the lateral restraint stiffness increases by about 46.21%, and the longitudinal restraint stiffness increases by about 72.72%. The static and dynamic characteristics of the modified finite element model are in good agreement with the measured responses, the errors of static responses are less than 4%, and the errors of dynamic responses are less than 3%. 7 tabs, 18 figs, 30 refs.
To overcome the local convergence and improve the corrective accuracy in the modified iterative optimization process of traditional finite element model, an updating method was proposed by combining the real coded genetic algorithm(RCGA) and measured data of static and dynamic characteristics. The quadrilateral isoparametric element theory and Newton iteration method were used to compile the macro command to realize the fast automatic loading of vehicle loads in the FEM. The objective function was constructed by the static and dynamic characteristics of the finite element model of the structure, the RCGA was taken as the optimization strategy, and the modification frame of the model was established by the MATLAB platform. Through the numerical simulation of a frame structure, the convergence efficiencies and updating results of the proposed optimization method and other methods were compared to verify the effectiveness of the proposed method. To determine the modified parameters, the Latin hypercube sampling method was used to analyze the parametric influence of finite element model on the dynamic responses of the bridge, and the proposed method was applied to modify the solid finite element model of a reconstructed hollow slab bridge. Analysis result shows that the zero order algorithm and the first order algorithm are depended on the sensibilities and correction ranges of the parameters. When the parameters have less sensitivities or the correction ranges are greater than 50%, the correction result of the model is erroneous. The RCGA is insensitive to the initial inputs, so the local convergence can be avoided. The main parameters to be corrected by the sensitivity analysis are the elastic modulus of hollow slab, the elastic modulus of cast-in-situ layer and the longitudinal and transversal restraint stiffnesses of the supports. After correction, the elastic modulus of hollow slab increases by about 19.13%, the elastic modulus of cast-in-situ layer increases by about 16.00%, the lateral restraint stiffness increases by about 46.21%, and the longitudinal restraint stiffness increases by about 72.72%. The static and dynamic characteristics of the modified finite element model are in good agreement with the measured responses, the errors of static responses are less than 4%, and the errors of dynamic responses are less than 3%. 7 tabs, 18 figs, 30 refs.
引文
[1] FRYBA L, PIRNER M.Load tests and modal analysis of bridges[J].Engineering Structures,2001,23(1):102-109.
[2] MOTTERSHEAD J E,FRISWELL M I.Model updating in structural dynamics:a survey[J].Journal of Sound and Vibration,1993,167(2):347-375.
[3] SANAYEI M,BELL E S,JAVDEKAR C N.Bridge deck finite element model updating using multi-response NDT data[C]//ASCE.Structures Congress 2005:Metropolis and Beyond.Reston:ASCE,2005:1-9.
[4] 魏来生.结构有限元动态模型修正方法综述[J].振动与冲击,1998,17(3):43-46.WEI Lai-sheng.A review on the updating methods of finite element model[J].Journal of Vibration and Shock,1998,17(3):43-46.(in Chinese)
[5] 田仲初,彭涛,陈政清.佛山东平大桥静动力分层次有限元模型修正研究[J].振动与冲击,2007,26(6):162-165.TIAN Zhong-chu,PENG Tao,CHEN Zheng-qing.Study on dynamic and static stratified finite element model updating for Foshan Dongping Bride[J].Journal of Vibration and Shock,2007,26(6):162-165.(in Chinese)
[6] 袁旭东,周晶,黄梅.基于静力位移及频率的结构损伤识别神经网络方法[J].哈尔滨工业大学学报,2005,37(4):488-490.YUAN Xu-dong,ZHOU Jing,HUANG Mei.A method of structural damage identification using neural networks based on static displacements and natural frequencies[J].Journal of Harbin Institute of Technology,2005,37(4):488-490.(in Chinese)
[7] 宗周红,夏樟华.联合模态柔度和静力位移的桥梁有限元模型修正方法[J].中国公路学报,2008,21(6):43-49.ZONG Zhou-hong,XIA Zhang-hua.Finite element model updating method of bridge combined modal flexibility and static displacement[J].China Journal of Highway and Transport,2008,21(6):43-49.(in Chinese)
[8] 韩万水,王涛,李永庆,等.基于模型修正梁格法的车桥耦合振动分析系统[J].中国公路学报,2011,24(5):47-55.HAN Wan-shui,WANG Tao,LI Yong-qing,et al.Analysis system of vehicle-bridge coupling vibration with grillage method based on model updating[J].China Journal of Highway and Transport,2011,24(5):47-55.(in Chinese)
[9] 郑惠强,陈鹏程,宓为建,等.大型桥吊结构动力有限元模型修正[J].同济大学学报,2001,29(12):1412-1415.ZHENG Hui-qiang,CHEN Peng-cheng,MI Wei-jian,et al.Dynamic model updating of the port crane[J].Journal of Tongji University,2001,29(12):1412-1415.(in Chinese)
[10] 韩建平,骆勇鹏,郑沛娟,等.基于响应面的刚构-连续组合梁桥有限元模型修正[J].工程力学,2013,30(12):85-90,106.HAN Jian-ping,LUO Yong-peng,ZHENG Pei-juan,et al.Finite element model updating for a rigid frame-continuous girders bridge based on response surface method[J].Engineering Mechanics,2013,30(12):85-90,106.(in Chinese)
[11] 邓苗毅,任伟新,王复明.基于静力响应面的结构有限元模型修正方法[J].实验力学,2008,23(2):103-109.DENG Miao-yi,REN Wei-xin,WANG Fu-ming.Structure finite element model (FEM) updating based on static-load response surface methodology[J].Journal of Experimental Mechanics,2008,23(2):103-109.(in Chinese)
[12] 单德山,孙松松,黄珍,等.基于试验数据的吊拉组合模型桥梁有限元模型修正[J].土木工程学报,2014,47(10):88-95.SHAN De-shan,SUN Song-song,HUANG Zhen,et al.Finite element model updating of combined cable-stayed suspension model bridge based on experimental data[J].China Civil Engineering Journal,2014,47(10):88-95.(in Chinese)
[13] 李永庆.基于模型修正的梁格法车桥耦合振动程序开发和验证[D].西安:长安大学,2010.LI Yong-qing.Program development and validation of vehicle-bridge coupling vibration with grillage method based on finite element model updating[D].Xi'an:Chang'an University,2010.(in Chinese)
[14] 韩万水,王涛,李永庆,等.大跨钢桁架悬索桥有限元模型实用修正方法[J].交通运输工程学报,2011,11(5):18-27.HAN Wan-shui,WANG Tao,LI Yong-qing,et al.Practical updating method of finite element model for long span steel truss suspension bridge[J].Journal of Traffic and Transportation Engineering,2011,11(5):18-27.(in Chinese)
[15] 孟庆伟.基于一阶优化算法的钢管混凝土拱桥有限元模型修正[D].西安:长安大学,2016.MENG Qing-wei.Finite element model updating of concrete filled steel tube arch bridge based on first order optimization algorithm[D].Xi'an:Chang'an University,2016.(in Chinese)
[16] 谢伟平,曹晓宇,肖伯强,等.基于模态测试的宽幅钢箱梁桥有限元模型建立、修正与分析[J].振动与冲击,2018,37(1):98-105.XIE Wei-ping,CAO Xiao-yu,XIAO Bo-qiang,et al.Finite element modelling,modification and analysis for wide steel box-girder bridges,based on modal tests[J].Journal of Vibration and Shock,2018,37(1):98-105.(in Chinese)
[17] 万华平,任伟新,魏锦辉.基于高斯过程响应面的结构有限元模型修正方法[J].振动与冲击,2012,31(24):82-87.WAN Hua-ping,REN Wei-xin,WEI Jin-hui.Structural finite element model updating based on Gaussian process response surface methodology[J].Journal of Vibration and Shock,2012,31(24):82-87.(in Chinese)
[18] WAN Hua-ping,REN Wei-xin.Parameter selection in finite-element-model updating by global sensitivity analysis using Gaussian process metamodel[J].Journal of Structural Engineering,2014,141(6):04014164-1-11.
[19] 张建新.基于贝叶斯方法的有限元模型修正研究[D].重庆:重庆大学,2014.ZHANG Jian-xin.Research on the modification of finite element model based on Bayesian method[D].Chongqing:Chongqing University,2014.(in Chinese)
[20] DENG Lu,CAI Chun-sheng.Bridge model updating using response surface method[C]//ASCE.Earth and Space 2010:Engineering,Science,Construction,and Operations in Challenging Environments.Reston:ASCE,2010:2311-2320.
[21] RIBEIRO D,CAL?ADA R,DELGADO R,et al.Finite element model updating of a bowstring-arch railway bridge based on experimental modal parameters[J].Engineering Structures,2012,40:413-435.
[22] BREHM M,ZABEL V,BUCHER C.An automatic mode pairing strategy using an enhanced modal assurance criterion based on modal strain energies[J].Journal of Sound and Vibration,2010,329(25):5375-5392.
[23] 易晓山,任钧国,周建平.一种精确积分的四边形四结点等参单元[J].国防科技大学学报,1998,20(1):1-4.YI Xiao-shan,REN Jun-guo,ZHOU Jian-ping.An accurately integrated 4-node quadrilateral element[J].Journal of National University of Defense Technology,1998,20(1):1-4.(in Chinese)
[24] 雷学敏.非线性方程迭代算法的收敛球研究及其分形表示[D].杭州:浙江大学,2009.LEI Xue-min.The convergence ball and fractal image of iterative algorithms for solving nonlinear equations[D].Hangzhou:Zhejiang University,2009.(in Chinese)
[25] KWAK N S,LEE J.An enhancement of selection and crossover operations in real-coded genetic algorithm for large-dimensionality optimization[J].Journal of Mechanical Science and Technology,2016,30(1):237-247.
[26] 任伟新,陈华斌.基于响应面的桥梁有限元模型修正[J].土木工程学报,2008,41(12):73-78.REN Wei-xin,CHEN Hua-bin.Response-surface based finite element model updating of bridge structures[J].China Civil Engineering Journal,2008,41(12):73-78.(in Chinese)
[27] 方志,张国刚,唐盛华,等.混凝土斜拉桥动力有限元建模与模型修正[J].中国公路学报,2013,26(3):77-85.FANG Zhi,ZHANG Guo-gang,TANG Sheng-hua,et al.Finite element modeling and model updating of concrete cable-stayed bridge[J].China Journal of Highway and Transport,2013,26(3):77-85.(in Chinese)
[28] FANG Sheng-en,REN Wei-xin,PEREARA R.A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation[J].Mechanical Systems and Signal Processing,2012,33:83-96.
[29] HELTON J C,JOHNSON J D,SALLABERRY C J,et al.Survey of sampling-based methods for uncertainty and sensitivity analysis[J].Reliability Engineering and System Safety,2006,91(10/11):1175-1209.
[30] KALA Z.Sensitivity assessment of steel members under compression[J].Engineering Structures,2009,31(6):1344-1348.
[2] MOTTERSHEAD J E,FRISWELL M I.Model updating in structural dynamics:a survey[J].Journal of Sound and Vibration,1993,167(2):347-375.
[3] SANAYEI M,BELL E S,JAVDEKAR C N.Bridge deck finite element model updating using multi-response NDT data[C]//ASCE.Structures Congress 2005:Metropolis and Beyond.Reston:ASCE,2005:1-9.
[4] 魏来生.结构有限元动态模型修正方法综述[J].振动与冲击,1998,17(3):43-46.WEI Lai-sheng.A review on the updating methods of finite element model[J].Journal of Vibration and Shock,1998,17(3):43-46.(in Chinese)
[5] 田仲初,彭涛,陈政清.佛山东平大桥静动力分层次有限元模型修正研究[J].振动与冲击,2007,26(6):162-165.TIAN Zhong-chu,PENG Tao,CHEN Zheng-qing.Study on dynamic and static stratified finite element model updating for Foshan Dongping Bride[J].Journal of Vibration and Shock,2007,26(6):162-165.(in Chinese)
[6] 袁旭东,周晶,黄梅.基于静力位移及频率的结构损伤识别神经网络方法[J].哈尔滨工业大学学报,2005,37(4):488-490.YUAN Xu-dong,ZHOU Jing,HUANG Mei.A method of structural damage identification using neural networks based on static displacements and natural frequencies[J].Journal of Harbin Institute of Technology,2005,37(4):488-490.(in Chinese)
[7] 宗周红,夏樟华.联合模态柔度和静力位移的桥梁有限元模型修正方法[J].中国公路学报,2008,21(6):43-49.ZONG Zhou-hong,XIA Zhang-hua.Finite element model updating method of bridge combined modal flexibility and static displacement[J].China Journal of Highway and Transport,2008,21(6):43-49.(in Chinese)
[8] 韩万水,王涛,李永庆,等.基于模型修正梁格法的车桥耦合振动分析系统[J].中国公路学报,2011,24(5):47-55.HAN Wan-shui,WANG Tao,LI Yong-qing,et al.Analysis system of vehicle-bridge coupling vibration with grillage method based on model updating[J].China Journal of Highway and Transport,2011,24(5):47-55.(in Chinese)
[9] 郑惠强,陈鹏程,宓为建,等.大型桥吊结构动力有限元模型修正[J].同济大学学报,2001,29(12):1412-1415.ZHENG Hui-qiang,CHEN Peng-cheng,MI Wei-jian,et al.Dynamic model updating of the port crane[J].Journal of Tongji University,2001,29(12):1412-1415.(in Chinese)
[10] 韩建平,骆勇鹏,郑沛娟,等.基于响应面的刚构-连续组合梁桥有限元模型修正[J].工程力学,2013,30(12):85-90,106.HAN Jian-ping,LUO Yong-peng,ZHENG Pei-juan,et al.Finite element model updating for a rigid frame-continuous girders bridge based on response surface method[J].Engineering Mechanics,2013,30(12):85-90,106.(in Chinese)
[11] 邓苗毅,任伟新,王复明.基于静力响应面的结构有限元模型修正方法[J].实验力学,2008,23(2):103-109.DENG Miao-yi,REN Wei-xin,WANG Fu-ming.Structure finite element model (FEM) updating based on static-load response surface methodology[J].Journal of Experimental Mechanics,2008,23(2):103-109.(in Chinese)
[12] 单德山,孙松松,黄珍,等.基于试验数据的吊拉组合模型桥梁有限元模型修正[J].土木工程学报,2014,47(10):88-95.SHAN De-shan,SUN Song-song,HUANG Zhen,et al.Finite element model updating of combined cable-stayed suspension model bridge based on experimental data[J].China Civil Engineering Journal,2014,47(10):88-95.(in Chinese)
[13] 李永庆.基于模型修正的梁格法车桥耦合振动程序开发和验证[D].西安:长安大学,2010.LI Yong-qing.Program development and validation of vehicle-bridge coupling vibration with grillage method based on finite element model updating[D].Xi'an:Chang'an University,2010.(in Chinese)
[14] 韩万水,王涛,李永庆,等.大跨钢桁架悬索桥有限元模型实用修正方法[J].交通运输工程学报,2011,11(5):18-27.HAN Wan-shui,WANG Tao,LI Yong-qing,et al.Practical updating method of finite element model for long span steel truss suspension bridge[J].Journal of Traffic and Transportation Engineering,2011,11(5):18-27.(in Chinese)
[15] 孟庆伟.基于一阶优化算法的钢管混凝土拱桥有限元模型修正[D].西安:长安大学,2016.MENG Qing-wei.Finite element model updating of concrete filled steel tube arch bridge based on first order optimization algorithm[D].Xi'an:Chang'an University,2016.(in Chinese)
[16] 谢伟平,曹晓宇,肖伯强,等.基于模态测试的宽幅钢箱梁桥有限元模型建立、修正与分析[J].振动与冲击,2018,37(1):98-105.XIE Wei-ping,CAO Xiao-yu,XIAO Bo-qiang,et al.Finite element modelling,modification and analysis for wide steel box-girder bridges,based on modal tests[J].Journal of Vibration and Shock,2018,37(1):98-105.(in Chinese)
[17] 万华平,任伟新,魏锦辉.基于高斯过程响应面的结构有限元模型修正方法[J].振动与冲击,2012,31(24):82-87.WAN Hua-ping,REN Wei-xin,WEI Jin-hui.Structural finite element model updating based on Gaussian process response surface methodology[J].Journal of Vibration and Shock,2012,31(24):82-87.(in Chinese)
[18] WAN Hua-ping,REN Wei-xin.Parameter selection in finite-element-model updating by global sensitivity analysis using Gaussian process metamodel[J].Journal of Structural Engineering,2014,141(6):04014164-1-11.
[19] 张建新.基于贝叶斯方法的有限元模型修正研究[D].重庆:重庆大学,2014.ZHANG Jian-xin.Research on the modification of finite element model based on Bayesian method[D].Chongqing:Chongqing University,2014.(in Chinese)
[20] DENG Lu,CAI Chun-sheng.Bridge model updating using response surface method[C]//ASCE.Earth and Space 2010:Engineering,Science,Construction,and Operations in Challenging Environments.Reston:ASCE,2010:2311-2320.
[21] RIBEIRO D,CAL?ADA R,DELGADO R,et al.Finite element model updating of a bowstring-arch railway bridge based on experimental modal parameters[J].Engineering Structures,2012,40:413-435.
[22] BREHM M,ZABEL V,BUCHER C.An automatic mode pairing strategy using an enhanced modal assurance criterion based on modal strain energies[J].Journal of Sound and Vibration,2010,329(25):5375-5392.
[23] 易晓山,任钧国,周建平.一种精确积分的四边形四结点等参单元[J].国防科技大学学报,1998,20(1):1-4.YI Xiao-shan,REN Jun-guo,ZHOU Jian-ping.An accurately integrated 4-node quadrilateral element[J].Journal of National University of Defense Technology,1998,20(1):1-4.(in Chinese)
[24] 雷学敏.非线性方程迭代算法的收敛球研究及其分形表示[D].杭州:浙江大学,2009.LEI Xue-min.The convergence ball and fractal image of iterative algorithms for solving nonlinear equations[D].Hangzhou:Zhejiang University,2009.(in Chinese)
[25] KWAK N S,LEE J.An enhancement of selection and crossover operations in real-coded genetic algorithm for large-dimensionality optimization[J].Journal of Mechanical Science and Technology,2016,30(1):237-247.
[26] 任伟新,陈华斌.基于响应面的桥梁有限元模型修正[J].土木工程学报,2008,41(12):73-78.REN Wei-xin,CHEN Hua-bin.Response-surface based finite element model updating of bridge structures[J].China Civil Engineering Journal,2008,41(12):73-78.(in Chinese)
[27] 方志,张国刚,唐盛华,等.混凝土斜拉桥动力有限元建模与模型修正[J].中国公路学报,2013,26(3):77-85.FANG Zhi,ZHANG Guo-gang,TANG Sheng-hua,et al.Finite element modeling and model updating of concrete cable-stayed bridge[J].China Journal of Highway and Transport,2013,26(3):77-85.(in Chinese)
[28] FANG Sheng-en,REN Wei-xin,PEREARA R.A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation[J].Mechanical Systems and Signal Processing,2012,33:83-96.
[29] HELTON J C,JOHNSON J D,SALLABERRY C J,et al.Survey of sampling-based methods for uncertainty and sensitivity analysis[J].Reliability Engineering and System Safety,2006,91(10/11):1175-1209.
[30] KALA Z.Sensitivity assessment of steel members under compression[J].Engineering Structures,2009,31(6):1344-1348.
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