Wind and Structures

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Dimension-reduction simulation of stochastic wind velocity fields by two continuous approaches

  • Liu, Zhangjun (School of Civil Engineering and Architecture, Wuhan Institute of Technology) ;
  • He, Chenggao (College of Civil Engineering & Architecture, China Three Gorges University) ;
  • Liu, Zenghui (School of Civil Engineering and Architecture, Wuhan Institute of Technology) ;
  • Lu, Hailin (School of Civil Engineering and Architecture, Wuhan Institute of Technology)
  • Received : 2019.01.22
  • Accepted : 2019.06.25
  • Published : 2019.12.25
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Abstract

In this study, two original spectral representations of stationary stochastic fields, say the continuous proper orthogonal decomposition (CPOD) and the frequency-wavenumber spectral representation (FWSR), are derived from the Fourier-Stieltjes integral at first. Meanwhile, the relations between the above two representations are discussed detailedly. However, the most widely used conventional Monte Carlo schemes associated with the two representations still leave two difficulties unsolved, say the high dimension of random variables and the incompleteness of probability with respect to the generated sample functions of the stochastic fields. In view of this, a dimension-reduction model involving merely one elementary random variable with the representative points set owing assigned probabilities is proposed, realizing the refined description of probability characteristics for the stochastic fields by generating just several hundred representative samples with assigned probabilities. In addition, for the purpose of overcoming the defects of simulation efficiency and accuracy in the FWSR, an improved scheme of non-uniform wavenumber intervals is suggested. Finally, the Fast Fourier Transform (FFT) algorithm is adopted to further enhance the simulation efficiency of the horizontal stochastic wind velocity fields. Numerical examplesfully reveal the validity and superiorityof the proposed methods.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51978543, 51778343 and 51278282). These financial supports are gratefully acknowledged. Ph.D. Candidate Zixin Liu is greatly appreciated for her constructive discussion and comment on the research.

References

  1. Benowitz, B.A. and Deodatis, G. (2015), "Simulation of wind velocities on long span structures: a novel stochastic wave based model". J. Wind Eng. Ind. Aerod., 147, 154-163. https://doi.org/10.1016/j.jweia.2015.10.004.
  2. Carassale, L. and Solari, G. (2002), "Wind modes for structural dynamics: a continuous approach", Probabilist. Eng. Mech., 17(2), 157-166. https://doi.org/10.1016/s0266-8920(01)00036-4.
  3. Chen, J.B., He, J.R., Ren, X.D. and Li, J. (2018), "Stochastic harmonic function representation of random fields for material properties of structures", J. Eng. Mech., 144(7), 04018049. https://doi.org/10.1061/(asce)em.1943-7889.0001469.
  4. Chen, J.B., Kong, F. and Peng, Y.B. (2017), "A stochastic harmonic function representation for non-stationary stochastic processes", Mech. Syst. Signal Pr., 96, 31-44. https://doi.org/10.1016/j.ymssp.2017.03.048.
  5. Chen, J.B., Sun, W.L., Li, J. and Xu, J. (2013), "Stochastic harmonic function representation of stochastic processes", J. Appl. Mech., 80(1), 011001. https://doi.org/10.1115/1.4006936.
  6. Chen, L.Z. and Letchford, C.W. (2005), "Simulation of multivariate stationary Gaussian stochastic processes: hybrid spectral representation and proper orthogonal decomposition approach", J. Eng. Mech., 131(8), 801-808. https://doi.org/10.1061/(asce)0733-9399(2005)131:8(801).
  7. Chen, X.Z. and Kareem, A. (2005), "Proper orthogonal decomposition-based modeling, analysis, and simulation of dynamic wind load effects on structures", J. Eng. Mech., 131(4), 325-339.https://doi.org/10.1061/(asce)0733-9399(2005)131:4(325).
  8. Davenport, A.G. (1961), "The spectrum of horizontal gustiness near the ground in high winds", Q. J. Roy. Meteor. Soc., 87, 194-211. https://doi.org/10.1002/qj.49708737208.
  9. Deodatis, G. and Shinozuka, M. (1989), "Simulation of seismic ground motion using stochastic waves", J. Eng. Mech., 115(12), 2723-2737.https://doi.org/10.1061/(asce)0733-9399(1989)115:12(2723).
  10. Di Paola, M. (1998), "Digital simulation of wind field velocity", J. Wind Eng. Ind. Aerod., 74-76, 91-109. https://doi.org/10.1016/s0167-6105(98)00008-7.
  11. Di Paola, M. and Gullo, I. (2001), "Digital generation of multivariate wind field processes", Probabilist. Eng. Mech., 16(1), 1-10. https://doi.org/10.1016/s0266-8920(99)00032-6.
  12. Ghanem, R.G. and Spanos, P.D. (1991), "Spectral stochastic finite-element formulation for reliability analysis", J. Eng. Mech., 117(10), 2351-2372. https://doi.org/10.1061/(asce)0733-9399(1991)117:10(2351).
  13. Glasserman, P. (2013), Monte Carlo Methods in Financial Engineering, Springer, New York, NY, USA.
  14. Huang, G.Q. (2015), "Application of proper orthogonal decomposition in fast Fourier transform-assisted multivariate nonstationary process simulation", J. Eng. Mech., 141(7), 04015015. https://doi.org/10.1061/(asce)em.1943-7889.0000923.
  15. Huang, G.Q., Ji, X.W., Zheng, H.T., Luo, Y., Peng, X.Y. and Yang, Q.S. (2018), "Uncertainty of peak value of non-Gaussian wind load effect: analytical approach", J. Eng. Mech., 144(2), 04017172. https://doi.org/10.1061/(asce)em.1943-7889.0001402.
  16. Kaimal, J.C., Wyngaard, J.C., Izumi, Y. and Cote, O.R. (1972), "Spectral characteristics of surface-layer turbulence", Q. J. Roy. Meteor. Soc., 98, 563-589. https://doi.org/10.1256/smsqj.41706.
  17. Kanwal, P. (1971), Linear Interval Equations, Academic Press, New York, NY, USA.
  18. Khanduri, A.C., Stathopoulos, T. and Bedard, C. (1998), "Windinduced interference effects on buildings - a review of the state-of-the-art", Eng. Struct., 20(7), 617-630. https://doi.org/10.1016/s0141-0296(97)00066-7.
  19. Li, J. and Chen, J.B. (2009), Stochastic Dynamics of Structures, John Wiley & Sons, Singapore.
  20. Liu, Z.H., Liu, Z.J., He, C.G. and Lu, H.L. (2019), "Dimensionreduced probabilistic approach of 3-D wind field for windinduced response analysis of transmission tower", J. Wind Eng. Ind. Aerod., 190, 309-321. https://doi.org/10.1016/j.jweia.2019.05.013.
  21. Liu, Z.J. and Liu, Z.H. (2018), "Random function representation of stationary stochastic vector processes for probability density evolution analysis of wind-induced structures", Mech. Syst. Signal Pr., 106, 511-525. https://doi.org/10.1016/j.ymssp.2018.01.011.
  22. Liu, Z.J., Liu, W. and Peng, Y.B. (2016), "Random function based spectral representation of stationary and non-stationary stochastic processes", Probabilist. Eng. Mech., 45, 115-126. https://doi.org/10.1016/j.probengmech.2016.04.004.
  23. Liu, Z.J., Liu, Z.H. and Peng, Y.B. (2018a), "Simulation of multivariate stationary stochastic processes using dimensionreduction representation methods", J. Sound Vib., 418, 144-162. https://doi.org/10.1016/j.jsv.2017.12.029.
  24. Liu, Z.J., Liu, Z.X. and Chen, D.H. (2018b), "Probability density evolution of a nonlinear concrete gravity dam subjected to nonstationary seismic ground motion", J. Eng. Mech., 144(1), 04017157. https://doi.org/10.1061/(asce)em.1943-7889.0001388.
  25. Liu, Z.J., Liu, Z.X. and Peng, Y.B. (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.
  26. Peng, L.L., Huang, G.Q., Kareem, A. and Li, Y.L. (2016), "An efficient space-time based simulation approach of wind velocity field with embedded conditional interpolation for unevenly spaced locations", Probabilist. Eng. Mech., 43, 156-168. https://doi.org/10.1016/j.probengmech.2015.10.006.
  27. Peng, Y.B., Wang, S.F. and Li, J. (2018), "Field measurement and investigation of spatial coherence for near-surface strong winds in Southeast China", J. Wind Eng. Ind. Aerod., 172, 423-440. https://doi.org/10.1016/j.jweia.2017.11.012.
  28. Priestley, M.B. (1965), "Evolutionary spectra and non-stationary processes", J. R. Stat. Soc. B, 27(2), 204-237. https://doi.org/10.1111/j.2517-6161.1965.tb01488.x.
  29. 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.
  30. Shinozuka, M. and Deodatis, G. (1996), "Simulation of multidimensional Gaussian stochastic fields by spectral representation", Appl. Mech. Rev., 49(1), 29-53. https://doi.org/10.1115/1.3101883.
  31. Shinozuka, M. and Jan, C.M. (1972), "Digital simulation of random processes and its applications", J. Sound Vib., 25(1), 111-128. https://doi.org/10.1016/0022-460X(72)90600-1.
  32. Solari, G. and Carassale, L. (2001), "Model transformation tools in structural dynamics and wind engineering", Wind Struct., 3(4), 221-241. https://doi.org/10.12989/was.2000.3.4.221.
  33. Song, Y.P., Chen, J.B., Peng, Y.B., Spanos, P.D. and Li, J. (2018), "Simulation of nonhomogeneous fluctuating wind speed field in two-spatial dimensions via an evolutionary wavenumberfrequency joint power spectrum", J. Wind Eng. Ind. Aerod., 179, 250-259. https://doi.org/10.1016/j.jweia. 2018.06.005.
  34. Wu, Y.X., Gao, Y.F., Li, D.Y., Xu, C.J. and Mahfouz A.H. (2013), "Approximation approach to the SRM based on root decomposition in the simulation of spatially varying ground motions". Earthq. Eng. Eng. Vib., 12(3), 363-372. https://doi.org/10.1007/s11803-013-0178-9.
  35. Wu, Y.X., Gao, Y.F., Zhang, N. and Zhang, F. (2018), "Simulation of spatially varying non-Gaussian and nonstationary seismic ground motions by the spectral representation method", J. Eng. Mech., 144(1), 04017143. https://doi.org/10.1061/(asce)em.1943-7889.0001371.
  36. Yang, J.N. (1972), "Simulation of random envelope processes", J. Sound Vib., 21(1), 73-85. https://doi.org/10.1016/0022-460x(72)90207-6.
  37. Zerva, A. (1992), "Seismic ground motion simulations from a class of spatial variability models", Earthq. Eng. Struct. D., 21(4), 351-361. https://doi.org/10.1002/eqe.4290210406.
  38. Zhu, S.Y., Li, Y.L., Togbenou, K., Yu, C.J. and Xiang, T.Y. (2018), "Case study of random vibration analysis of train-bridge systems subjected to wind loads", Wind Struct., 27(6), 399-416. https://doi.org/10.12989/was.2018.27.6.399.
  39. Zu, G.B. and Lam, K.M. (2018), "Across-wind excitation mechanism for interference of twin tall buildings in tandem arrangement", J. Wind Eng. Ind. Aerod., 177, 167-185. https://doi.org/10.1016/j.jweia.2018.04.019.