Specification of the design wind load based on wind tunnel experiments considering the statistical uncertainties due to limited ensemble sizes

• Applicant: Privatdozent Dr.-Ing. Michael Kasperski
• Subject Area: Structural Engineering, Building Informatics and Construction Operation
• Term: from 2015 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 282761584

For the specification of the design wind load based on wind tunnel experiments statistical uncertainties have to be considered which are obtained from confined ensembles. The basic strategy for meeting a chosen confidence interval uses an adjusting factor which especially depends on the ensemble size. A corresponding procedure is implemented e.g. in the Eurocode DIN-EN 1990:2010-12 in the annex Design by testing for the specification of the design value of the resistance. The project aims in developing the adjusting factors for an optimal method for the estimation of the design value of the aerodynamic coefficient. While these adjusting factors guarantee that the ratio of unsafe solutions remains constant independent of the ensemble size, the ratio of uneconomic solutions in terms of considerable overestimated design wind loads increases for decreasing ensemble size. Fundamentally new, this ratio is developed to obtain an aid to decision-making in regard to the required number of wind tunnel runs following the basic principle as few runs as possible and as many runs as necessary. Opposite to the resistance side, there is no uniform target fractile value for the design value of the aerodynamic coefficients; the target value rather depends on the variation coefficient of the extremes. Consequently, adjusting factors are required depending on the ensemble size and the variation coefficient. Two alternative approaches are available for the estimation of the design value. The first approach directly uses independent extremes, either picked from single runs or from subsets. The basic advantage of using subsets lies in an enlarged ensemble size, basically leading to an increased statistical stability. However, for subsets the target fractile value increases, leading to decreasing statistical stability. Furthermore, for subsets becoming shorter and shorter there is the basic danger that the subset is no longer representative. Fundamentally new, an enlarged ensemble size is obtained by peaks-over-threshold sampling. Estimations especially are performed based on the Best Linear Unbiased Estimator (BLUE). The second approach estimates the design values based on an equivalent normal distribution using the Rice method. The fundamental elements of this approach are the estimation of the translation rule using CDF-mapping or Hermite polynomials, and the estimation of the cycling rate either using the variance of the time derivative or the frequency-weighted integration of the estimated spectral density function. The optimal method is obtained by comparing quality features of the estimations obtained by the different methods, especially the ratio of considerable uneconomic estimations.

• DFG Programme: Research Grants