基于小波变换的非平稳脉动风时变功率谱估计方法研究
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摘要
为揭示非平稳随机脉动风的时频特性,基于小波变换原理推导了时变功率谱的时间、频率和幅值与小波变换系数的关系,建立了非平稳随机脉动风时变功率谱估计的小波函数加权和法,并采用模拟非平稳脉动风和实测台风过程对理论推导结果进行了验证。研究结果表明:非平稳随机过程在某一时刻的不同尺度小波变换系数是一个以此非平稳随机过程的调制函数与小波函数的乘积为调制函数的非平稳随机过程的傅里叶变换,非平稳随机过程的时变功率谱等于不同尺度和不同时移的小波函数模平方的加权和,小波函数加权和法计算的非平稳随机脉动风的时变功率谱与理论结果具有良好的一致性。小波函数加权和法可有效地估计非平稳随机脉动风的时变功率谱,估计的时变功率谱可为进一步理解强(台)风的随机脉动特性奠定基础。
To further understand the time-frequency characteristics of non-stationary fluctuating wind,the relationship between time,frequency and amplitude of the evolutionary power spectrum(EPS) and wavelet transform coefficients are analyzed based on the principle of wavelet transform.The weighted wavelet function method(WWFM) is proposed to estimate the EPS of non-stationary fluctuating wind.The theoretical results are demonstrated by a series of simulated non-stationary fluctuating wind and field measurement typhoon process.The study results show that the wavelet transformation coefficients under different scales of a certain non-stationary stochastic process at a certain time are the Fourier transform of a new non-stationary stochastic process and the modulating function of the new non-stationary stochastic process is the product of the modulating function of this certain non-stationary stochastic processes and the wavelet function.The EPS of non-stationary stochastic processes can be calculated by the sum of weighted square modulus of wavelet functions at different scales and different time parameters,and the weighted coefficients are defined by the wavelet transformation results.The EPS of simulated non-stationary stochastic wind estimated by the WWFM is accordant well to the analytical results.The WWFM can estimate the EPS of non-stationary fluctuating wind effectively and the computed EPS can aid to understand the randomness of fluctuate wind further more.
To further understand the time-frequency characteristics of non-stationary fluctuating wind,the relationship between time,frequency and amplitude of the evolutionary power spectrum(EPS) and wavelet transform coefficients are analyzed based on the principle of wavelet transform.The weighted wavelet function method(WWFM) is proposed to estimate the EPS of non-stationary fluctuating wind.The theoretical results are demonstrated by a series of simulated non-stationary fluctuating wind and field measurement typhoon process.The study results show that the wavelet transformation coefficients under different scales of a certain non-stationary stochastic process at a certain time are the Fourier transform of a new non-stationary stochastic process and the modulating function of the new non-stationary stochastic process is the product of the modulating function of this certain non-stationary stochastic processes and the wavelet function.The EPS of non-stationary stochastic processes can be calculated by the sum of weighted square modulus of wavelet functions at different scales and different time parameters,and the weighted coefficients are defined by the wavelet transformation results.The EPS of simulated non-stationary stochastic wind estimated by the WWFM is accordant well to the analytical results.The WWFM can estimate the EPS of non-stationary fluctuating wind effectively and the computed EPS can aid to understand the randomness of fluctuate wind further more.
引文
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[25]樊剑,刘铁,胡亮.基于现代时频分析技术的地震波时变谱估计[J].振动与冲击,2007,26(11):79―84.Fan Jian,Lin Tie,Hu Liang.Time-varying spectrumestimation of earthquake ground motion via moderntime-frequency analysis[J].Journal of Vibration andShock,2007,26(11):79―84.(in Chinese)
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[27]Shinozuka M,Yun C B.Stochastic methods in windengineering[J].Journal of Wind Engineering andIndustrial Aerodynamics,1990,36:829―843.
[2]陈政清.桥梁风工程[M].北京:人民交通出版社,2005:50―53.Chen Zhengqing.Bridge wind engineering[M].Beijing:China Communication Press,2005:50―53.(in Chinese)
[3]曹映泓,项海帆,周颖.大跨度桥梁随机风场的模拟[J].土木工程学报,1998,31(3):72―79.Cao Yinghong,Xiang Haifan,Zhou Ying.Simulation ofstochastic wind field on Long-Span Bridge[J].ChinaCivil Engineering Journal,1998,31(3):72―79.(inChinese)
[4]李永乐,周述华,强士中.大跨度斜拉桥三维脉动风场模拟[J].土木工程学报,2003,36(10):60―65.Li Yongle,Zhou Shuhua,Qiang Shizhong.Simulation ofthree-dimesional fluctuating wind field for large spancable-stayed bridge[J].China Civil Engineering Journal,2003,36(10):60―65.(in Chinese)
[5]丁泉顺,陈艾荣,项海帆.大跨度桥梁结构耦合抖振响应频域分析[J].土木工程学报,2003,36(4):86―93.Ding Quanshun,Chen Airong,Xiang Haifan.Responseof coupled buffeting to long-span Bridges infrequency-domain[J].China Civil Engineering Journal,2003,36(4):86―93.(in Chinese)
[6]项海帆.现代桥梁抗风理论与实践[M].北京:人民交通出版社,2005:50―120.Xiang Haifan.Modern theory and practice on bridgewind resistance[M].Beijing:China CommunicationsPress,2005:50―120.(in Chinese)
[7]Simiu E,Scanlan R H.Wind effects on structures[M].New York:John Wiley&Sons,1996:80―96.
[8]Xu Y L,Chen J.Characterizing nonstationary windspeed using empirical mode decomposition[J].Journalof Structural Engineering,2004,130(6):912―920.
[9]韩艳,陈政清.利用小波逆变换模拟随机风场的脉动风[J].振动工程学报,2007,20(1):52―56.Han Yan,Chen Zhengqing.A wavelet method for thesimulation of a stochastic wind field[J].Journal ofVibration Engineering,2007,20(1):52―56.(in Chinese)
[10]Chen J,Michael C H H,Xu Y L.A comparative study ofstationary and non-stationary wind models using fieldmeasurements[J].Boundary-Layer Meteorol,2007,122:105―121.
[11]李锦华,李春祥,申建红.非平稳脉动风速的数值模拟[J].振动与冲击,2009,28(1):18―24.Li Jinhua,Li Chunxiang,Shen Jianhong.Numericalsimulation of non-stationary fluctuating wind velocity[J].Journal of Vibration and Shock,2009,28(1):18―24.(inChinese)
[12]庞加斌,林志兴,葛耀君.浦东地区近地强风特性观测研究[J].流体力学试验与测量,2002,16(3):32―39.Pang Jiabin,Lin Zhixing,Ge Yaojun.Field measurementof strong wind characteristics near ground in Pudongdistrict[J].Experiments and measurement in FluidMechanics,2002,16(3):32―39.(in Chinese)
[13]Wang H,Li A Q,Jiao C K,et al.Characteristics of strongwinds at the Runyang Suspension Bridge based on fieldtests from 2005 to 2008[J].Journal of ZhejiangUniversity-SCIENCE A(Applied Physics&Engineering),2010,11(7):465―476.
[14]李秋胜,戴益民,李正农,等.强台风“黑格比”登陆过程中近地风场特性[J].建筑结构学报,2010,31(4):54―81.Li Qiusheng,Dai Yimin,Li Zhengnong,et al.Surfacelayerwind field characteristics during a severe typhoon‘Hagupit’landfalling[J].Journal of Building Structures,2010,31(4):54―81.(in Chinese)
[15]Kameda H.Evolutionary spectra of seismogram bymulti-filter[J].Journal of Engineering MechanismDivision,ASCE,1975,101:787―801.
[16]Goto H,Sugito M,Kameda H,et al.Prediction ofnonstationary earthquake motions formoderate and Greatearthquakes on rock surface[R].Kyoto University:Annuals Disaster Prevention Research Institute,1984,127(B-2):19―48.
[17]Iyama J,Kuwamura H.Application of wavelets toanalysis and simulation of earthquake motions[J].Earthquake Engineering and Structural Dynamics,1999,28:255―272.
[18]曹晖,赖明,白绍良.适合于地震工程信号分析的快速小波变换法研究[J].工程力学,2002,19(4):141―148.Cao Hui,Lai Ming,Bai Shaoliang.Fast algorithm forwavelet transform adaptive to the ANALYSIS of signalsin earthquake engineering[J].Engineering Mechanics,2002,19(4):141―148.(in Chinese)
[19]Spanos P D,Failla G.Evolutionary spectra estimationusing wavelets[J].Journal of Engineering Mechanics,ASCE,2004,130(8):952―960.
[20]Failla G,Pappatico M,Cundari G A.A wavelet-basedspectrum for non-stationary processes[J].MechanicsResearch Communications,2011(38):361―367.
[21]白泉,鲍文博,金生吉.基于小波变换的地震波时变功率谱估计[J].沈阳工业大学学报,2010,32(3):342―348.Bai Quan,Bao Wenbo,Jin Shengji.Estimation oftime-dependent power spectral density of seismic wavebased on wavelet transform[J].Journal of ShenyangUniversity of Technology,2010,32(3):342―348.(inChinese)
[22]田运生.爆破地震地面运动的演变功率谱密度函数分析[J].爆炸与冲击,2007,27(1):7―12.Tian Yunsheng.Analysis of evolutionary power spectradensity function of ground motion induced by blastingseismic[J].Explosion and Shock Waves,2007,27(1):7―12.(in Chinese)
[23]Priestley M B.Power spectral analysis of nonstationaryrandom processes[J].Journal of Sound and Vibration,1967,6:86―97.
[24]张亚辉,林家浩.多点非均匀调制演变随机激励下结构地震响应[J].力学学报,2001,33(1):87―95.Zhang Yahui,Lin Jiahao.Seismic responses of structuressubjected to non-stationary modulated differentialevolutionary random excitations[J].ACTA MechanicaSinica,2001,33(1):87―95.(in Chinese)
[25]樊剑,刘铁,胡亮.基于现代时频分析技术的地震波时变谱估计[J].振动与冲击,2007,26(11):79―84.Fan Jian,Lin Tie,Hu Liang.Time-varying spectrumestimation of earthquake ground motion via moderntime-frequency analysis[J].Journal of Vibration andShock,2007,26(11):79―84.(in Chinese)
[26]Shinozuka M,Jan C M.Digital simulation of randomprocesses and its applications[J].Sound and Vibration,1972,25(1):111―128.
[27]Shinozuka M,Yun C B.Stochastic methods in windengineering[J].Journal of Wind Engineering andIndustrial Aerodynamics,1990,36:829―843.
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