Preconditioning wind speeds for standardised structural design

Abstract The statistical treatment of historical wind data has a significant impact on the design wind load, standardisation of which requires characterisation of the wind climate across a large region. Improved spatial resolution is afforded by asymptotic extreme value distributions as they require a lower temporal data resolution. The Gumbel distribution is shown to be preferred, given the available South African data, according to the Akaike Information Criterion. However, its relative inflexibility means that estimates of small probability fractiles could be significantly biased, a difficulty illustrated by disagreement on which is more appropriate: fitting the Gumbel distribution to the wind speed versus to the wind-induced pressure (squared wind speed). By generalising this choice to the problem of finding the most appropriate real-valued exponent to raise the wind speeds by (i.e. not just 1 or 2), this paper aims to reduce this modelling-bias. As estimates of this exponent parameter from a single station would have low confidence given the typical quantity of data, a method of estimating the exponent that maximises the likelihood of observing the entire dataset is developed instead. The method is demonstrated using over 3500 annual gust measurements at 131 stations throughout South Africa, the most likely exponent is found to be 1.59 with confidence intervals sufficiently narrow to reject fitting to both the wind speed as well as to the squared wind speed. It is shown that using an exponent of 1.6 in deriving the design wind load for structural design would result in a substantial reduction in modelling-bias, providing a suitable baseline for future South African loading standards.

[1]  N. Cook,et al.  Extreme wind speeds in mixed climates revisited , 2003 .

[2]  Hp Hong,et al.  Sample size effect on the reliability and calibration of design wind load , 2016 .

[3]  Peter J. Vickery,et al.  ASCE 7-10 Wind Loads , 2011 .

[4]  R. V. Milford.  Annual maximum wind speeds from parent distribution functions , 1987 .

[5]  A. Jimoh,et al.  Wind distribution and capacity factor estimation for wind turbines in the coastal region of South Africa , 2012 .

[6]  Emil Simiu,et al.  Recent approaches to extreme value estimation with application to wind speeds. Part I: the pickands method , 1992 .

[7]  Nicholas J. Cook,et al.  Towards better estimation of extreme winds , 1982 .

[8]  H. Hong.  Application of the Box-Cox power transformation in extreme value analysis of wind speed , 2015 .

[9]  Giovanni Solari,et al.  Extreme wind speeds from long-term synthetic records , 2013 .

[10]  Giuliano Di Baldassarre,et al.  Model selection techniques for the frequency analysis of hydrological extremes , 2009 .

[11]  Alan G. Davenport,et al.  The relationship of reliability to wind loading , 1983 .

[12]  MorrisR.,et al.  Basis for recommending an update of wind velocity pressures in Canadian design codes , 2014 .

[13]  Irving I. Gringorten,et al.  A plotting rule for extreme probability paper , 1963 .

[14]  Nicholas J. Cook,et al.  The parent wind speed distribution: Why Weibull? , 2014 .

[15]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  Celeste Viljoen,et al.  Uncertainties in the South African wind load design formulation , 2018 .

[17]  H. Hong,et al.  Performance of the generalized least-squares method for the Gumbel distribution and its application to annual maximum wind speeds , 2013 .

[18]  Jochen Köhler,et al.  On the probabilistic representation of the wind climate for calibration of structural design standards , 2018 .

[19]  Nicholas John Cook,et al.  Postscript to “Exact and general FT1 penultimate distributions of extreme wind speeds drawn from tail-equivalent Weibull parents” , 2008 .

[20]  H. Gulvanessian,et al.  Eurocodes: using reliability analysis to combine action effects , 2005 .

[21]  Jean Palutikof,et al.  A review of methods to calculate extreme wind speeds , 1999 .

[22]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[23]  Bruce R. Ellingwood,et al.  Wind Load Statistics for Probability-Based Structural Design , 1999 .

[24]  Nicholas J. Cook,et al.  Exact and general FT1 penultimate distributions of extreme wind speeds drawn from tail-equivalent Weibull parents , 2004 .

[25]  R. V. Milford.  Annual maximum wind speeds for South Africa : technical paper , 1987 .

[26]  B. J. Vickery,et al.  Extreme wind speeds in mixed wind climates , 1978 .

[27]  Clifford M. Hurvich,et al.  Regression and time series model selection in small samples , 1989 .

[28]  Celeste Viljoen,et al.  Reliability assessment of the South African wind load design formulation , 2018 .

[29]  David Walshaw,et al.  Getting the Most From Your Extreme Wind Data: A Step by Step Guide , 1994, Journal of research of the National Institute of Standards and Technology.

[30]  E. Simiu,et al.  Extreme wind load estimates based on the Gumbel distribution of dynamic pressures: an assessment , 2001 .