Estimation of probabilistic extreme wind load effect with consideration of directionality and uncertainty

Estimation of wind load effects with various mean recurrence intervals (MRIs) requires consideration of uncertainty and directionality of wind climate, aerodynamics and structural dynamics. The approaches addressing the directionality effect are either unable to be used for parametric study of uncertainties of wind load effects due to lack of analytical formulations or inaccurate in prediction. On the other hand, the approaches to quantify the influence of uncertainties of wind speed and wind load effect are not formulated for the consideration of directionality. The objective of this research is to establish new and refined approaches to include the considerations of directionality and uncertainty in a unified framework, which also offer reasonable predictions of wind load effect of given MRIs. An attempt of using long-term wind speed record is conducted for the purpose of reducing uncertainty of wind climate modeling. Information of various wind speed record resources is investigated. Yearly maximum wind speeds from these resources are standardized and compared. The long-term wind speed record that contains wind speeds from multiple wind speed resources should be cautiously used with a further comprehensive investigation of the data. A reasonable choice of a period of wind speed record at a particular station is presented and the wind speed record is processed as the example wind climate information for the analysis in the following studies. A multivariate approach is proposed to estimate wind load effects for various MRIs with consideration of both directionality and uncertainty of wind speed and wind load effects within a unified framework. The joint probability distribution model of directional extreme wind speeds is established based on extreme wind speed data using multivariate extreme value theory with Gaussian Copula. The distribution of yearly maximum wind load effect is then calculated through the exceeding probability of directional wind speeds over the corresponding levels. The uncertainty of extreme response conditional on wind speed and direction is further considered using the theorem of conditional probability. The proposed analytical framework can be considered as an analytical formulation of the existing approach based on historical directional wind speed data, but with an additional capability of accounting for the uncertainty of extreme response conditional on wind speed and direction. It can also be regarded as an extension of the existing fully probability methods with an additional capability of accounting for directionality. The proposed approach is validated by the predictions with those from the existing approach. The characteristics of directionality factor for wind load effects are discussed. Finally, the influence of uncertainty of extreme response conditional on wind speed and direction is further examined. An improved understanding of the influence of dependence between directional wind speeds in the estimation of probabilistic extreme wind load effect is provided based on the proposed multivariate approach. Several factors that influence the prediction with and without consideration of dependence are discussed by using Gaussian copula model. Directional wind speed masking problem is introduced and the significance of an empirical treatment to the wind effect estimation is discussed. The difference of brought by dependence structure is discussed by a comparison between multivariate Gaussian and Gumbel copula models. The necessity of using multivariate approach is discussed and a simplified method is proposed to account for directional dependence which not only leads to the accurate solution but also reduces calculation effort. Discussion is also made on the partition of directional sectors which concerns the balance of number of sectors and modeling uncertainty. A refined process upcrossing rate approach is introduced to improve the accuracy of prediction by replacing the Weibull distribution with a mixed distribution model for the parent distribution of mean wind speed. Within this mixed model, the distribution below a prescribed wind speed threshold is given by an empirical distribution estimated from the observation data directly, while above the threshold, it is described in terms of the General Pareto distribution (GPD). The performance of the mixed distribution model is examined in estimating the yearly maximum distributions of wind speeds in each direction and regardless of direction. It is further investigated in estimating the wind load effect of buildings with consideration of directionality effect. The uncertainty of wind load effect at given wind speed and direction is further accounted for. Numerical examples for buildings with various response characteristics demonstrate the effectiveness of the proposed framework. An extension of a fully probabilistic method for the estimation of extreme wind speed of given MRIs with an additional capability of consideration of directionality is derived. The yearly maximum distributions of wind load effect in each direction are determined by the full-order method without consideration of directionality which is then weighted summed with weighting factors in terms of ratio of independent numbers of each direction and regardless of direction and the frequency of occurrence of each direction. Independent storm maximum wind speeds are selected for the estimation of the yearly maximum wind speed distribution and the independent numbers. The influence of choice of threshold on the determination of weighting factors is discussed. The performance of the method is investigated by comparing the predictions with those determined from existing methods that based on extreme data. This research provides a novel solution for the structural design concerning the directionality and uncertainty effect. With the in-depth investigation into the directional dependence structure of wind speeds, this research not only produces a more accurate result for a risk-consistent and cost-effective structural design but also assists the engineers in the decision making of laboratory tests and interpretation of wind climate information. Better understandings of the process upcrossing rate approach and of the fully probabilistic methods benefit users of these approaches with a more accurate long-term prediction. Moreover, the introduction of multivariate extreme value theory enables potential applications to other engineering problem such as performance-based design of structures for multiple hazards.