Accurate estimation of extreme values of non-Gaussian wind pressures is important for building structural wind resistance design. Due to its ease of use, translation process method is widely used to estimate the non-Gaussian extremes. Hermite polynomial model (HPM), Johnson transformation model (JTM) and Shifted generalized lognormal distribution (SGLD) model are representatives of the translation function used in the translation process method. The model coefficients in three models are usually estimated based on the first four statistical moments from data, thus the three models are described as moment-based translation function models. In practical design, the length of wind pressure data used for analysis is often limited, resulting in sampling errors in the first four moments. These sampling errors will subsequently cause some sampling errors of the estimated extreme values. However, the differences among the sampling errors in moments and uncertainties in estimation of extremes by these three models are unclear. To compare the sampling errors in estimation of extremes by three models, HPM、JTM and SGLD are firstly introduced in this study; Next, the method of estimating the sampling error of peak factors based on moment-based translation function models are given; Then, the sampling errors of moments and peak factors by three models are given and compared based on the theoretical analysis. Finally, the performance of sampling errors in HPM, JTM and SGLD are compared with each other using a very long wind pressure data. Results showed the performance of estimating sampling errors of non-Gaussian extremes by HPM is generally more satisfactory compared to that by JTM and SGLD. The results can provide the guidance for reasonable selection of models.
Key words
Non-Gaussian wind pressures /
Extremes /
Translate process method /
Hermite polynomial model /
Johnson
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References
[1] Kumar, K.S. and Stathopoulos, T. Wind loads on low building roofs: A stochastic perspective [J]. Journal of Structure Engineering, 2000, 126(8), 944–956.
[2] Ding, J. and Chen, X. Assessment of methods for extreme value analysis of non-Gaussian wind effects with short-term time history samples [J]. Engineering Structures, 2014, 80:75-88.
[3] Grigoriu， M. Crossings of Non-Gaussian Translation Processes [J]. Journal of Engineering Mechanics, 1984, 110(4):610-620.
[4] Winterstein， S. R. Nonlinear vibration models for extremes and fatigue [J]. Journal of Engineering Mechanics, 1988, 114(10):1772–1790.
[5] Johnson, N.L. Systems of Frequency Curves Generated by Methods of Translation [J]. Biometrika, 1949, 36(1-2):149-176.
[6] Low, Y.M. A new distribution for fitting four moments and its applications to reliability analysis [J]. Structural Safety, 2013, 42(3):12-25.
[7] Li, Y., and Ellingwood, B.R. Hurricane damage to residential construction in the US: Importance of uncertainty modeling in risk assessment. [J]. Engineering structures, 2006, 28(7), 1009–1018.
[8] Yang, Q. and Tian, Y. A model of probability density function of non-Gaussian wind pressure with multiple samples [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2015, 140, 67–78.
[9] Huang, G., Ji, X., Zheng, H., Luo, Y., Peng, X., and Yang, Q. Uncertainty of peak value of non-Gaussian wind load effect: analytical approach [J]. Journal of Engineering Mechanics, 2017, 144(2), 04017172.
[10] Yang, Q., Chen, X., and Liu, M. Bias and sampling errors in estimation of extremes of non-Gaussian wind pressures by moment-based translation process models [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2019, 186, 214-233.
[11] Winterstein, S.R., Kashef, T. Moment-Based Load and Response Models With Wind Engineering Applications[J]. Journal of Solar Energy Engineering, 2000, 122(3):122-128.
[12] Ding, J., Chen, X. Moment-based translation model for hardening non-Gaussian response processes[J]. Journal of Engineering Mechanics, 2015, 14(2):06015006.
[13] Hill, I.D., Hill, R., Holder, R.L. Algorithm AS 99: Fitting Johnson Curves by Moments[J]. Journal of the Royal Statistical Society, 1976, 25(2):180-189.
[14] Liu, M., Chen, X., and Yang, Q. Estimation of Peak Factor of Non-Gaussian Wind Pressures by Improved Moment-Based Hermite Model[J]. Journal of Engineering Mechanics, 2017, 143(7).
[15] Davenport, A. G. Note on the distribution of the largest value of a random function with application to gust loading[J]. Proceedings of the Institution of Civil Engineers, 1964, 28(2):187-196.
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