不同平均時間風速之機率分佈特性及其對設計風速模擬之影響

我國處於多颱風及地震之地理位置，高層建築在設計上不僅要考慮到耐震，風力對於結構物的影響也是相當重要的一環。台灣目前的建築物耐風設計規範以50年回歸期之10分鐘平均風速進行設計風速值的估算。然而不同國家所採用的平均風速時間不同，不同平均時間間應當具有恆定的轉換模式，如Durst Curve用以計算不同平均時間的風速值轉換。本研究首先利用日本的五個測站資料，分別為八戶市、東京、名古屋、大阪、鹿兒島，統計2001年至2007年年間，經過測站三百公里以內之颱風篩選出來，並計算出每個經過颱風之平均值、標準差、偏度、峰度之基本統計特性，再將所有篩選出之颱風的統計特性合併計算出四個區域統計特性，並利用MATLAB產生高斯分布亂數，且採用Kwon and Kareem 及 Kanda and Lo所提出的非高斯轉換式以及韋伯模擬，產生出一個模擬颱風的一個模擬極值，也就是模擬風速最大值。利用每一百個極值做一累積機率密度分佈函數曲線。重複一百組分佈曲線並取其平均線為代表此測站特性的累積機率密度分佈函數曲線，觀察其非高斯特性的分佈狀況。將其尾部特性分類為甘保分佈(Gumbel distribution)、韋伯分佈(Weibull distribution)、弗雷歇分佈(Frechet distribution),探討其尾部特性。接著，利用Durst curve 公式中之平均時間長短對平均風速轉換公式，將1分鐘平均時間模擬風速轉換成10分鐘平均時間理論風速以及60分鐘平均時間模擬風速轉換成10分鐘平均時間理論風速，探討其理論公式轉換過後之10分鐘平均時間理論風速與模擬之10分鐘平均時間模擬風速之關係。為了瞭解非高斯特性對於平均時間轉換的影響性，另外針對各測站的颱風平均風速值及標準差值進行高斯極值模擬，並與非高斯結果進行比較。最後列表找出不同回歸周期下的轉換誤差百分比，並標示出採用Durst Curve可能出現的不穩定性的原因。

關鍵字

極值分佈；統計特性；非高斯轉換； The Durst curve ；風工程

並列摘要

Taiwan is in the geographical position of multiple typhoons and earthquakes. The design of high-rise buildings must not only consider earthquake resistance, but also the impact of wind on structures. Taiwan's current building wind resistance design specification estimates the design wind speed value based on the 10-minute average wind speed during the 50-year regression period. However, the average wind speed time used in different countries is different. There should be a constant conversion mode between different averaging time. For example, Durst Curve is used to calculate the wind speed value conversion at different averaging time. This study first used the five stations in Japan, namely Hachinohe, Tokyo, Nagoya, Osaka, and Kagoshima. The statistics were collected from the typhoon within 300 kilometers of the station from 2001 to 2007, and calculated. Each of the basic statistical characteristics of the typhoon's mean, standard deviation, skewness, and kurtosis, and then combine the statistical characteristics of all the selected typhoons to calculate the statistical characteristics of the four regions, and use MATLAB to generate Gaussian distribution random numbers, and Using the non-Gaussian transformations proposed by Kwon and Kareem and Kanda and Lo, and the Weber simulation, a simulated extremum of the simulated typhoon is generated, which is the maximum simulated wind speed. A cumulative probability density distribution function curve is made using every hundred extreme values. Repeat one hundred sets of distribution curves and take the average line as the cumulative probability density distribution function curve representing the characteristics of this station, and observe its non-Gaussian distribution. The tail characteristics are classified into Gumbel distribution, Weibull distribution, and Frechet distribution, and the tail characteristics are discussed. Then, using the average time length in the Durst curve formula, the average wind speed conversion formula is converted into a 10-minute average time simulated wind speed and a 60-minute average time simulated wind speed converted into a 10-minute average time theoretical wind speed. The relationship between the theoretical wind speed of the 10-minute average time after the theoretical formula conversion and the simulated 10 minute average time simulated wind speed. In order to understand the influence of non-Gaussian on the average time conversion, Gaussian extremum simulations were performed for the typhoon mean wind speed values and standard deviations of each station, and compared with non-Gaussian results. The final list identifies the percentage of conversion error for different regression periods and indicates the reasons for the instability that may occur with the Durst Curve.