基于多目标优化的磁浮轨道梁有限元模型修正
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摘要
基于精细有限元建模与多目标优化算法,建立一种适用于具有复杂附属结构的磁浮轨道梁有限元模型修正方法。以一座典型的磁浮连续轨道梁桥为研究对象,建立其精细初始有限元模型;在灵敏度分析的基础上选择待修正参数,利用模态频率和振型等结构实测动力响应构造修正目标函数;采用带精英策略的快速非支配排序遗传算法(NSGA-Ⅱ)对多目标优化问题进行求解,得到其Pareto最优解集。研究结果表明:模型修正后结构的模态频率和振型计算值与实测值吻合良好,修正后的有限元模型能够精确全面地模拟实际结构,且能确保设计参数合理且具有明确物理意义。
Based on the fine finite element modeling and multi-objective optimization algorithm, a method for finite element model updating was proposed to get the baseline finite element model of maglev track beams with complex auxiliary structures. Taking a typical maglev continuous track beam bridge as the research object, a fine initial finite element model was established. Based on sensitivity analysis, we choose the parameters to be corrected, and used the measured dynamic responses of modal frequencies and mode shapes to construct the modified objective function. The multi-objective optimization problem was solved by NSGA-Ⅱ algorithm. Thus, the Pareto optimal set of multi-objective optimization problem with finite element model updating was obtained. The results show that the modal frequency and the calculated value of the model are in good agreement with the measured values. The modified finite element model can accurately and comprehensively simulate the actual structure, and it can ensure that the design parameters are reasonable and have clear physical meaning.
Based on the fine finite element modeling and multi-objective optimization algorithm, a method for finite element model updating was proposed to get the baseline finite element model of maglev track beams with complex auxiliary structures. Taking a typical maglev continuous track beam bridge as the research object, a fine initial finite element model was established. Based on sensitivity analysis, we choose the parameters to be corrected, and used the measured dynamic responses of modal frequencies and mode shapes to construct the modified objective function. The multi-objective optimization problem was solved by NSGA-Ⅱ algorithm. Thus, the Pareto optimal set of multi-objective optimization problem with finite element model updating was obtained. The results show that the modal frequency and the calculated value of the model are in good agreement with the measured values. The modified finite element model can accurately and comprehensively simulate the actual structure, and it can ensure that the design parameters are reasonable and have clear physical meaning.
引文
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[2]SHAN Deshan,LI Qiao,Inamullah Khan,et al.A novel finite element model updating method based on substructure and response surface model[J].Engineering Structures,2015,103:147-156.
[3]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 Zhouhong,XIA Zhanghua.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.
[4]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 Guogang,TANG Shenghua,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.
[5]REN W X,CHEN H B.Finite element model updating in structural dynamics by using the response surface method[J].Engineering Structures,2010,32(8):2455-2465.
[6]钟儒勉,樊星辰,黄学漾,等.基于两阶段响应面方法的结合梁斜拉桥多尺度有限元模型修正[J].东南大学学报(自然科学版),2013,43(5):993-999.ZHONG Rumian,FAN Xingchen,HUANG Xueyang,et al.Multi-scale finite element model updating of composite cable-stayed bridge based on two-phase response surface methods[J].Journal of Southeast University(Natural Science Edition),2013,43(5):993-999.
[7]周林仁,欧进萍.斜拉桥结构模型修正的子结构方法[J].振动与冲击,2014,33(19):52-58.ZHOU Linren,OU Jinping.A substructure method for structural model upating of long span cable stayed bridges[J].Journal of Vibration and Shock,2014,33(19):52-58.
[8]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 Junliang,YAN Quansheng,ZHENG Hengbin,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.
[9]郁胜,周林仁,欧进萍.基于径向基函数响应面方法的超大跨悬索桥有限元模型修正[J].铁道科学与工程学报,2014,11(1):1-9.YU Sheng,ZHOU Linren,OU Jingping.Finite element model updating of large suspension bridge based on radial basis function response surface[J].Journal of Railway Science and Engineering,2014,11(1):1-9.
[10]骆勇鹏,黄方林,廖明皓,等.基于逐步回归分析的既有铁路钢桁桥有限元模型修正[J].铁道科学与工程学报,2015,12(5):1111-1115.LUO Yongpeng,HUANG Fanglin,LIAO Minghao,et al.Existing railway steel truss bridge finite element model updating based on stepwise regression[J].Journal of Railway Science and Engineering,2015,12(5):1111-1115.
[11]何涛,张巍,吴植安.基于动静载试验数据的预应力混凝土梁模型修正方法试验研究[J].公路交通科技,2015,32(12):75-80.HE Tao,ZHANG Wei,WU Zhian.Experimental research on model updating method of prestressed concrete girder based on dynamic and static loading test data[J].Journal of Highway and Transportation Research and Development,2015,32(12):75-80.
[12]邬晓光,刘英,冯宇,等.基于动态系数的静动力有限元模型修正研究[J].铁道科学与工程学报,2017,14(3):543-551.WU Xiaoguang,LIU Ying,FENG Yu,et al.Research on static and dynamics finite element model updating method based on dynamic coefficient[J].Journal of Railway Science and Engineering,2017,14(3):543-551.
[13]肖晓伟,肖迪,林锦国,等.多目标优化问题的研究概述[J].计算机应用研究,2011,28(3):805-808.XIAO Xiaowei,XIAO Di,LIN Jinguo,et al.Overview on multi-objective optimization problem research[J].Application Research of Computers,2011,28(3):805-808.
[14]Kalyanmoy Deb,Shivam Gupta.Understanding knee points in bicriteria problems and their implications as preferred solution principles[J].Engineering Optimization,2011,43(11):1175-1204.
[15]Deb K,Pratap A,Agarwal S,et al.A fast and elitist multiobjective genetic algorithm:NSGA-II[J].IEEETransactions on Evolutionary Computation,2002,6(2):182-197.
[16]卢小亭.多目标优化遗传算法选择方法的研究与改进[D].淮南:安徽理工大学,2008.LU Xiaoting.The research and improvement on selection method of multi-objective optimization genetic algorithms[D].Huainan:Anhui University of Science&Technology,2008.