基于多维AR模型的风速时程模拟
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摘要
目的生成空间多点的顺风向风速时程,比较不同阶AR模型的模拟效果,评价由BIC准则判定的AR模型最优阶数的合理性.方法根据工程中普遍采用的顺风向脉动风速谱,利用MATLAB软件编制空间多点风速时程的自回归线性模型程序,并嵌入BIC准则以判定多维AR模型的最优阶数,使用不同阶模型对风场进行模拟并比较各阶模型的模拟效果.结果通过对西堠门大桥风场的模拟发现,BIC准则判定得到的AR模型最优阶数为2阶,同时2阶模型取得了不错的模拟效果;不同阶模型的模拟效果有较大差异,1阶模型离散性较大,6阶、8阶模型模拟精度稍好,4阶模型模拟效果最好.结论 BIC准则判定得到的AR模型最优阶数偏低,但根据其最优阶数进行的模拟也可取得不错的模拟效果;模型阶数对模拟效果有很大影响,阶数过低将导致结果离散性较大,阶数过高并不一定取得更高的模拟精度,选择合理的模型阶数既可取得最优的模拟效果又可节省计算时间.
Wind velocity time-history is simulated using multidimensional auto regressive model,where velocities are correlated in accordance with the Kaimal power spectrum.In order to determine the optimal order of the model,BIC criterion is utilized.The multidimensional AR model is programmed by MATLAB in which BIC criterion is embedded.Simulation performed on the wind field of Xihoumen bridge shows that the optimal order of AR model is 2,and the 2nd order model performs effectively by comparing the simulated power spectrum with the target one.Models of different orders have different performance:1st order model has larger discreteness than others;6th and 8th order models perform better than 1st and 2nd order models in low frequency region;4th order model performs best among all models.These results indicate that the optimal order determined by BIC criterion is lower than the actual one.Different order models can lead to much different results.When order is too low,the discreteness will be high.When order is too high,it can′t obtain higher accuracy but just waste time.An appropriate order of AR model is important to get the best result.
Wind velocity time-history is simulated using multidimensional auto regressive model,where velocities are correlated in accordance with the Kaimal power spectrum.In order to determine the optimal order of the model,BIC criterion is utilized.The multidimensional AR model is programmed by MATLAB in which BIC criterion is embedded.Simulation performed on the wind field of Xihoumen bridge shows that the optimal order of AR model is 2,and the 2nd order model performs effectively by comparing the simulated power spectrum with the target one.Models of different orders have different performance:1st order model has larger discreteness than others;6th and 8th order models perform better than 1st and 2nd order models in low frequency region;4th order model performs best among all models.These results indicate that the optimal order determined by BIC criterion is lower than the actual one.Different order models can lead to much different results.When order is too low,the discreteness will be high.When order is too high,it can′t obtain higher accuracy but just waste time.An appropriate order of AR model is important to get the best result.
引文
[1]Simiu E,Scanlan R H.Wind effects on structures:Anintroduction to w ind engineering[M].3rd ed.NewYork:Wiley,1996.
[2]舒新玲,周岱,王泳芳.风荷载测试与模拟技术的回顾及展望[J].振动与冲击,2002,21(3):6-10.(Shu Xinling,Zhou Dai,Wang Yongfang.Reviewand prospect on measurement and simulation tech-niques of w ind load[J].Journal of Vibration andShock,2002,21(3):6-10.)
[3]曾宪武,韩大建.大跨度桥梁风场模拟方法对比研究[J].地震工程与工程振动,2004,24(1):135-140.(Zeng Xianwu,Han Dajian.A comparative study ofsimulation methods for w ind field of long-spanbridges[J].Earthquake Engineering and EngineeringVibration,2004,24(1):135-140.)
[4]赵建飞,谢步瀛.大跨度桥梁风荷载模拟及程序编制[J].结构工程师,2006,22(2):42-49.(Zhao Jianfei,Xie Buying.The simulation of sto-chastic w ind loading on long-span bridges and devel-opment of the program[J].Structure Engineers,2006,22(2):42-49.)
[5]胡雪莲,李正良,晏致涛.大跨度桥梁结构风荷载模拟研究[J].重庆建筑大学学报,2005,27(3):63-67.(Hu Xuelian,Li Zhengliang,Yan Zhitao.Simulationof w ind loading for large-span bridge structures[J].Journal of Chongqing Jianzhu University,2005,27(3):63-67.)
[6]Iwatani Y.Simulation of multidimensional wind fluc-tuations having any arbitrary pow er spectra and crossspectra[J].Journal of Wind Engineering,1982,(11):5-18.
[7]王修琼,崔剑峰.Davenport谱中系数K的计算公式及其工程应用[J].同济大学学报,2002,30(7):849-852.(Wang Xiuqiong,Cui Jianfeng.Formula of coeffi-cient K in expression of Davenport spectrum and itsengineering application[J].Journal of Tongji Uni-versity,2002,30(7):849-852.)
[8]王浩,李爱群,谢以顺,等.基于实测风谱的润扬悬索桥桥址区三维脉动风场模拟[J].东南大学学报:自然科学版,2009,39(6):1206-1211.(Wang Hao,Li Aiqun,Xie Yishun,et al.Digitalsimulation of 3-dimensional turbulence w ind field ofRunyang Suspension Bridge based on measured w indspectra[J].Journal of Southeast University:NaturalScience,2009,39(6):1206-1211.)
[9]何迎晖,钱伟民.随机过程简明教程[M].上海:同济大学出版社,2004.(He Yinghui,Qian Weimin.A concise course in sto-chastic processes[M].Shanghai:Tongji UniversityPress,2004.)
[10]潘红宇.时间序列分析[M].北京:对外经济贸易大学出版社,2005.(Pan Hongyu.Time series analysis[M].Beijing:U-niversity of International Business and EconomicsPress,2005.)
[11]包龙生,刘克同,于玲,等.大跨度桥梁空间脉动风场的数值模拟[J].沈阳建筑大学学报:自然科学版,2010,26(2):238-243.(Bao Longsheng,Liu Ketong,Yu Ling,et al.Nu-merical simulation of spatial fluctuating w ind field onlong-span bridges[J].Journal of Shenyang JianzhuUniversity:Natural Science,2010,26(2):238-243.)
[12]舒新玲,周岱.风速时程AR模型及其快速实现[J].空间结构,2003,9(4):27-46.(Shu Xinling,Zhou Dai.AR model of wind speedtime series and its rapid implementation[J].SpatialStructures,2003,9(4):27-46.)
[13]阎石,郑伟.简谐波叠加法模拟风谱[J].沈阳建筑大学学报:自然科学版,2005,21(1):1-4.(Yan Shi,Zheng Wei.Wind load simulation by su-perposition of harmonic[J].Journal of ShenyangJianzhu University:Natural Science,2005,21(1):1-4.)
[14]刘锡良,周颖.风荷载的几种模拟方法[J].工业建筑,2005,35(5):81-84.(Liu Xiliang,Zhou Ying.Numerical simulationmethods of w ind load[J].Industrial Construction,2005,35(4):81-84.)
[15]曹丰产,葛耀君.浙江省舟山大陆连岛工程西堠门大桥:侧风行车安全及其控制措施研究[R].上海:同济大学土木工程防灾国家重点实验室,2009.(Cao Fengchan,Ge Yaojun.Xihoumen Bridge ofZhoushan island-land project of Zhejiang Province-Crossw ind driving safety and control measures[R].Shanghai:State Key Laboratory for disaster reductionin civil engineering of Tongji University,2009.)
[16]袁波,应惠清,徐佳炜.基于线性滤波法的脉动风速模拟及其MATLAB程序的实现[J].结构工程师,2007,23(4):55-61.(Yuan Bo,Ying Huiqing,Xu Jiawei.Simulation ofturbulent w ind velocity based on linear filter methodand MATLAB program realization[J].StructuralEngineers,2007,23(4):55-61.)
[2]舒新玲,周岱,王泳芳.风荷载测试与模拟技术的回顾及展望[J].振动与冲击,2002,21(3):6-10.(Shu Xinling,Zhou Dai,Wang Yongfang.Reviewand prospect on measurement and simulation tech-niques of w ind load[J].Journal of Vibration andShock,2002,21(3):6-10.)
[3]曾宪武,韩大建.大跨度桥梁风场模拟方法对比研究[J].地震工程与工程振动,2004,24(1):135-140.(Zeng Xianwu,Han Dajian.A comparative study ofsimulation methods for w ind field of long-spanbridges[J].Earthquake Engineering and EngineeringVibration,2004,24(1):135-140.)
[4]赵建飞,谢步瀛.大跨度桥梁风荷载模拟及程序编制[J].结构工程师,2006,22(2):42-49.(Zhao Jianfei,Xie Buying.The simulation of sto-chastic w ind loading on long-span bridges and devel-opment of the program[J].Structure Engineers,2006,22(2):42-49.)
[5]胡雪莲,李正良,晏致涛.大跨度桥梁结构风荷载模拟研究[J].重庆建筑大学学报,2005,27(3):63-67.(Hu Xuelian,Li Zhengliang,Yan Zhitao.Simulationof w ind loading for large-span bridge structures[J].Journal of Chongqing Jianzhu University,2005,27(3):63-67.)
[6]Iwatani Y.Simulation of multidimensional wind fluc-tuations having any arbitrary pow er spectra and crossspectra[J].Journal of Wind Engineering,1982,(11):5-18.
[7]王修琼,崔剑峰.Davenport谱中系数K的计算公式及其工程应用[J].同济大学学报,2002,30(7):849-852.(Wang Xiuqiong,Cui Jianfeng.Formula of coeffi-cient K in expression of Davenport spectrum and itsengineering application[J].Journal of Tongji Uni-versity,2002,30(7):849-852.)
[8]王浩,李爱群,谢以顺,等.基于实测风谱的润扬悬索桥桥址区三维脉动风场模拟[J].东南大学学报:自然科学版,2009,39(6):1206-1211.(Wang Hao,Li Aiqun,Xie Yishun,et al.Digitalsimulation of 3-dimensional turbulence w ind field ofRunyang Suspension Bridge based on measured w indspectra[J].Journal of Southeast University:NaturalScience,2009,39(6):1206-1211.)
[9]何迎晖,钱伟民.随机过程简明教程[M].上海:同济大学出版社,2004.(He Yinghui,Qian Weimin.A concise course in sto-chastic processes[M].Shanghai:Tongji UniversityPress,2004.)
[10]潘红宇.时间序列分析[M].北京:对外经济贸易大学出版社,2005.(Pan Hongyu.Time series analysis[M].Beijing:U-niversity of International Business and EconomicsPress,2005.)
[11]包龙生,刘克同,于玲,等.大跨度桥梁空间脉动风场的数值模拟[J].沈阳建筑大学学报:自然科学版,2010,26(2):238-243.(Bao Longsheng,Liu Ketong,Yu Ling,et al.Nu-merical simulation of spatial fluctuating w ind field onlong-span bridges[J].Journal of Shenyang JianzhuUniversity:Natural Science,2010,26(2):238-243.)
[12]舒新玲,周岱.风速时程AR模型及其快速实现[J].空间结构,2003,9(4):27-46.(Shu Xinling,Zhou Dai.AR model of wind speedtime series and its rapid implementation[J].SpatialStructures,2003,9(4):27-46.)
[13]阎石,郑伟.简谐波叠加法模拟风谱[J].沈阳建筑大学学报:自然科学版,2005,21(1):1-4.(Yan Shi,Zheng Wei.Wind load simulation by su-perposition of harmonic[J].Journal of ShenyangJianzhu University:Natural Science,2005,21(1):1-4.)
[14]刘锡良,周颖.风荷载的几种模拟方法[J].工业建筑,2005,35(5):81-84.(Liu Xiliang,Zhou Ying.Numerical simulationmethods of w ind load[J].Industrial Construction,2005,35(4):81-84.)
[15]曹丰产,葛耀君.浙江省舟山大陆连岛工程西堠门大桥:侧风行车安全及其控制措施研究[R].上海:同济大学土木工程防灾国家重点实验室,2009.(Cao Fengchan,Ge Yaojun.Xihoumen Bridge ofZhoushan island-land project of Zhejiang Province-Crossw ind driving safety and control measures[R].Shanghai:State Key Laboratory for disaster reductionin civil engineering of Tongji University,2009.)
[16]袁波,应惠清,徐佳炜.基于线性滤波法的脉动风速模拟及其MATLAB程序的实现[J].结构工程师,2007,23(4):55-61.(Yuan Bo,Ying Huiqing,Xu Jiawei.Simulation ofturbulent w ind velocity based on linear filter methodand MATLAB program realization[J].StructuralEngineers,2007,23(4):55-61.)
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