超高层建筑风压场的重构与预测
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摘要
本征正交分解(POD)是以能量表述的随机场最优分解,是一种数据压缩和特征萃取的工具。本文分别运用Mercer定理、瑞利商概念及其极值性质推导了POD原理。并利用POD分解技术,仅采用前若干阶本征模态对超高层建筑表面的风压场进行了重建,对重建结果及规律进行了分析。
根据风洞试验同步测量的风压数据,利用POD技术对超高层未布置测压点位置的风压时间序列进行了预测。文中分别采用曲面插值、反距离插值、B样条插值、三次样条插值及双线性插值五种方法得到预测点位置上的本征模态值。结合由原风压场协方差分析得到的主坐标和上述新本征模态值,获得未布置测压点位置的风压时间序列。通过在时间域和频率域内五种插值方法预测出的风压与实测风压的比较,得出三次样条插值的预测精度最高,稳定性最好,曲面插值预测效果次之,同时也说明了利用POD技术预测超高层建筑表面风压场是有效的。
最后,应用归一化POD技术对原始风压场进行了进一步的细化,把脉动风压时间序列分解为方差和归一化后的时间序列。在风压场的预测中,每种插值方法对方差和归一化后的时间序列影响不同,应用归一化POD技术可选择不同的插值方法分别预测,克服了局部风压预测不准确的缺点,提高了预测精度。
The Proper Orthogonal Decomposition (POD) is an optimal decomposition of random fields in terms of an energy representation. It is a tool for data compression and characteristic analysis of extractable. the principle of POD is deduced separately by the Mercer theorem and the concept of Rayleigh quotient and its extreme property in this article. Based on the Proper Orthogonal Decomposition, the surface of high-rise building wind pressure field is reconstructed with only a number of eigen modes , Analysis and summarization is also made to law of the reconstruction.
Combined with simultaneous measurement wind pressure data of wind tunnel tests, the POD technique has been used to predict the wind pressure time series on the high-rise building where the pressure taps are not distributed. Surface interpolation, inverse distance interpolation, B-spline interpolation, cubic spline interpolation and bilinear interpolation five methods are employed to obtain the values of the proper modes on high-rise building where wind pressure time series are to be predicted. using the principal coordinates from the covariance analysis of the original pressure field and the new proper mode values, the wind pressure time series on the high-rise building without the pressure taps are acquired. In the time domain and frequency domain comparison of prediction by five interpolation methods with the measured wind pressure, we can see that the result of the cubic spline interpolation is the highest prediction accuracy and stability of the best, followed by surface interpolation prediction, also that the POD in the prediction of the surface wind field .on high-rise building is effective.
Finally, Application of normalized POD technology , the original field pressure is further refined, The fluctuating wind pressure time series is decomposed into variance and normalized the time series, In the prediction of wind pressure field, the each interpolation method has different impact in two parts, with the help of normalized POD technology, the best interpolation method is choose to predict each part, that overcomes the disadvantage of inaccurate in partial pressure prediction and improves prediction accuracy.
根据风洞试验同步测量的风压数据,利用POD技术对超高层未布置测压点位置的风压时间序列进行了预测。文中分别采用曲面插值、反距离插值、B样条插值、三次样条插值及双线性插值五种方法得到预测点位置上的本征模态值。结合由原风压场协方差分析得到的主坐标和上述新本征模态值,获得未布置测压点位置的风压时间序列。通过在时间域和频率域内五种插值方法预测出的风压与实测风压的比较,得出三次样条插值的预测精度最高,稳定性最好,曲面插值预测效果次之,同时也说明了利用POD技术预测超高层建筑表面风压场是有效的。
最后,应用归一化POD技术对原始风压场进行了进一步的细化,把脉动风压时间序列分解为方差和归一化后的时间序列。在风压场的预测中,每种插值方法对方差和归一化后的时间序列影响不同,应用归一化POD技术可选择不同的插值方法分别预测,克服了局部风压预测不准确的缺点,提高了预测精度。
The Proper Orthogonal Decomposition (POD) is an optimal decomposition of random fields in terms of an energy representation. It is a tool for data compression and characteristic analysis of extractable. the principle of POD is deduced separately by the Mercer theorem and the concept of Rayleigh quotient and its extreme property in this article. Based on the Proper Orthogonal Decomposition, the surface of high-rise building wind pressure field is reconstructed with only a number of eigen modes , Analysis and summarization is also made to law of the reconstruction.
Combined with simultaneous measurement wind pressure data of wind tunnel tests, the POD technique has been used to predict the wind pressure time series on the high-rise building where the pressure taps are not distributed. Surface interpolation, inverse distance interpolation, B-spline interpolation, cubic spline interpolation and bilinear interpolation five methods are employed to obtain the values of the proper modes on high-rise building where wind pressure time series are to be predicted. using the principal coordinates from the covariance analysis of the original pressure field and the new proper mode values, the wind pressure time series on the high-rise building without the pressure taps are acquired. In the time domain and frequency domain comparison of prediction by five interpolation methods with the measured wind pressure, we can see that the result of the cubic spline interpolation is the highest prediction accuracy and stability of the best, followed by surface interpolation prediction, also that the POD in the prediction of the surface wind field .on high-rise building is effective.
Finally, Application of normalized POD technology , the original field pressure is further refined, The fluctuating wind pressure time series is decomposed into variance and normalized the time series, In the prediction of wind pressure field, the each interpolation method has different impact in two parts, with the help of normalized POD technology, the best interpolation method is choose to predict each part, that overcomes the disadvantage of inaccurate in partial pressure prediction and improves prediction accuracy.
引文
[1]黄本才.结构抗风分析原理及应用.第一版.上海.同济大学出版社.2001.8-13
[2]Holmes J.D.Wind Loading of Structures.London.Spon Press 2001
[3]张相庭.结构风工程.上海.中国建筑工业出版社.2005
[4]GB50009-2001.建筑结构荷载规范.北京.中国建筑工业出版社.2002
[5]Davenport A.G.The spectrum of horizontal gustiness near the ground in high winds.J.Royal Meteorol.Soc.1961.87.194-211
[6]Simid E.,Scanlan.R.H.著,刘尚培,项海帆等译.风对结构的作用-风工程导论.上海.同济大学出版社.1998
[7]Kaimal J.Cl.Spectral characteristics of surface layer turbulence.J.Royal Meteorol.Soc.1972.98.563-589
[8]Architectural Institute of Japan.AIJ Recommendations for loads on Building.1996
[9]张相庭.结构风压和风振计算.上海.同济大学出版社.1985
[10]上海科技情报研究所.国外高层建筑抗风译文集.上海科技文献出版社.1979
[11]M.Shiotani,H.Avai.International Conference on the Wind Effect on Buildings and Structures,Vol.1 1967
[12]全涌 顾明.典型超高层建筑气动弹性模型的风洞试验研究.工程力学.1999(2)882-888
[13]张亮亮 吴云芳 余洋 李正良.高层建筑风荷载高频测力天平试验技术.重庆大学学报(自然科学版).2006 29(2)99-102
[14]倪振华 姚伟军 谢壮宁.高层建筑风致振动研究的瞬态风压积分法.振动工程学报.200013(4)544-549
[15]Clarence Rowley W,Jerrold Marsden E.Reconstruction equations and the Karhunen-Loeve expansion for systems with symmetry[J].Physica D.2000 142:1.19
[16]Cheri Y Z.Time series simulation of wind-induced pressures on low buildings[D].Chapter 7-London,Ontario,Canada,Dept of Civil and Environmental Engineering,The University of Western Ontario,2002
[17]Armitt J.Eigenvector analysis of pressure fluctuations on the West Burton instrumented cooling tower,Central Electricity Research(UK),Internal Report RD/L/N 114/68 1968
[18]Tamura Y,Suganuma S.Proper orthogonal decomposition of random wind pressure field[J].Journal of Fluids and Structures 1999,13:1069-1095
[19]Bienkiewicz B,Tamura Y,Ham H J,Ueda H,Hibi K.Proper orthogonal decomposition and reconstruction of multi-channel roof pressure[J].J.Wind Eng.Ind.Aerodyne.1995,54-55: 369-381
[20]Jeong S H,Bienkiewicz B,Ham J H.Proper orthogonal decomposition of building wind pressure specified at non-uniformly distributed pressure Taps[J].Wind Eng.Ind.Aerodyn.2000,87,1:14.
[21]肖智勇.本征正交分解(POD)方法在高层建筑风荷载及其动态响应中的应用研究.硕士学位论文.汕头.汕头大学.2001
[22]Best R.J,Holmes J D.Use of eigenvalues in the Covariance integration method for determination of wind load effects.Journal of Wind Engineering and Industrial Aerodunamics (1983) 13,359-370.
[23]J.d.Holmes.R Sankaran,Eigenvector modes of fluctuating pressures on low-rise building model.Journal of Wind Engineering and Industrial Aerodynamics(1997) 64-71.697-707
[24]Kikuchi,H.,Tamura,Y.,Ueda,K.Hibi,K.Dynamic wind pressure acting on a tall building model Proper Orthogonal Decomposition,Journal of Wind Engineering and Industrial Aerodunamies(1997)69-71,531-646.
[25]李小康.POD方法中的协方差模态截断准则与方差补偿技术.硕士学位论文。汕头.汕头大学.2007
[26]王志坤.块Lanczos法及其在大跨屋盖风致响应分析中的应用.硕士学位论文.汕头.汕头大学.2007
[27]Chen Y,Kopp G.A,Surry D.Spatial extrapolation of pressure time series on low building using proper orthogonal decomposition.Journal of Wind and Structure(2004) 7(6),373-342.
[28]周福.双坡屋盖风压场的重建和预测.硕士学位论文.汕头.汕头大学.2005
[29]江悼荣.POD技术以及在屋盖风压场中的应用,硕士学位论文.汕头.汕头大学.2006
[30]夏法宝.武汉国际证券大厦风洞试验研究.硕士学位论文.2004
[31]李方慧 倪振华 谢壮宁.POD方法在重建双坡屋盖风压场中的应用.工程力学(2005)22增刊.177-182
[32]李元齐 沈祖炎.本征正交分解法在曲面模型风场重构中的应用.同济大学学报(自然科学版).2006 34(1)22-26
[33]Clarance R W,Jerrold ME.Reconstruction equations and the Karhunen-Loeve expansion for systems with symmetry[J].Physica D,2000,142:1-19.
[34]Cizmas P C,Palacios A,Brien T O,Syamlal M.Proper-orthogonal decomposition of spatio-temporal patterns in fluidized beds[J].Chemical Engineering Science,2003,584417-4427
[35]Loeve M.Probability Theory[M],fourth Edition,Chapter Ⅺ:Second Order Properties,37,5Orthogonal decomposition,Springer-Verlag New York Inc.1978.
[36]刘杰 乐嘉海.二次曲面在空间插位中的应用及程序实现.[J].水运工程.2002,8;12-13
[37]潘日晶.满足数据点切向约束的二次B样条插值曲线.[J].计算机学报,2007 30(12)2132-2141
[38]韩旭里 庄陈坚 刘新儒.基于径向基函数与B样条的散乱数据拟合方法.[J].计算技术与自动化.2007 26(1)63-65,69
[39]李新 程国栋 卢玲.空间内插方法比较.[J].地球科学进展.2000 15(3)261-264
[40]彭楠峰.距离反比插值算法与Kriging插值算法的比较.[J].大众科技.2008(5)57-58
[41]Husar R B,Falke S R.Uncertainty in the spatial interpolation of PM 10 monitoring data in Southern California,1997-03-03/1999-10-25.
[42]许小勇 钟太勇.三次样条插值函数的构造与Matlab实现.兵工自动化.2006 25(11)76-78
[43]冯慧君 陶素娟 李隆.基于双线性插值算法的图像放缩技术与实现。计算机应用与软件.2004 21(7)117-119
[2]Holmes J.D.Wind Loading of Structures.London.Spon Press 2001
[3]张相庭.结构风工程.上海.中国建筑工业出版社.2005
[4]GB50009-2001.建筑结构荷载规范.北京.中国建筑工业出版社.2002
[5]Davenport A.G.The spectrum of horizontal gustiness near the ground in high winds.J.Royal Meteorol.Soc.1961.87.194-211
[6]Simid E.,Scanlan.R.H.著,刘尚培,项海帆等译.风对结构的作用-风工程导论.上海.同济大学出版社.1998
[7]Kaimal J.Cl.Spectral characteristics of surface layer turbulence.J.Royal Meteorol.Soc.1972.98.563-589
[8]Architectural Institute of Japan.AIJ Recommendations for loads on Building.1996
[9]张相庭.结构风压和风振计算.上海.同济大学出版社.1985
[10]上海科技情报研究所.国外高层建筑抗风译文集.上海科技文献出版社.1979
[11]M.Shiotani,H.Avai.International Conference on the Wind Effect on Buildings and Structures,Vol.1 1967
[12]全涌 顾明.典型超高层建筑气动弹性模型的风洞试验研究.工程力学.1999(2)882-888
[13]张亮亮 吴云芳 余洋 李正良.高层建筑风荷载高频测力天平试验技术.重庆大学学报(自然科学版).2006 29(2)99-102
[14]倪振华 姚伟军 谢壮宁.高层建筑风致振动研究的瞬态风压积分法.振动工程学报.200013(4)544-549
[15]Clarence Rowley W,Jerrold Marsden E.Reconstruction equations and the Karhunen-Loeve expansion for systems with symmetry[J].Physica D.2000 142:1.19
[16]Cheri Y Z.Time series simulation of wind-induced pressures on low buildings[D].Chapter 7-London,Ontario,Canada,Dept of Civil and Environmental Engineering,The University of Western Ontario,2002
[17]Armitt J.Eigenvector analysis of pressure fluctuations on the West Burton instrumented cooling tower,Central Electricity Research(UK),Internal Report RD/L/N 114/68 1968
[18]Tamura Y,Suganuma S.Proper orthogonal decomposition of random wind pressure field[J].Journal of Fluids and Structures 1999,13:1069-1095
[19]Bienkiewicz B,Tamura Y,Ham H J,Ueda H,Hibi K.Proper orthogonal decomposition and reconstruction of multi-channel roof pressure[J].J.Wind Eng.Ind.Aerodyne.1995,54-55: 369-381
[20]Jeong S H,Bienkiewicz B,Ham J H.Proper orthogonal decomposition of building wind pressure specified at non-uniformly distributed pressure Taps[J].Wind Eng.Ind.Aerodyn.2000,87,1:14.
[21]肖智勇.本征正交分解(POD)方法在高层建筑风荷载及其动态响应中的应用研究.硕士学位论文.汕头.汕头大学.2001
[22]Best R.J,Holmes J D.Use of eigenvalues in the Covariance integration method for determination of wind load effects.Journal of Wind Engineering and Industrial Aerodunamics (1983) 13,359-370.
[23]J.d.Holmes.R Sankaran,Eigenvector modes of fluctuating pressures on low-rise building model.Journal of Wind Engineering and Industrial Aerodynamics(1997) 64-71.697-707
[24]Kikuchi,H.,Tamura,Y.,Ueda,K.Hibi,K.Dynamic wind pressure acting on a tall building model Proper Orthogonal Decomposition,Journal of Wind Engineering and Industrial Aerodunamies(1997)69-71,531-646.
[25]李小康.POD方法中的协方差模态截断准则与方差补偿技术.硕士学位论文。汕头.汕头大学.2007
[26]王志坤.块Lanczos法及其在大跨屋盖风致响应分析中的应用.硕士学位论文.汕头.汕头大学.2007
[27]Chen Y,Kopp G.A,Surry D.Spatial extrapolation of pressure time series on low building using proper orthogonal decomposition.Journal of Wind and Structure(2004) 7(6),373-342.
[28]周福.双坡屋盖风压场的重建和预测.硕士学位论文.汕头.汕头大学.2005
[29]江悼荣.POD技术以及在屋盖风压场中的应用,硕士学位论文.汕头.汕头大学.2006
[30]夏法宝.武汉国际证券大厦风洞试验研究.硕士学位论文.2004
[31]李方慧 倪振华 谢壮宁.POD方法在重建双坡屋盖风压场中的应用.工程力学(2005)22增刊.177-182
[32]李元齐 沈祖炎.本征正交分解法在曲面模型风场重构中的应用.同济大学学报(自然科学版).2006 34(1)22-26
[33]Clarance R W,Jerrold ME.Reconstruction equations and the Karhunen-Loeve expansion for systems with symmetry[J].Physica D,2000,142:1-19.
[34]Cizmas P C,Palacios A,Brien T O,Syamlal M.Proper-orthogonal decomposition of spatio-temporal patterns in fluidized beds[J].Chemical Engineering Science,2003,584417-4427
[35]Loeve M.Probability Theory[M],fourth Edition,Chapter Ⅺ:Second Order Properties,37,5Orthogonal decomposition,Springer-Verlag New York Inc.1978.
[36]刘杰 乐嘉海.二次曲面在空间插位中的应用及程序实现.[J].水运工程.2002,8;12-13
[37]潘日晶.满足数据点切向约束的二次B样条插值曲线.[J].计算机学报,2007 30(12)2132-2141
[38]韩旭里 庄陈坚 刘新儒.基于径向基函数与B样条的散乱数据拟合方法.[J].计算技术与自动化.2007 26(1)63-65,69
[39]李新 程国栋 卢玲.空间内插方法比较.[J].地球科学进展.2000 15(3)261-264
[40]彭楠峰.距离反比插值算法与Kriging插值算法的比较.[J].大众科技.2008(5)57-58
[41]Husar R B,Falke S R.Uncertainty in the spatial interpolation of PM 10 monitoring data in Southern California,1997-03-03/1999-10-25.
[42]许小勇 钟太勇.三次样条插值函数的构造与Matlab实现.兵工自动化.2006 25(11)76-78
[43]冯慧君 陶素娟 李隆.基于双线性插值算法的图像放缩技术与实现。计算机应用与软件.2004 21(7)117-119