基于试验数据的大跨度拱桥有限元模型修正
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摘要
为了获取菜园坝长江大桥的基准有限元模型,结合Kriging代理模型和一种改进的粒子群优化算法,利用荷载试验数据对其初始有限元模型进行修正。首先,叙述模型修正和Kriging模型基本理论,在基本粒子群算法中引入交叉变异计算,提出一种改进的粒子群算法,并通过测试函数对改进的粒子群算法进行验证;其次,简要介绍菜园坝长江大桥荷载试验、荷载试验结果及初始有限元模型;最后,根据敏感性分析选定6个待修正参数,通过试验设计得到频率和位移关于修正的参数的样本,并建立有限元模型的Kriging代理模型以预测结构响应;以频率和位移的试验值和计算值残差为目标函数,分别利用基本粒子群算法和改进的粒子群算法在修正参数的设计空间内寻找目标函数的最小值,并对比分析模型修正的结果。结果表明:测试函数表明改进的粒子群算法具有较好的稳定性和成功率,并能获得更为精确的优化结果;建立的Kriging代理模型均方根误差较小,可以替代有限元模型预测结构频率和位移;经过模型修正,菜园坝长江大桥前5阶频率计算值与试验值相对误差均控制在5%之内;除个别测点外,位移相对误差均控制在10%以内;相比基本粒子群算法,改进的粒子群算法获得了更小的目标函数值,修正后的频率和位移的相对误差更小。
In order to develop the baseline finite element model of the Caiyuanba Yangtze River Bridge, model updating based on data obtained from load tests using the Kriging model and an improved particle swarm optimization(IPSO) technique was implemented. First, the fundamental theory of model updating and the Kriging model were summarized. Then, an IPSO technique was proposed by introducing crossover and mutation operations in the standard particle swarm optimization(PSO) technique. The proposed IPSO was verified by two test functions. Then, the load test of Caiyuanba Yangtze River bridge, the test results and the initial finite element model are briefly presented. Finally, six updating parameters were chosen based on the sensitive analysis. The data samples of the chosen updating parameters and the corresponding frequency/displacement responses were obtained through design experiments. The Kriging model was established using the data samples, and it served as a surrogate for the finite element model in predicting the analytical responses. The objective function was constructed using the error functions between the experimental and analytical values of frequencies and displacements. The PSO and IPSO were employed to search the design space for updating parameters to minimize the objective function. The updating results of PSO and IPSO were analyzed and compared. The results indicate that the IPSO has higher stability and success rate, as shown by test functions. The updated Kriging model shows very small mean squared errors, and hence can be used as a surrogate for the finite element model in predicting the analytical responses. It was observed that the first five frequencies of the bridge are closer to the experimental values after model updating. The relative errors of frequencies are all under 5%. Except in an isolated case, the relative errors of displacements are approximately 10% after model updating. Hence, compared to PSO, the proposed IPSO can achieve a smaller objective function value, and the relative errors of frequencies/displacements are also smaller.
In order to develop the baseline finite element model of the Caiyuanba Yangtze River Bridge, model updating based on data obtained from load tests using the Kriging model and an improved particle swarm optimization(IPSO) technique was implemented. First, the fundamental theory of model updating and the Kriging model were summarized. Then, an IPSO technique was proposed by introducing crossover and mutation operations in the standard particle swarm optimization(PSO) technique. The proposed IPSO was verified by two test functions. Then, the load test of Caiyuanba Yangtze River bridge, the test results and the initial finite element model are briefly presented. Finally, six updating parameters were chosen based on the sensitive analysis. The data samples of the chosen updating parameters and the corresponding frequency/displacement responses were obtained through design experiments. The Kriging model was established using the data samples, and it served as a surrogate for the finite element model in predicting the analytical responses. The objective function was constructed using the error functions between the experimental and analytical values of frequencies and displacements. The PSO and IPSO were employed to search the design space for updating parameters to minimize the objective function. The updating results of PSO and IPSO were analyzed and compared. The results indicate that the IPSO has higher stability and success rate, as shown by test functions. The updated Kriging model shows very small mean squared errors, and hence can be used as a surrogate for the finite element model in predicting the analytical responses. It was observed that the first five frequencies of the bridge are closer to the experimental values after model updating. The relative errors of frequencies are all under 5%. Except in an isolated case, the relative errors of displacements are approximately 10% after model updating. Hence, compared to PSO, the proposed IPSO can achieve a smaller objective function value, and the relative errors of frequencies/displacements are also smaller.
引文
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[9] 周林仁,欧进萍.基于径向基函数响应面方法的大跨度斜拉桥有限元模型修正[J].中国铁道科学,2012,33(3):8-15 ZHOU Lin-ren,OU Jin-ping.Finite Element Model Updating of Long-span Cable-stayed Bridge Based on the Response Surface Method of Radial Basis Function [J].China Railway Science,2012,33 (3):8-15.
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[11] DENG L,CAI C S.Bridge Model Updating Using Response Surface Method and Genetic Algorithm [J].Journal of Bridge Engineering,2010,15 (5):553-564.
[12] 胡俊亮,颜全胜,郑恒斌,等.基于Kriging模型的钢管混凝土连续梁拱桥有限元模型修正[J].振动与冲击.2014,33(14):33-39.HU Jun-liang,YAN Quan-sheng,ZHENG Heng-bin,et al.CFST Arch/Continuous Beam Bridge FEM Model Updating Based on Kriging Model [J].Journal of Vibration and Shock,2014,33 (14):33-39.
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[14] BROWNJOHN J,XIA P,HAO H,et al.Civil Structure Condition Assessment by FE Model Updating:Methodology and Case Studies [J].Finite Elements in Analysis and Design,2001,37 (10):761-775.
[15] ?IVANOVI■.Finite Element Modelling and Updating of a Lively Footbridge:The Complete Process [J].Journal of Sound and Vibration,2007,301 (1):126-145.
[16] SHABBIR F,OMENZETTER P.Particle Swarm Optimization with Sequential Niche Technique for Dynamic Finite Element Model Updating [J].Computer-aided Civil and Infrastructure Engineering,2015,30 (5):359-375.
[17] LI J,ZHANG X,XING J,et al.Optimal Sensor Placement for Long-span Cable-stayed Bridge Using a Novel Particle Swarm Optimization Algorithm [J].Journal of Civil Structural Health Monitoring,2015,5 (5):677-685.
[18] CHEN Z,CAO H,YE K,et al.Improved Particle Swarm Optimization-based Form-finding Method for Suspension Bridge Installation Analysis [J].Journal of Computing in Civil Engineering,2015,29 (3):1-13.
[19] CAO H,QIAN X,ZHOU Y.Large-scale Structural Optimization Using Metaheuristic Algorithms with Elitism and a Filter Strategy [J].Structural and Multidisciplinary Optimization,2018,57 (2):799-814.
[20] XIONG W,LI M,CHENG Y.An Improved Particle Swarm Optimization Algorithm for Unit Commitment [J].International Journal of Electrical Power and Energy Systems,2008,28 (7):482-490.
[21] REYNDERS E,PINTELON R,DE ROECK G.Uncertainty Bounds on Modal Parameters Obtained from Stochastic Subspace Identification [J].Mechanical Systems and Signal Processing,2008,22 (4):948-969.
[22] WANG F,XU Y,SUN B,et al.Updating Multiscale Model of a Long-span Cable-stayed Bridge [J].Journal of Bridge Engineering,2018,23 (3):1-15.
[2] 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.
[3] 万华平,任伟新,黄天立.基于贝叶斯推理的随机模型修正方法[J].中国公路学报,2016,29(4):67-76.WAN Hua-ping,REN Wei-xin,HUANG Tian-li.Stochastic Model Updating Approach by Using Bayesian Inference [J].China Journal of Highway and Transport,2016,29 (4):67-76.
[4] JAISHI B,REN W.Finite Element Model Updating Based on Eigenvalue and Strain Energy Residuals Using Multi-objective Optimization Technique [J].Mechanical Systems and Signal Processing,2007,21 (5):2295-2317.
[5] MARWALA T.Finite-element-model Updating Using Computational Intelligence Techniques:Applications to Structural Dynamics [M].New York:Springer,2010.
[6] REN W,CHEN H.Finite Element Model Updating in Structural Dynamics by Using the Response Surface Method [J].Engineering Structures,2010,32 (8):2455-2465.
[7] 宗周红,高铭霖,夏樟华.基于健康监测的连续刚构桥有限元模型确认(Ⅰ)——基于响应面法的有限元模型修正[J].土木工程学报,2011,44(2):90-98.ZONG Zhou-hong,GAO Ming-lin,XIA Zhang-hua.Finite Element Model Validation of the Continuous Rigid Frame Bridge Based on Structural Health Monitoring Part I:FE Model Updating Based on the Response Surface Method [J].China Civil Engineering Journal,2011,44 (2):90-98.
[8] 宗周红,高铭霖,夏樟华.基于健康监测的连续刚构桥有限元模型确认(Ⅱ)——不确定性分析与模型精度评价[J].土木工程学报,2011,44(3):85-92.ZONG Zhou-hong,GAO Ming-lin,XIA Zhang-hua.Finite Element Model Validation of the Continuous Rigid Frame Bridge Based on Structural Health Monitoring Part Ⅱ:Uncertainty Analysis and Evaluation of Model Accuracy [J].China Civil Engineering Journal,2011,44 (3):85-92.
[9] 周林仁,欧进萍.基于径向基函数响应面方法的大跨度斜拉桥有限元模型修正[J].中国铁道科学,2012,33(3):8-15 ZHOU Lin-ren,OU Jin-ping.Finite Element Model Updating of Long-span Cable-stayed Bridge Based on the Response Surface Method of Radial Basis Function [J].China Railway Science,2012,33 (3):8-15.
[10] 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.
[11] DENG L,CAI C S.Bridge Model Updating Using Response Surface Method and Genetic Algorithm [J].Journal of Bridge Engineering,2010,15 (5):553-564.
[12] 胡俊亮,颜全胜,郑恒斌,等.基于Kriging模型的钢管混凝土连续梁拱桥有限元模型修正[J].振动与冲击.2014,33(14):33-39.HU Jun-liang,YAN Quan-sheng,ZHENG Heng-bin,et al.CFST Arch/Continuous Beam Bridge FEM Model Updating Based on Kriging Model [J].Journal of Vibration and Shock,2014,33 (14):33-39.
[13] LIU Y,WANG D,MA J,et al.Performance Comparison of Two Meta-model for the Application to Finite Element Model Updating of Structures [J].Journal of Harbin Institute of Technology (New Series),2014,21 (3):68-78.
[14] BROWNJOHN J,XIA P,HAO H,et al.Civil Structure Condition Assessment by FE Model Updating:Methodology and Case Studies [J].Finite Elements in Analysis and Design,2001,37 (10):761-775.
[15] ?IVANOVI■.Finite Element Modelling and Updating of a Lively Footbridge:The Complete Process [J].Journal of Sound and Vibration,2007,301 (1):126-145.
[16] SHABBIR F,OMENZETTER P.Particle Swarm Optimization with Sequential Niche Technique for Dynamic Finite Element Model Updating [J].Computer-aided Civil and Infrastructure Engineering,2015,30 (5):359-375.
[17] LI J,ZHANG X,XING J,et al.Optimal Sensor Placement for Long-span Cable-stayed Bridge Using a Novel Particle Swarm Optimization Algorithm [J].Journal of Civil Structural Health Monitoring,2015,5 (5):677-685.
[18] CHEN Z,CAO H,YE K,et al.Improved Particle Swarm Optimization-based Form-finding Method for Suspension Bridge Installation Analysis [J].Journal of Computing in Civil Engineering,2015,29 (3):1-13.
[19] CAO H,QIAN X,ZHOU Y.Large-scale Structural Optimization Using Metaheuristic Algorithms with Elitism and a Filter Strategy [J].Structural and Multidisciplinary Optimization,2018,57 (2):799-814.
[20] XIONG W,LI M,CHENG Y.An Improved Particle Swarm Optimization Algorithm for Unit Commitment [J].International Journal of Electrical Power and Energy Systems,2008,28 (7):482-490.
[21] REYNDERS E,PINTELON R,DE ROECK G.Uncertainty Bounds on Modal Parameters Obtained from Stochastic Subspace Identification [J].Mechanical Systems and Signal Processing,2008,22 (4):948-969.
[22] WANG F,XU Y,SUN B,et al.Updating Multiscale Model of a Long-span Cable-stayed Bridge [J].Journal of Bridge Engineering,2018,23 (3):1-15.