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DOI QR Code

SHM-based probabilistic representation of wind properties: Bayesian inference and model optimization

  • Ye, X.W. (Department of Civil Engineering, Zhejiang University) ;
  • Yuan, L. (Department of Civil Engineering, Zhejiang University) ;
  • Xi, P.S. (Department of Civil Engineering, Zhejiang University) ;
  • Liu, H. (China Railway Major Bridge (Nanjing) Bridge and Tunnel Inspect & Retrofit Co., Ltd.)
  • 투고 : 2017.12.06
  • 심사 : 2018.03.25
  • 발행 : 2018.05.25

초록

The estimated probabilistic model of wind data based on the conventional approach may have high discrepancy compared with the true distribution because of the uncertainty caused by the instrument error and limited monitoring data. A sequential quadratic programming (SQP) algorithm-based finite mixture modeling method has been developed in the companion paper and is conducted to formulate the joint probability density function (PDF) of wind speed and direction using the wind monitoring data of the investigated bridge. The established bivariate model of wind speed and direction only represents the features of available wind monitoring data. To characterize the stochastic properties of the wind parameters with the subsequent wind monitoring data, in this study, Bayesian inference approach considering the uncertainty is proposed to update the wind parameters in the bivariate probabilistic model. The slice sampling algorithm of Markov chain Monte Carlo (MCMC) method is applied to establish the multi-dimensional and complex posterior distribution which is analytically intractable. The numerical simulation examples for univariate and bivariate models are carried out to verify the effectiveness of the proposed method. In addition, the proposed Bayesian inference approach is used to update and optimize the parameters in the bivariate model using the wind monitoring data from the investigated bridge. The results indicate that the proposed Bayesian inference approach is feasible and can be employed to predict the bivariate distribution of wind speed and direction with limited monitoring data.

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과제정보

연구 과제 주관 기관 : National Science Foundation of China, Central Universities of China

참고문헌

  1. Alduse, B.P., Jung, S., Vanli, O.A. and Kwon, S.D. (2015), "Effect of uncertainties in wind speed and direction on the fatigue damage of long-span bridges", Eng. Struct., 100, 468-478. https://doi.org/10.1016/j.engstruct.2015.06.031
  2. Andrieu, C., De Freitas, N., Doucet, A. and Jordan, M.I. (2003), "An introduction to MCMC for machine learning", Mach. Learn., 50(1), 5-43. https://doi.org/10.1023/A:1020281327116
  3. Bayes, T. (1763), "An essay towards solving a problem in the doctrine of chances", Reprint of R. Soc. Lond. Philos. Trans. 53, 370-418. https://doi.org/10.1098/rstl.1763.0053
  4. Box, G. and Tiao, G. (1992), Bayesian Inference in Statistical Analysis, John Wiley & Sons, New York, USA.
  5. Bernardo, J. and Smith, A. (2000), Bayesian Theory, John Wiley & Sons, New York, USA.
  6. Beck, K., Niendorf, B. and Peterson, P. (2012), "The use of Bayesian methods in financial research", Invest. Manage. Financ. Innov., 9(3), 68-75.
  7. Damien, P., Wakefield, J. and Walker, S. (1999), "Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables", J. Roy. Stat. Soc. B., 61(2), 331-344. https://doi.org/10.1111/1467-9868.00179
  8. Erto, P, Lanzotti, A and Lepore, A. (2010), "Wind speed parameter estimation from one-month sample via Bayesian approach", Qual. Reliab. Eng. Int., 26(8), 853-862. https://doi.org/10.1002/qre.1184
  9. Geyer, C.J. (1992), "Practical markov chain monte carlo", Stat. Sci., 7(4), 473-483. https://doi.org/10.1214/ss/1177011137
  10. Geman, S. and Geman, D. (1984), "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images". IEEE T. Pattern. Anal., 6(6), 721-741.
  11. Gelfand, A.E. and Smith, A.F.M. (1990), "Sampling-based approaches to calculating marginal densities", J. Am. Stat. Assoc., 85(409), 398-409. https://doi.org/10.1080/01621459.1990.10476213
  12. Hastings, W.K. (1970), "Monte Carlo sampling method using Markov chains and their Applications", Biometrika, 5(1), 97-109.
  13. Higdon, D.M. (1998), "Auxiliary variable methods for Markov chain Monte Carlo with application", J. Am. Stat. Assoc., 93(442), 585-595. https://doi.org/10.1080/01621459.1998.10473712
  14. Lam, H.F., Peng, H.Y. and Au, S.K. (2014), "Development of a practical algorithm for Bayesian model updating of a coupled slab system utilizing field test data", Eng. Struct., 79, 182-194. https://doi.org/10.1016/j.engstruct.2014.08.014
  15. Marin, J.M., Pierre P., Christian P. R., and Robin J. R. (2012), "Approximate Bayesian computational methods", Stat. Comput., 22(6), 1167-1180. https://doi.org/10.1007/s11222-011-9288-2
  16. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. (1953), "Equations of state calculations by fast computing machines", J. Chem. Phys., 21(6), 1087-1091. https://doi.org/10.1063/1.1699114
  17. Neal and Radford, M. (2003), "Slice sampling", Ann. Stat., 31(3), 705-767. https://doi.org/10.1214/aos/1056562461
  18. Pardo-lguzquiza, E. (1999), "Bayesian inference of spatial covariance parameters", Math. Geol., 31(1), 47-65. https://doi.org/10.1023/A:1007522230013
  19. Pang, W.K., Foster, J.J. and Troutt, M.D. (2001), "Estimation of wind speed distribution using Markov chain Monte Carlo techniques", J. Appl. Meteorol., 40, 1476-1484. https://doi.org/10.1175/1520-0450(2001)040<1476:EOWSDU>2.0.CO;2
  20. Smith, R.L. and Naylor, J.C. (1987), "A comparison of maximum likelihood estimation and Bayesian estimators for the threeparameter Weibull distribution", Appl. Stat., 36, 358-369. https://doi.org/10.2307/2347795
  21. Wakefield, J.C., Gelfand, A.E. and Smith, A.F.M. (1991), "Efficient generation of random variates via the ratio-ofuniforms methods", Stat. Comput., 1(2), 129-133. https://doi.org/10.1007/BF01889987
  22. Weibull, W. (1951), "A statistical distribution function of wide applicability", J. Appl. Mech., 18(3), 293-297.
  23. Yang, J, Astitha, M, Anagnostou, E. and Hartman, B. (2017), "Using a Bayesian regression approach on dual-model windstorm simulations to improve wind speed prediction", J. Appl. Meteorol. Clim., 56(4), 1155-1174. https://doi.org/10.1175/JAMC-D-16-0206.1

피인용 문헌

  1. Critical review of data-driven decision-making in bridge operation and maintenance vol.18, pp.1, 2018, https://doi.org/10.1080/15732479.2020.1833946