基于二阶泰勒级数展开和风驱动优化算法的结构有限元模型修正
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摘要
为得到结构响应与修正参数之间的函数关系、简化参数迭代过程,通过推导结构响应关于修正参数的一阶与二阶泰勒级数展开,并选用具有寻优效率高、全局搜索能力强的风驱动优化算法,建立了基于二阶泰勒级数展开和风驱动优化算法的结构有限元模型修正方法。同时,为求解响应关于修正参数的二阶泰勒级数展开,采用差分法近似求得响应关于修正参数的一阶和二阶偏导数。利用该方法对算例模型进行了修正,并对比了一阶和二阶泰勒级数展开的修正效果。结果表明:二阶泰勒级数展开的修正效果明显优于一阶泰勒级数展开,增加二阶偏导数项可以更好地反映响应与修正参数之间的函数关系。基于该方法,采用实桥的静动力测试数据对青林湾大桥的有限元模型进行了修正,修正后的有限元模型能够较好地反映大桥的实际状况。
In the updating of finite element model(FEM), in order to obtain the functional relationship between structural responses and updating parameters, and to simplify the process of parameter iteration, this paper proposes an updating method for FEM which adopts second-order Taylor expansions and wind driven optimization. This method was developed through deriving first-order and second-order Taylor expansions of structural responses of updating parameters and selecting a wind driven optimization algorithm with high searching efficiency and global searching ability. In addition, to obtain the second-order Taylor expansions of structural responses of update parameters, the difference method was used to get approximate first-order and second-order partial derivatives. Then, a numerical example was updated using this FEM updating method and the updating effects of first-order Taylor expansions and second-order Taylor expansions were compared. It was found that the updating effects of second-order Taylor expansions is obviously superior to those of the first-order Taylor expansions, and that increasing the number of second-order partial derivative terms can better express the functional relationship between structural responses and updating parameters. Lastly, based on the proposed method and the static and dynamic field measurement data of an actual bridge, the FEM of Qinglin Bay bridge was updated, and it can be concluded that the actual structural responses of the bridge can be better simulated and reflected by the updated FEM.
In the updating of finite element model(FEM), in order to obtain the functional relationship between structural responses and updating parameters, and to simplify the process of parameter iteration, this paper proposes an updating method for FEM which adopts second-order Taylor expansions and wind driven optimization. This method was developed through deriving first-order and second-order Taylor expansions of structural responses of updating parameters and selecting a wind driven optimization algorithm with high searching efficiency and global searching ability. In addition, to obtain the second-order Taylor expansions of structural responses of update parameters, the difference method was used to get approximate first-order and second-order partial derivatives. Then, a numerical example was updated using this FEM updating method and the updating effects of first-order Taylor expansions and second-order Taylor expansions were compared. It was found that the updating effects of second-order Taylor expansions is obviously superior to those of the first-order Taylor expansions, and that increasing the number of second-order partial derivative terms can better express the functional relationship between structural responses and updating parameters. Lastly, based on the proposed method and the static and dynamic field measurement data of an actual bridge, the FEM of Qinglin Bay bridge was updated, and it can be concluded that the actual structural responses of the bridge can be better simulated and reflected by the updated FEM.
引文
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[5] 郭彤, 李爱群, 费庆国. 零阶与一阶优化算法在悬索桥模型修正中的应用对比分析[J]. 振动与冲击, 2007, 26(4): 35-38.(GUO Tong, LI Aiqun, FEI Qingguo. Application comparison between zero-order and first-order optimization methods in model updating of suspension bridges[J]. Journal of Vibration and Shock, 2007, 26(4): 35-38. (in Chinese))
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[7] BAYRAKTAR A, ALTUNISIK A C, SEVIM B. Finite element model updating of K?mürhan highway bridge based on experimental measurements[J]. Smart Structures and Systems, 2010, 6(4): 373-388.
[8] SMITH M J, HUTTON S G. Frequency modification using Newton’s method and inverse iteration eigenvector updating[J]. AIAA Journal, 1992, 30(7): 1886-1891.
[9] 刘纲, 黄宗明, 杨溥. 一种基于动态序列二次规划的模型修正方法[J]. 重庆大学学报, 2008, 31(1): 106-109.(LIU Gang, HUANG Zongming, YANG Pu. Method of modal updating based on nonlinear optimization[J]. Journal of Chongqing University, 2008, 31(1): 106-109. (in Chinese))
[10] ZIKRI B, MUGE K, DOUGLAS H W. Wind driven optimization (WDO): a novel nature-inspired optimization algorithm and its application to electromagnetics[C]// IEEE Antennas & Propagation Society International Symposium. Toronto: IEEE, 2010: 1- 4.
[11] ZIKRI B, MUGE K. Stub-loaded inverted-F antenna synthesis via wind driven optimization[C]// IEEE International Symposium on Antennas & Propagation.[s.l.]:IEEE, 2011: 2920-2913.
[12] ZIKRI B, MUGE K, JEREMY A B, DOUGLAS H W. The wind driven optimization technique and its application in electromagnetics[J]. IEEE Transaction on Antennas & Propagation,2013,61(5):2745-2757.
[13] 同济大学应用数学系. 高等数学(上)[M]. 6版. 上海: 同济大学出版社, 2007:140.(Department of Mathematics. Higher mathematics(1)[M]. 6th ed. Shanghai: Tongji University Press,2007:140.(in Chinese))
[14] NAGARAJ Y, MADIPALLI P, RAJAN J, et al. Segmentation of intima media complex from carotid ultrasound images using wind driven optimization technique[J]. Biomedical Signal Processing and Control, 2018,40: 462- 472.
[15] PANDEY A, PARHI D R. Optimum path planning of mobile robot in unknown static and dynamic environments using fuzzy-wind driven optimization algorithm[J]. Defence Technology,2017,13(1):47-58.
[16] 陈彬彬, 曹中清, 余胜威. 基于风驱动优化算法WDO的PID参数优化[J]. 计算机工程与应用, 2016, 52(14):250-253.
[17] GHOSH T K. DAS S. Efficient job scheduling in computational grid systems using wind driven optimization technique[J]. International Journal of Applied Metaheuristic Computing, 2018,9(1):49-59.
[2] 张德文. 模型修正与破损诊断[M]. 北京: 科学出版社, 1999:1- 4.(ZHANG Dewen. Model updating and damage detection[M]. Beijing: Science Press, 1999:1- 4.(in Chinese))
[3] ZAPICO J L, GONZALEZ M P, FRISWELL M I. Finite element model updating of a small scale bridge[J]. Journal of Sound and Vibration, 2003, 268(5): 993-1012.
[4] 方志, 唐盛华, 张国刚. 基于多状态下静动态测试数据的斜拉桥模型修正[J]. 中国公路学报, 2011, 24(1): 34- 41.(FANG Zhi, TANG Shenghua, ZHANG Guogang. Cable-stayed bridge model updating based on static and dynamic test data of multi-state[J]. China Journal of Highway and Transport, 2011, 24(1): 34- 41. (in Chinese))
[5] 郭彤, 李爱群, 费庆国. 零阶与一阶优化算法在悬索桥模型修正中的应用对比分析[J]. 振动与冲击, 2007, 26(4): 35-38.(GUO Tong, LI Aiqun, FEI Qingguo. Application comparison between zero-order and first-order optimization methods in model updating of suspension bridges[J]. Journal of Vibration and Shock, 2007, 26(4): 35-38. (in Chinese))
[6] 韩万水, 王涛, 李永庆. 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 Wanshui, WANG Tao, LI Yongqing. 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))
[7] BAYRAKTAR A, ALTUNISIK A C, SEVIM B. Finite element model updating of K?mürhan highway bridge based on experimental measurements[J]. Smart Structures and Systems, 2010, 6(4): 373-388.
[8] SMITH M J, HUTTON S G. Frequency modification using Newton’s method and inverse iteration eigenvector updating[J]. AIAA Journal, 1992, 30(7): 1886-1891.
[9] 刘纲, 黄宗明, 杨溥. 一种基于动态序列二次规划的模型修正方法[J]. 重庆大学学报, 2008, 31(1): 106-109.(LIU Gang, HUANG Zongming, YANG Pu. Method of modal updating based on nonlinear optimization[J]. Journal of Chongqing University, 2008, 31(1): 106-109. (in Chinese))
[10] ZIKRI B, MUGE K, DOUGLAS H W. Wind driven optimization (WDO): a novel nature-inspired optimization algorithm and its application to electromagnetics[C]// IEEE Antennas & Propagation Society International Symposium. Toronto: IEEE, 2010: 1- 4.
[11] ZIKRI B, MUGE K. Stub-loaded inverted-F antenna synthesis via wind driven optimization[C]// IEEE International Symposium on Antennas & Propagation.[s.l.]:IEEE, 2011: 2920-2913.
[12] ZIKRI B, MUGE K, JEREMY A B, DOUGLAS H W. The wind driven optimization technique and its application in electromagnetics[J]. IEEE Transaction on Antennas & Propagation,2013,61(5):2745-2757.
[13] 同济大学应用数学系. 高等数学(上)[M]. 6版. 上海: 同济大学出版社, 2007:140.(Department of Mathematics. Higher mathematics(1)[M]. 6th ed. Shanghai: Tongji University Press,2007:140.(in Chinese))
[14] NAGARAJ Y, MADIPALLI P, RAJAN J, et al. Segmentation of intima media complex from carotid ultrasound images using wind driven optimization technique[J]. Biomedical Signal Processing and Control, 2018,40: 462- 472.
[15] PANDEY A, PARHI D R. Optimum path planning of mobile robot in unknown static and dynamic environments using fuzzy-wind driven optimization algorithm[J]. Defence Technology,2017,13(1):47-58.
[16] 陈彬彬, 曹中清, 余胜威. 基于风驱动优化算法WDO的PID参数优化[J]. 计算机工程与应用, 2016, 52(14):250-253.
[17] GHOSH T K. DAS S. Efficient job scheduling in computational grid systems using wind driven optimization technique[J]. International Journal of Applied Metaheuristic Computing, 2018,9(1):49-59.
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