Extreme Value Theory And Its Application On Wind Load And Response Of Structure

Owing to the development of the national economy and the advance in science and technology,long-span bridges with types of suspension bridges and cable-stayed bridges continue to spring up for satisfying the requirement of the transportation.Since the span of the bridges increases,there is a reduction of the structural stiffness.As a result,the bridge is sensitive to wind action.Hence the wind-resistant design becomes a crucial part in the bridge design.In the wind-resistant design,it is necessary to estimate the extreme wind speed,wind load and wind-induced response properly to make sure the safety and reliability of the bridge structure.For the sake of the estimation of the extreme value,scholars proposed a series of methods.In these methods,the applied samples can be mainly divided into three types:extreme samples,samples over threshold and parent samples.For the calculation of the extreme wind load,parent samples are usually adopted.Among the methods based on parent samples,Davenport's formula and Hermite polynomial model are generally discussed.Since they are based on parent data to estimate the extreme value,their accuracy needs to be further evaluated according to actual extreme data.Different from the calculation of the extreme wind load,the extreme wind speed is often estimated through extreme samples directly,which are selected from long-term wind speed data of neighboring meteorological station.Thus the distribution of the extreme wind speed can be fitted based on one of three extreme value distributions(i.e.,Frechet distribution,Gumbel distribution,and Weibull distribution).Nevertheless,for the region with complex terrain such as southwestern mountainous area,it is usually unsuitable to establish a meteorological station.Hence the observational data of the wind speed are not available in these areas.For the reasonable estimation of the design wind speed about a proposed bridge located in these areas,a stationary observation station can be established in the bridge site to carry out field measurement.In consideration of the actual situation,the measured data are short-term in general.Therefore it is desired to investigate the issue that how to calculate the design wind speed based on short-term measured data.In addition,because the wind has directionality,the extreme wind speed and wind-induced response are related with the wind directionality.The simplification is adopted previously to consider the wind directionality.For providing a more reasonable estimation of the extreme wind speed and extreme response,the influence of the wind directionality should be analyzed in further.The research of the dissertation is concentrated on the extreme wind speed,wind load and response.The main work is summarized as follows.Firstly,the calculation methods of the extreme value are briefly introduced.Then Davenport's formula and Hermite polynomial model(HPM),which are commonly applied in the calculation of the extreme wind load,are reviewed.In the specification,Davenport's formula is usually utilized.However,when the wind load is non-Gaussian,it may underestimate the corresponding extreme value.Hence HPM is proposed for the extreme value of non-Gaussian wind load.Nevertheless,both Davenport's formula and HPM are based on parent data.Thus their accuracy should be further evaluated by actual extreme data.Since long-term wind load data of the bridge are scarce,the data on low-rise buildings are applied instead for analysis.Based on wind tunnel data,the accuracy of Davenport's formula and HPM is evaluated in detail,which can provide a reference for the reasonable estimation of extreme wind load.Meanwhile,in the review of HPM,it can be found that recent methods for estimation of parameters in HPM need to be improved for engineering practice.Hence,based on HPM,the semi-analytical formula for estimation of non-Gaussian extreme wind load is proposed.The accuracy of the formula is evaluated and compared with current calculation methods of HPM through wind tunnel data.Secondly,considering the dependence of extreme wind speed,wind load and response among different wind directions or positions,the modeling of multivariate extreme value is involved.Hence,three method used to describe the dependence of extreme value are introduced,including multivariate extreme value theory,copula function and Nataf transformation.Meanwhile,according to the asymptotic property for extreme values of the Gaussian random vector,the counterparts of the non-Gaussian random vector is discussed.Wind tunnel data on low-rise buildings are used as an example for illustration of the aforementioned methods in the application of the modeling of multivariate extreme value.This content will be utilized in the subsequent analysis about extreme wind speed and extreme buffeting response of bridge considering the wind direction.Measured wind speed data of temporary observation station for Puli Bridge site with more than two years are adopted to investigate the issue of the calculation of the design wind speed through short-term data.Based on these data,various methods are applied to calculate design wind speed,including block maximum method,peak-over-threshold method,the method based on the dependence of wind speeds and virtual standard meteorological station method.Through the comparison of the results by these methods,the proposal is provided for the estimation of design wind speed under the condition of short-term measured data.It can be helpful for the wind-resistant design of the bridge.At last,since there is difference between the terrain of the observation station and that of the bridge,the design wind speed is modified based on numerical simulation.In general,the wind directionality is neglected in the estimation of extreme wind speed based on meteorological data.In the analysis for buffeting response of the bridge,the wind direction is supposed to be normal to the bridge axis,which means the wind directionality is also not considered.Nevertheless,the wind characteristics under various directions may be different.Meanwhile,the difference generally exists among wind-induced responses of strucutres under different directions.To explore the effect of the wind direction,based on the aforementioned analysis method of multivariate extreme value,the extreme wind and extreme response considering the wind directionality are analyzed.The result will contribute to the better evaluation of the design wind speed and extreme wind-induced response for the bridge.