Simulation of Homogeneous Fluctuating Wind Field in Two Spatial Dimensions via a Joint Wave Number–Frequency Power Spectrum
Publication: Journal of Engineering Mechanics
Volume 144, Issue 11
Abstract
Simulation of fluctuating wind-speed fields is a critical task in determining the wind loads for wind-resistant design of high-rise buildings, long-span bridges, and large-size flexible structural systems such as latticed shells and wind turbines. Due to its simple algorithmic and rigorous theoretical basis, the spectral representation method (SRM) is a widely used simulation tool in practice. However, it may often exhibit low efficiency in its traditional procedure due to the involvement of decomposition of the cross-power spectrum density (PSD) matrix at each discretized frequency. Circumventing this challenge, a joint wave number–frequency power spectrum-based SRM associated with a one-spatial-dimension wind field was proposed recently, allowing an accurate simulation without the Cholesky decomposition. In this paper, the extension of SRM to wind fields in two spatial dimensions is done. Further, to reduce the computational costs associated with the threefold summation over one-dimensional frequency domain and two-dimensional wave-number domain, uneven discretization techniques by tensor-product and acceptance-rejection method are developed. Numerical examples relating to the simulation of fluctuating wind-speed fields in one spatial dimension and two spatial dimensions are included, showing the effectiveness of the proposed method.
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Acknowledgments
The support of the National Natural Science Foundation of China (NSFC) (Grant Nos. 11672209, 51538010, and 11761131014), the National Outstanding Youth Science Funds of NSFC (Grant No. 51725804), the Committee of Science and Technology of Shanghai China (Grant No. 18160712800), the National Key R&D Program of China (Grant No. 2017YFC0803300), and the Ministry of Science and Technology of the People’s Republic of China (Grant Nos. SLDRCE14-B-17 and SLDRCE14-B-20) are highly appreciated. Mr. Jingran is gratefully appreciated for his constructive suggestions.
References
Bendat, J. S., and A. G. Piersol. 2010. Random data. 4th ed. Hoboken, NJ: Wiley.
Benowitz, B. A., and G. Deodatis. 2015. “Simulation of wind velocities on long span structures: A novel stochastic wave based model.” J. Wind Eng. Ind. Aerodyn. 147: 154–163. https://doi.org/10.1016/j.jweia.2015.10.004.
Burton, T., N. Jenkins, D. Sharpe, and E. Bossanyi. 2011. Wind energy handbook. 2nd ed. Hoboken, NJ: Wiley.
Cao, Y. H., H. F. Xiang, and Y. Zhou. 2000. “Simulation of stochastic wind velocity field on long-span bridges.” J. Eng. Mech. 126 (1): 1–6. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(1).
Chen, J. B., F. Kong, and Y. B. Peng. 2017a. “A stochastic harmonic function representation for non-stationary stochastic processes.” Mech. Syst. Signal Process. 96: 31–44. https://doi.org/10.1016/j.ymssp.2017.03.048.
Chen, J. B., W. L. Sun, J. Li, and J. Xu. 2013. “Stochastic harmonic function representation of stochastic processes.” J. Appl. Mech. 80 (1): 011001. https://doi.org/10.1115/1.4006936.
Chen, J. B., X. S. Zeng, and Y. B. Peng. 2017b. “Probabilistic analysis of wind-induced vibration mitigation of structures by fluid viscous dampers.” J. Sound Vib. 409: 287–305. https://doi.org/10.1016/j.jsv.2017.07.051.
Davenport, A. G. 1961a. “The application of statistical concepts to the wind loading of structures.” Proc. Inst. Civ. Eng. 19 (4): 449–472. https://doi.org/10.1680/iicep.1961.11304.
Davenport, A. G. 1961b. “The spectrum of horizontal gustiness near the ground in high winds.” Q. J. R. Meteorol. Soc. 87 (372): 194–211. https://doi.org/10.1002/qj.49708737208.
Desmond, C., J. Murphy, L. Blonk, and W. Haans. 2016. “Description of an 8 MW reference wind turbine.” J. Phys. Conf. Ser. 753 (9): 092013. https://doi.org/10.1088/1742-6596/753/9/092013.
Dick, J., and F. Pillichshammer. 2010. Digital nets and sequences: Discrepancy theory and quasi-Monte Carlo integration. Cambridge, UK: Cambridge University Press.
Ding, Q. S., L. D. Zhu, and H. F. Xiang. 2011. “An efficient ergodic simulation of multivariate stochastic processes with spectral representation.” Probab. Eng. Mech. 26 (2): 350–356. https://doi.org/10.1016/j.probengmech.2010.09.006.
Di Paola, M. 1998. “Digital simulation of wind field velocity.” J. Wind Eng. Ind. Aerodyn. 74–76 (2): 91–109. https://doi.org/10.1016/S0167-6105(98)00008-7.
Di Paola, M., and I. Gullo. 2001. “Digital generation of multivariate wind field processes.” Probab. Eng. Mech. 16 (1): 1–10. https://doi.org/10.1016/S0266-8920(99)00032-6.
Di Paola, M., and G. Navarra. 2009. “Stochastic seismic analysis of MDOF structures with nonlinear viscous dampers.” Struct. Control Health Monit. 16 (3): 303–318. https://doi.org/10.1002/stc.254.
Gerstner, T., and M. Griebel. 2003. “Dimension-adaptive tensor-product quadrature.” Computing 71 (1): 65–87. https://doi.org/10.1007/s00607-003-0015-5.
He, G. L., and J. Li. 2010. “Wind field simulation of wind turbine systems.” [In Chinese.] J. Tongji Univ. 38 (7): 976–981.
IEC (International Electrotechnical Commission). 2005. Wind turbines. Part 1: Design requirements. IEC 61400-1. Geneva: IEC.
Kaimal, J. C., J. C. Wyngaard, Y. Izumi, and O. R. Cote. 1972. “Spectral characteristics of surface-layer turbulence.” J. R. Meteorol. Soc. 98 (417): 563–589. https://doi.org/10.1002/qj.49709841707.
Kareem, A. 2008. “Numerical simulation of wind effects: A probabilistic perspective.” J. Wind Eng. Ind. Aerodyn. 96 (10): 1472–1497. https://doi.org/10.1016/j.jweia.2008.02.048.
Li, J., and J. B. Chen. 2009. Stochastic dynamics of structures. Hoboken, NJ: Wiley.
Li, J., Y. B. Peng, and Q. Yan. 2013. “Modeling and simulation of fluctuating wind speeds using evolutionary phase spectrum.” Probab. Eng. Mech. 32: 48–55. https://doi.org/10.1016/j.probengmech.2013.01.001.
Li, J., Q. Yan, and J. B. Chen. 2012. “Stochastic modeling of engineering dynamic excitations for stochastic dynamics of structures.” Probab. Eng. Mech. 27 (1): 19–28. https://doi.org/10.1016/j.probengmech.2011.05.004.
Li, Y. L., H. L. Liao, and S. Z. Qiang. 2002. “Research on the wind characteristics of the site of Nanjing Changjiang River Bridge on Beijing- Shanghai high speed railway.” [In Chinese.] Bridge Constr. 4 (5): 5–7.
Lin, J. H., Y. Zhao, and Y. H. Zhang. 2001. “Accurate and highly efficient algorithms for structural stationary/non-stationary random responses.” Comput. Methods Appl. Mech. Eng. 191 (1–2): 103–111. https://doi.org/10.1016/S0045-7825(01)00247-X.
Liu, Z. J., W. Liu, and Y. B. Peng. 2016. “Random function based spectral representation of stationary and non-stationary stochastic processes.” Probab. Eng. Mech. 45: 115–126. https://doi.org/10.1016/j.probengmech.2016.04.004.
Liu, Z. J., Z. X. Liu, and Y. B. Peng. 2017. “Dimension reduction of Karhunen-Loeve expansion for simulation of stochastic processes.” J. Sound Vib. 408: 168–189. https://doi.org/10.1016/j.jsv.2017.07.016.
Mantoglou, A., and J. L. Wilson. 1982. “The turning bands method for simulation of random fields using line generation by a spectral method.” Water Resour. Res. 18 (5): 1379–1394. https://doi.org/10.1029/WR018i005p01379.
Nielsen, S. R. K. 2005. Structural dynamics: Dynamics of wind turbines (Part 1). Aalborg, Denmark: Aalborg University Press.
Panofsky, H. A., and R. A. McCormick. 1954. “Properties of spectra of atmospheric turbulence at 100 metres.” Q. J. R. Meteorol. Soc. 80 (346): 546–564. https://doi.org/10.1002/qj.49708034604.
Peng, L. L., G. Q. Huang, X. Z. Chen, and A. Kareem. 2017. “Simulation of multivariate nonstationary random processes: Hybrid stochastic wave and proper orthogonal decomposition approach.” J. Eng. Mech. 143 (9): 04017064. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001273.
Peng, L. L., G. Q. Huang, A. Kareem, and Y. Li. 2016. “An efficient space-time based simulation approach of wind velocity field with embedded conditional interpolation for unevenly spaced locations.” Probab. Eng. Mech. 43: 156–168. https://doi.org/10.1016/j.probengmech.2015.10.006.
Peng, Y. B., J. B. Chen, and J. Li. 2014. “Nonlinear response of structures subjected to stochastic excitations via probability density evolution method.” Adv. Struct. Eng. 17 (6): 801–816. https://doi.org/10.1260/1369-4332.17.6.801.
Peng, Y. B., S. F. Wang, and J. Li. 2018. “Field measurement and investigation of spatial coherence for near-surface strong winds in southeast China.” J. Wind Eng. Ind. Aerodyn. 172: 423–440. https://doi.org/10.1016/j.jweia.2017.11.012.
Roberts, J. B., and P. D. Spanos. 1990. Random vibration and statistical linearization. Chichester, UK: Wiley.
Samali, B., J. N. Yang, and C. T. Yeh. 1985. “Control of lateral-torsional motion of wind-excited buildings.” J. Eng. Mech. 111 (6): 777–796. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:6(777).
Shinozuka, M. 1971. “Simulation of multivariate and multidimensional random processes.” J. Acoust. Soc. Am. 49 (1): 357–368. https://doi.org/10.1121/1.1912338.
Shinozuka, M., and G. Deodatis. 1996. “Simulation of multi-dimensional Gaussian stochastic fields by spectral representation.” Appl. Mech. Rev. 49 (1): 29–53. https://doi.org/10.1115/1.3101883.
Simiu, E., and R. H. Scanlan. 1996. Wind effects on structures. 3rd ed. New York: Wiley.
Spanos, P. D., and B. A. Zeldin. 1998. “Monte Carlo treatment of random fields: A broad perspective.” ASME. Appl. Mech. Rev. 51 (3): 219–237. https://doi.org/10.1115/1.3098999.
Terenzi, G. 1999. “Dynamics of SDOF systems with nonlinear viscous damping.” J. Eng. Mech. 125 (8): 956–963. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:8(956).
Xu, Y. L. 2013. Wind effects on cable-supported bridges. Singapore: Wiley.
Xu, Y. L., W. S. Zhang, J. M. Ko, and J. H. Lin. 1999. “Pseudo-excitation method for vibration analysis of wind-excited structures.” J. Wind Eng. Ind. Aerodyn. 83 (1–3): 443–454. https://doi.org/10.1016/S0167-6105(99)00092-6.
Yan, Q., Y. B. Peng, and J. Li. 2013. “Scheme and application of phase delay spectrum towards spatial stochastic wind fields.” Wind Struct. 16 (5): 433–455. https://doi.org/10.12989/was.2013.16.5.433.
Yang, J. N., and Y. K. Lin. 1981. “Along-wind motion of a multi-storey building.” J. Eng. Mech. 107 (2): 295–307.
Yang, W. W., T. Y. P. Chang, and C. C. Chang. 1997. “An efficient wind field simulation technique for bridges.” J. Wind Eng. Ind. Aerodyn. 67 (97): 697–708. https://doi.org/10.1016/S0167-6105(97)00111-6.
Zeng, X. S., Y. B. Peng, and J. B. Chen. 2017. “Serviceability based damping optimization of randomly wind-excited high-rise buildings.” In The structural design of tall and special buildings, e1371. Hoboken, NJ: Wiley.
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 11 • November 2018
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©2018 American Society of Civil Engineers.
History
Received: Dec 6, 2017
Accepted: May 16, 2018
Published online: Aug 28, 2018
Published in print: Nov 1, 2018
Discussion open until: Jan 28, 2019
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