两种AR模型模拟空间相关性风场的比较
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摘要
风场模拟中广泛应用的AR模型主要有标量过程的AR模型和向量过程的AR模型.通过取数学期望的方法,可以得到标量过程AR模型模拟空间相关性风场所采用的参数,但该参数并未考虑时滞的情况.向量过程AR模型建立在联合平稳的假设之上,可以很好地综合考虑各点的空间相关性,且回归系数矩阵包含时滞的影响,可以考虑较长时间范围内各点风速时程的时间相关性,从理论来说,要相对完善一些.本文算例表明,向量过程AR模型所模拟的风场精确度总体上要高于标量过程AR模型所模拟的风场,但也存在所模拟风场各点的自相关函数偏差大和总体运算时间多等缺点.
There are two kinds of AR models,i.e.scalar and vector process,applied into wind field simulation widely.In the case of AR model of scalar process,spatial correlation parameter of AR model for simulating wind field is derived from mathematic exception and time-lag is not considered in the parameter of AR model of scalar process.While in the case of AR model of vector process,various points' space correlation is considered well because hypothesis of jointly stationary random processes is adopted,and its regressive parameter matrix includes effects of time-lag.Therefore,from the theoretical point of view,AR model of vector process is perfect.Numerical examples show that the more accuracy of the wind field simulated by AR model of vector process can be obtained,while there are few shortcomings in this model,e.g.bigger error for auto-correlation and more running time.
There are two kinds of AR models,i.e.scalar and vector process,applied into wind field simulation widely.In the case of AR model of scalar process,spatial correlation parameter of AR model for simulating wind field is derived from mathematic exception and time-lag is not considered in the parameter of AR model of scalar process.While in the case of AR model of vector process,various points' space correlation is considered well because hypothesis of jointly stationary random processes is adopted,and its regressive parameter matrix includes effects of time-lag.Therefore,from the theoretical point of view,AR model of vector process is perfect.Numerical examples show that the more accuracy of the wind field simulated by AR model of vector process can be obtained,while there are few shortcomings in this model,e.g.bigger error for auto-correlation and more running time.
引文
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[3]曾宪武,韩大建.大跨度桥梁模拟方法对比研究[J].地震工程与工程振动,2004,24(1):135-140.ZENG Xian-wu,HAN Da-jian.Acomparative study onsi mulation methods for wind field of long-span bridges[J].Earthquake Engineering and Engineering Vibra-tion,2004,24(1):135-140.
[4]赵臣,张小刚,吕伟平.具有空间相关性风场的计算机模拟[J].空间结构,1996,2(2):21-25.ZHAO Chen,ZHANG Xiao-gang,LU Wei-ping.Com-puter modeling on wind histories with spatial correlativi-ty[J].Spatial Structures,1996,2(2):21-25.
[5]董军,邓洪洲,刘学利.高层建筑脉动风荷载时程模拟的AR模型方法[J].南京建筑工程学院学报,2000,(2):20-25.DONGJun,DENG Hong-zhou,LI U Xue-li.AR modelmethod for ti me-historyi mitation of pulse windload act-ing on high-rise buildings[J].Journal of Nanjing Archi-tectural and Civil Engineering Institute,2000,(2):20-25.
[6]黄国辉,徐国彬.基于数值模拟法的张力膜结构风振响应分析[J].空间结构,2005,11(3):56-59.HUANG Guo-hui,XU Guo-bin.Analysis of wind-in-duced response of tensile membrane structure based ondigital si mulation method[J].Spatial Structures,2005,11(3):56-59.
[7]李元齐,董石麟.大跨度空间结构风荷载模拟技术研究及程序编制[J].空间结构,2001,7(3):3-11.LI Yuan-qi,DONG Shi-lin.Random wind load si mula-tion and computer programfor large-span spatial struc-tures[J].Spatial Structures,2001,7(3):3-11.
[8]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):27-32.SHU Xin-ling,ZHOU Dai.AR model of wind speedti me series and its rapid i mplementation[J].SpatialStructures,2003,9(4):27-32.
[9]黄本才.结构抗风分析原理及应用[M].上海:同济大学出版社,2001.
[10]胡广书.数字信号处理理论、算法与实现(第二版)[M].北京:清华大学出版社,2003.
[11]张文福,马昌恒.基于小波分析的一点处脉动风速时程模拟[J].空气动力学学报,2008,26(4):425-429.ZHANG Wen-fu,MA Chang-heng.One point s fluctu-ating wind velocity ti me history si mulation based onwavelet analysis method[J].Acta Aerodynamica Sini-ca,2008,26(4):425-429.
[12]沈世钊,徐崇宝,赵臣.悬索结构设计[M].北京:中国建筑工业出版社,1997.
[13]潘士先.谱估计与自适应滤波[M].北京:航空航天大学出版社,1991.
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