Multivariate Extreme Wind Loads: Copula-Based Analysis
This article has been corrected.
VIEW CORRECTIONPublication: Journal of Engineering Mechanics
Volume 149, Issue 1
Abstract
A probabilistic approach is developed to estimate multivariate extreme wind loads by introducing copula theory. Three major concerns are addressed: (1) the characterization of pairwise dependence among extreme load coefficients, (2) the construction of a probability model of multivariate extreme load coefficients, and (3) the probabilistic estimation of multivariate extreme wind loads with randomness of the mean wind speed (i.e., wind climate change). Theoretical and numerical analyses are carried out with the aid of wind tunnel data. The results show that using rank dependence (Kendall’s tau and Spearman’s rho) is more appropriate than using Pearson correlation coefficient in defining dependence for extreme load coefficients. The Gaussian copula is convenient for deriving the joint distribution of multivariate extreme load coefficients but is not applicable for high-dimensional problems. In contrast, the vine copula is flexible and can provide a better estimate of the joint distribution function without dimension limitations. Multivariate annual maximum wind loads can be estimated via either first- or full-order methods. Dependence of the extreme load coefficients and randomness of the wind speed are both found having effects on the dependence of extreme wind loads. Moreover, the procedure of simulating multivariate annual maximum wind loads is presented to facilitate the use in practical problems.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. Data item: wind tunnel data.
Acknowledgments
The support by the National Natural Science Foundation of China (Grant No. 51908014) is greatly acknowledged.
References
Akaike, H. 1974. “A new look at the statistical model identification.” IEEE Trans. Autom. Control 19 (6): 716–723. https://doi.org/10.1109/TAC.1974.1100705.
Chen, X., and G. Huang. 2010. “Estimation of probabilistic extreme wind load effects: Combination of aerodynamic and wind climate data.” J. Eng. Mech. 136 (6): 747–760. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000118.
Chen, X., and A. Kareem. 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).
Cook, N. J., and J. R. Mayne. 1979. “A novel working approach to the assessment of wind loads for equivalent static design.” J. Wind Eng. Ind. Aerodyn. 4 (2): 149–164. https://doi.org/10.1016/0167-6105(79)90043-6.
Cook, N. J., and J. R. Mayne. 1980. “A refined working approach to the assessment of wind loads for equivalent static design.” J. Wind Eng. Ind. Aerodyn. 6 (1–2): 125–137. https://doi.org/10.1016/0167-6105(80)90026-4.
Cooke, R. M., H. Joe, and K. Aas. 2010. “Vine arise.” Chap. 3 in Dependence modeling, edited by D. Kurowicka and H. Joe, 37–71. Singapore: World Scientific.
Cope, A. D., K. R. Gurley, M. Gioffre, and T. A. Reinhold. 2005. “Low-rise gable roof wind loads: Characterization and stochastic simulation.” J. Wind Eng. Ind. Aerodyn. 93 (9): 719–738. https://doi.org/10.1016/j.jweia.2005.07.002.
Ding, J., and X. Chen. 2014. “Assessment of methods for extreme value analysis of non-Gaussian wind effects with short-term time history samples.” Eng. Struct. 80 (Dec): 75–88. https://doi.org/10.1016/j.engstruct.2014.08.041.
Fawad, M., T. Yan, L. Chen, K. Huang, and V. P. Singh. 2019. “Multiparameter probability distributions for at-site frequency analysis of annual maximum wind speed with L-moments for parameter estimation.” Energy 181 (Aug): 724–737. https://doi.org/10.1016/j.energy.2019.05.153.
Genest, C., and A. C. Favre. 2007. “Everything you always wanted to know about copula modeling but were afraid to ask.” J. Hydrol. Eng. 12 (4): 347–368. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(347).
Gioffre, M., V. Gusellaa, and M. Grigoriu. 2000. “Simulation of non-Gaussian field applied to wind pressure fluctuations.” Probab. Eng. Mech. 15 (4): 339–345. https://doi.org/10.1016/S0266-8920(99)00035-1.
Gumbel, E. J., and C. K. Mustafi. 1967. “Some analytical properties of bivariate extremal distributions.” J. Am. Stat. Assoc. 62 (318): 569–588. https://doi.org/10.1080/01621459.1967.10482930.
Gumley, S. J., and C. J. Wood. 1982. “A discussion of extreme wind-loading probabilities.” J. Wind Eng. Ind. Aerodyn. 10 (1): 31–45. https://doi.org/10.1016/0167-6105(82)90052-6.
Harris, R. I. 1982. “An improved method for the prediction of extreme values of wind effects on simple buildings and structures.” J. Wind Eng. Ind. Aerodyn. 9 (3): 343–379. https://doi.org/10.1016/0167-6105(82)90023-X.
Harris, R. I. 2004. “Discussion of ‘Specification of the design wind load based on wind tunnel experiments’ [J. Wind. Eng. Ind. Aerodyn. 91 (2003) 527–541].” J. Wind Eng. Ind. Aerodyn. 92 (1): 71–76. https://doi.org/10.1016/j.jweia.2003.10.001.
Harris, R. I. 2005. “A new direct version of the Cook–Mayne method for wind pressure probabilities in temperate storms.” J. Wind Eng. Ind. Aerodyn. 93 (Jul): 581–600. https://doi.org/10.1016/j.jweia.2005.05.004.
Ho, T. C. E., D. Surry, D. Morrish, and G. A. Kopp. 2005. “The UWO contribution to the NIST aerodynamic database for wind loads on low buildings: Part 1. Archiving format and basic aerodynamic data.” J. Wind Eng. Ind. Aerodyn. 93 (1): 1–30. https://doi.org/10.1016/j.jweia.2004.07.006.
Holmes, J. D., and L. S. Cochran. 2003. “Probability distributions of extreme pressure coefficients.” J. Wind Eng. Ind. Aerodyn. 91 (7): 893–901. https://doi.org/10.1016/S0167-6105(03)00019-9.
Hong, H. P., S. H. Li, and T. G. Mara. 2013. “Performance of the generalized least-squares method for the Gumbel distribution and its application to annual maximum wind speeds.” J. Wind Eng. Ind. Aerodyn. 119 (Aug): 121–132. https://doi.org/10.1016/j.jweia.2013.05.012.
Huang, G., X. Ji, Y. Luo, and K. R. Gurley. 2016. “Damage estimation of roof panels considering wind loading correlation.” J. Wind Eng. Ind. Aerodyn. 155 (Aug): 141–148. https://doi.org/10.1016/j.jweia.2016.05.009.
Huang, G., X. Ji, H. Zheng, Y. Luo, X. Peng, and Q. Yang. 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.
Hui, Y., Y. Tamura, and Q. Yang. 2017. “Estimation of extreme wind load on structures and claddings.” J. Eng. Mech. 143 (9): 04017081. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001304.
Hult, H., and F. Lindskog. 2002. “Multivariate extremes, aggregation and dependence in elliptical distributions.” Adv. Appl. Probab. 34 (3): 587–608. https://doi.org/10.1239/aap/1033662167.
Ji, X., G. Huang, F. Wu, and Z.-H. Lu. 2020. “Wind-induced hazard assessment for low-rise building envelope considering potential openings.” J. Struct. Eng. 146 (4): 04020039. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002553.
Ji, X., G. Huang, X. Zhang, and G. A. Kopp. 2018. “Vulnerability analysis of steel roofing cladding: Influence of wind directionality.” Eng. Struct. 156 (Feb): 587–597. https://doi.org/10.1016/j.engstruct.2017.11.068.
Ji, X., B. Zhang, Z.-H. Lu, and Y.-G. Zhao. 2021. “Fragility assessment of typhoon-induced hazard to roof sheathing panels of low-rise building.” J. Struct. Eng. 147 (7): 04021081. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003016.
Kwon, D. K., and A. Kareem. 2011. “Peak factors for non-Gaussian load effects revisited.” J. Struct. Eng. 137 (2): 1611–1619. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000412.
Lebrun, R., and A. Dutfoy. 2009. “An innovating analysis of the Nataf transformation from the copula viewpoint.” Probab. Eng. Mech. 24 (3): 312–320. https://doi.org/10.1016/j.probengmech.2008.08.001.
Li, D.-Q., X.-S. Tang, K.-K. Phoon, Y.-F. Chen, and C.-B. Zhou. 2013. “Bivariate simulation using copula and its application to probabilistic pile settlement analysis.” Int. J. Numer. Anal. Methods Geomech. 37 (6): 597–617. https://doi.org/10.1002/nag.1112.
Liu, P., and A. Der Kiureghian. 1986. “Multivariate distribution models with prescribed marginals and covariances.” Probab. Eng. Mech. 1 (2): 105–112. https://doi.org/10.1016/0266-8920(86)90033-0.
Lü, T.-J., X.-S. Tang, D.-Q. Li, and X.-H. Qi. 2020. “Modeling multivariate distribution of multiple soil parameters using vine copula model.” Comput. Geotech. 118 (Feb): 103340. https://doi.org/10.1016/j.compgeo.2019.103340.
Luo, Y., and G. Huang. 2017. “Characterizing dependence of extreme wind pressures.” J. Struct. Eng. 143 (4): 04016208. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001699.
Matsumoto, M., H. Shirato, K. Araki, T. Haramura, and T. Hashimoto. 2003. “Spanwise coherence characteristics of surface pressure field on 2-D bluff bodies.” J. Wind Eng. Ind. Aerodyn. 91 (1): 155–163. https://doi.org/10.1016/S0167-6105(02)00342-2.
Naess, A., and O. Gaidai. 2009. “Estimation of extreme values from sampled time series.” Struct. Saf. 31 (4): 325–334. https://doi.org/10.1016/j.strusafe.2008.06.021.
Nelsen, R. B. 2006. An introduction to copulas. New York: Springer.
Pearson, K. 1920. “Notes on the history of correlation.” Biometrika 13 (1): 25–45. https://doi.org/10.1093/biomet/13.1.25.
Sadek, F., and E. Simiu. 2002. “Peak non-Gaussian wind effects for database-assisted low-rise building design.” J. Eng. Mech. 128 (5): 530–539. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:5(530).
Salinas-Gutiérrez, R., A. Hernández-Aguirre, and E. R. Villa-Diharce. 2014. “Copula selection for graphical models in continuous Estimation of Distribution Algorithms.” Comput. Stat. 29 (3): 685–713. https://doi.org/10.1007/s00180-013-0457-y.
Sklar, A. 1959. Fonctions de répartition à n dimensions et leurs marges. Saint-Denis, France: Université Paris 8.
Zhang, B., X. Ji, Y. Zhao, and G. Huang. 2021. “Wind hazard analysis of low-rise building envelopes considering typhoon duration effect.” China Civ. Eng. J. 54 (6): 53–61. https://doi.org/10.15951/j.tmgcxb.2021.06.006.
Zhang, Z., and B. Zhu. 2016. “Copula structured M4 processes with application to high-frequency financial data.” J. Econ. 194 (2): 231–241. https://doi.org/10.1016/j.jeconom.2016.05.004.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 21, 2022
Accepted: Aug 18, 2022
Published online: Oct 26, 2022
Published in print: Jan 1, 2023
Discussion open until: Mar 26, 2023
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.