基于波数-频率联合演变功率谱的一维空间非均匀脉动风场模拟
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摘要
在高层建筑、大跨桥梁和大型风力发电系统等大型工程中,风荷载对结构的安全性至关重要、甚至是起控制作用的要素。因此,脉动风速场的模拟具有重要意义。谱表达方法得到了广泛的应用。但经典的谱表达方法需要对互功率谱矩阵的逐个频率点进行Cholesky分解或本征正交分解(POD),当模拟的空间点数较多时,分解效率非常低下、甚至可能出现矩阵奇异而难以实现。基于波数-频率联合功率谱或联合演变谱,不需要Cholesky分解或POD,可以方便地实现均匀或非均匀脉动风场的模拟。当模拟点为等间距点时,该方法能够使用FFT技术提高模拟效率,而当模拟点为非等间距点、不能使用FFT技术时,模拟效率依然有待提高。鉴于此,该文引入"结构化"非均匀离散方法和"舍选法"思想,建议了二维波数-频率域的非均匀离散策略,显著地提高了模拟效率。以某桥塔的一维空间非均匀脉动风场的数值模拟为例,验证了该方法的有效性。
The simulation of fluctuating wind speed field is of a great significance, considering that the wind load is critical or even dominating for the safe design of large-sized engineering structures such as high-rise buildings, long-span bridges and megawatt wind turbines. The spectral representation method(SRM) is a kind of widely used simulation technique at present, which has to, however, deal with the challenge of unbearable computational efforts owing to the Cholesky decomposition or proper orthogonal decomposition(POD) at each discretized frequency with respect to the cross-power spectrum density(PSD) matrix. The wavenumber-frequency joint power spectrum and evolutionary wavenumber-frequency joint power spectrum based SRM were proposed recently, allowing an effective simulation of a homogeneous or nonhomogeneous wind field without Cholesky decomposition or POD. Further, the FFT technique can be utilized to improve the simulation efficiency when the spatial simulation points are evenly distributed. However, in the case of unevenly-distributed spatial simulation points, the FFT technique cannot be adopted. Thus, the simulation efficiency still needs to be enhanced. In order to reduce the computational costs resulted from the twofold summation over a frequency-wavenumber domain, the uneven discretization strategies, including structured method and acceptance-rejection method, are suggested in the present paper. The numerical examples of simulation in nonhomogeneous fluctuating wind speed fields in one-dimensional space for a bridge tower are performed, demonstrating the effectiveness of the proposed method.
The simulation of fluctuating wind speed field is of a great significance, considering that the wind load is critical or even dominating for the safe design of large-sized engineering structures such as high-rise buildings, long-span bridges and megawatt wind turbines. The spectral representation method(SRM) is a kind of widely used simulation technique at present, which has to, however, deal with the challenge of unbearable computational efforts owing to the Cholesky decomposition or proper orthogonal decomposition(POD) at each discretized frequency with respect to the cross-power spectrum density(PSD) matrix. The wavenumber-frequency joint power spectrum and evolutionary wavenumber-frequency joint power spectrum based SRM were proposed recently, allowing an effective simulation of a homogeneous or nonhomogeneous wind field without Cholesky decomposition or POD. Further, the FFT technique can be utilized to improve the simulation efficiency when the spatial simulation points are evenly distributed. However, in the case of unevenly-distributed spatial simulation points, the FFT technique cannot be adopted. Thus, the simulation efficiency still needs to be enhanced. In order to reduce the computational costs resulted from the twofold summation over a frequency-wavenumber domain, the uneven discretization strategies, including structured method and acceptance-rejection method, are suggested in the present paper. The numerical examples of simulation in nonhomogeneous fluctuating wind speed fields in one-dimensional space for a bridge tower are performed, demonstrating the effectiveness of the proposed method.
引文
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[25]Shinozuka M,Deodatis G.Stochastic process models for earthquake ground motion[J].Probabilistic Engineering Mechanics,1988,3(3):114-123.
[26]Liang J W,Chaudhuri S R,Shinozuka M.Simulation of nonstationary stochastic processes by spectral representation[J].Journal of Engineering Mechanics,2007,133(6):616-627.
[27]Chen J B,Kong F,Peng Y B.A stochastic harmonic function representation for non-stationary stochastic processes[J].Mechanical Systems&Signal Processing,2017,96:31-44.
[28]Gerstner T,Griebel M.Dimension-adaptive tensorproduct quadrature[J].Computing,2003,71(1):65-87.
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[30]李永乐,廖海黎,强士中.京沪高速铁路南京长江大桥桥址区风特性研究[J].桥梁建设,2002(4):5-7.Li Yongle,Liao Haili,Qiang Shizhong.Research on the wind characteristics of the site of Nanjing Changjiang river bridge on Beijing-Shanghai high-speed railway[J].Bridge Construction,2002(4):5-7.(in Chinese)
[31]Chen J B,Song Y P,Peng Y B,et al.Simulation of homogeneous fluctuating wind field in two spatial dimensions via a wavenumber-frequency joint power spectrum[J].Journal of Engineering Mechanics,2018,144(11):04018100.
[32]Song Y P,Chen J B,Peng Y B,et al.Simulation of nonhomogeneous fluctuating wind speed field in two-spatial dimensions via an evolutionary wavenumberfrequency joint power spectrum[J].Journal of Wind Engineering&Industrial Aerodynamics,2018,179:250-259.
[2]Davenport A G.The spectrum of horizontal gustiness near the ground in high winds[J].Quarterly Journal of the Royal Meteorological Society,1961,87(372):194-211.
[3]Kaimal J C,Wyngaard J C,Izumi Y,et al.Spectral characteristics of surface-layer turbulence[J].Journal of Royal Meteorological Society,1972,98(417):563-589.
[4]Simiu E,Scanlan R H.Wind Effects on Structures(The3rd edition)[M].New York:John Wiley&Sons,1996.
[5]Shinozuka M.Simulation of multivariate and multidimensional random processes[J].Journal of the Acoustical Society of America,1971,49(1):357-368.
[6]Benowitz B A.Modeling and simulation of random processes and fields in Civil Engineering and Engineering Mechanics[D].New York:Columbia University,2013.
[7]Benowitz B A,Deodatis G.Simulation of wind velocities on long span structures:A novel stochastic wave based model[J].Journal of Wind Engineering&Industrial Aerodynamics,2015,147:154-163.
[8]柯世堂,王同光,胡丰,等.基于塔架-叶片耦合模型风力机全机风振疲劳分析[J].工程力学,2015,32(8):36-41.Ke Shitang,Wang Tongguang,Hu Feng,et al.Wind-induced fatigue analysis of wind turbine system based on tower-blade coupled model[J].Engineering Mechanics,2015,32(8):36-41.(in Chinese)
[9]宫成,刘志文,谢钢,等.高墩大跨斜拉桥悬臂施工期风致振动控制[J].工程力学,2015,32(增刊1):122-128.Gong Cheng,Liu Zhiwen,Xie Gang,et al.Control of wind-induced vibration in large span cable-stayed bridge with high piers during cantilever construction stages[J].Engineering Mechanics,2015,32(Suppl 1):122-128.(in Chinese)
[10]Shinozuka M,Deodatis G.Simulation of multi-dimensional Gaussian stochastic fields by spectral representation[J].Applied Mechanics Reviews,1996,49(1):29-53.
[11]Spanos P D,Zeldin B A.Monte Carlo treatment of random fields:a broad perspective[J].ASME.Applied Mechanics Reviews,1998,51(3):219-237.
[12]Shinozuka M,Jan C M.Digital simulation of random processes and its applications[J].Journal of Sound&Vibration,1972,25(1):111-128.
[13]Paola M D.Digital simulation of wind field velocity[J].Journal of Wind Engineering&Industrial Aerodynamics,1998,74/75/76(2):91-109.
[14]Zhao N,Huang G Q.Fast simulation of multivariate nonstationary process and its application to extreme winds[J].Journal of Wind Engineering&Industrial Aerodynamics,2017,170:118-127.
[15]Li Y L,Togbenou K,Xiang H Y,et al.Simulation of non-stationary wind velocity field on bridges based on Taylor series[J].Journal of Wind Engineering&Industrial Aerodynamics,2017,169:117-127.
[16]Cao Y H,Xiang H F,Zhou Y.Simulation of stochastic wind velocity field on long-span bridges[J].Journal of Engineering Mechanics,2000,126(1):1-6.
[17]陶天友,王浩.基于Hermite插值的简化风场模拟[J].工程力学,2017,34(3):182-188.Tao Tianyou,Wang Hao.Reduced simulation of the wind field based on Hermite interpolation[J].Engineering Mechanics,2017,34(3):182-188.(in Chinese)
[18]Togbenou K,Xiang H Y,Li YL,et al.Improved spectral representation method for the simulation of stochastic wind velocity field based on fft algorithm and polynomial decomposition[J].Journal of Engineering Mechanics,2018,144(2):04017171.
[19]Peng L L,Huang G Q,Kareem A,et al.An efficient space-time based simulation approach of wind velocity field with embedded conditional interpolation for unevenly spaced locations[J].Probabilistic Engineering Mechanics,2016,43:156―168.
[20]刘章军,叶永友,刘增辉.脉动风速连续随机场的降维模拟[J].工程力学,2018,35(11):8―16.Liu Zhangjun,Ye Yongyou,Liu Zenghui.Simulation of fluctuating wind velocity continuous stochastic filed by dimension reduction approach[J].Engineering Mechanics,2018,35(11):8―16.(in Chinese)
[21]Peng L L,Huang G Q,Chen X,et al.Simulation of multivariate nonstationary random processes:hybrid stochastic wave and proper orthogonal decomposition approach[J].Journal of Engineering Mechanics,2017,143(9):04017064.
[22]Bendat J S,Piersol A G.Random data[M].4th ed.Hoboken:John Wiley&Sons,2010.
[23]Priestley M B.Evolutionary spectra and non-stationary processes[J].Journal of the Royal Statistical Society,1965,27(2):204-237.
[24]Li J,Chen J B.Stochastic dynamics of structures[M].Singapore:John Wiley&Sons,2009.
[25]Shinozuka M,Deodatis G.Stochastic process models for earthquake ground motion[J].Probabilistic Engineering Mechanics,1988,3(3):114-123.
[26]Liang J W,Chaudhuri S R,Shinozuka M.Simulation of nonstationary stochastic processes by spectral representation[J].Journal of Engineering Mechanics,2007,133(6):616-627.
[27]Chen J B,Kong F,Peng Y B.A stochastic harmonic function representation for non-stationary stochastic processes[J].Mechanical Systems&Signal Processing,2017,96:31-44.
[28]Gerstner T,Griebel M.Dimension-adaptive tensorproduct quadrature[J].Computing,2003,71(1):65-87.
[29]Dick J,Pillichshammer F.Digital Nets and sequences:discrepancy theory and Quasi-Monte Carlo integration[M].New York:Cambridge University Press,2010.
[30]李永乐,廖海黎,强士中.京沪高速铁路南京长江大桥桥址区风特性研究[J].桥梁建设,2002(4):5-7.Li Yongle,Liao Haili,Qiang Shizhong.Research on the wind characteristics of the site of Nanjing Changjiang river bridge on Beijing-Shanghai high-speed railway[J].Bridge Construction,2002(4):5-7.(in Chinese)
[31]Chen J B,Song Y P,Peng Y B,et al.Simulation of homogeneous fluctuating wind field in two spatial dimensions via a wavenumber-frequency joint power spectrum[J].Journal of Engineering Mechanics,2018,144(11):04018100.
[32]Song Y P,Chen J B,Peng Y B,et al.Simulation of nonhomogeneous fluctuating wind speed field in two-spatial dimensions via an evolutionary wavenumberfrequency joint power spectrum[J].Journal of Wind Engineering&Industrial Aerodynamics,2018,179:250-259.