基于广义Pareto分布的波高极值序列频率分析

应用广义Pareto分布(GPD)分析超阈值波高序列的设计值。以位于美国北卡罗来纳州的FRF历时32年连续测量的逐日波高序列为例,检验了不同波高阈值样本的泊松分布,采用多种方法综合确定最佳阈值的拟合优度指标。对最优广义Pareto分布和GEV分布及P-Ⅲ分布推算的波高重现水平做了对比分析。得到以下结论:(1)波高的GPD属于短尾型分布;(2)拟合优度指标表明构建的波高GPD模型普遍优于GEV和P-Ⅲ型;(3)GPD的参数估计方法对设计波高的计算结果有较大影响。     

波高的长期极值统计分布

通过对国内外常用的４种极值波高分布模式的拟合与比较,得到了以下结论：（１）由于地区差异,港口工程技术规范给出的一单一模式并非具有普遍性,对同一工程应该采用多种理论分布进行计算比较,从中选择最佳模式。（２）应用麦奎尔特法拟合Ｗｅｉｂｕｌｌ分布实现了对未知参数的一举寻优,解的收敛速度快,结果稳定且精度高。同时对其它几种分布实现了资料的微机化处理;（３）本文算例用４种极值分布对不同重视值波高进行了比较,     

设计波高推算的一种新模型

考虑台风影响海域的设计波高,结合复合极值理论和最大熵原则,构造了1种新型的具有4个待定参量和1个台风频次参量的poisson-最大熵分布函数模型,并推导出求解参数的方程组,参数的数值解可通过年极值实测数据的期望、方差、偏度和峰度得到.以黄海某观测站26 a极值波高的实测数据为例计算了新模型中4个待定参量和多年一遇设计波高,并与传统常用计算方法得到的结果进行比较.比较表明,新模型相比传统方法具有一定的优势.     

复合极值分布的参数估计及其在工程设计中的应用

在海洋工程、水利工程等建筑工程中，合理地确定多年一遇波高、洪水量等，对于建筑物设计的安全和造价问题是十分重要的。兼顾安全和费用两方面的要求，就得在各种各样的计算方法中选择较为理想的方法进行推算。就海浪波高设计而言，     

江苏滨海海域海上风电场的极值波高推算

为了给江苏滨海海域海上风电场的结构设计提供更为合理的设计参数,本文利用定量分析法对比分析了采用不同推算方法推算得到的工程海域极值波高,讨论了不同推算方法的差异及影响。结果表明：采用年极值法、条件极值法（包括风暴统计法、阈值上限法）和组合法推算出的工程海域极值波高受理论频率曲线、热带风暴年均频次、极端设计风速和特定水位的影响较大。其中,热带风暴年均频次主要影响风暴统计法推算的结果,当热带风暴年均频次不小于1时,推算的结果趋于稳定,相对偏差小于5%;极端设计风速和特定水位主要影响组合法推算的结果,极端设计风速的选择主要影响极值波高在各个方向上的分布,特定水位的叠加主要影响极值波高的幅值;对于非特定水位下的极值波高,利用条件极值法中的风暴统计法推算的结果最大,为6.55 m;利用年极值法中P-Ⅲ型曲线推算的结果最小,为5.48 m;两者相对偏差约20%;对于特定水位下的极值波高,利用组合法推算出的NW—SE方向极值波高与水位呈正相关,即叠加正水位时,极值波高增大,叠加负水位时,极值波高减小,幅值变化可达±15%;且极值波高的方向分布与所采用的极端设计风速的方向分布相同,利用极值波高对应的设计...     

广义帕雷托分布在波浪极值推算中的应用

以CCMP风场(1988年1月~2010年12月)为驱动,本文采用第三代海浪数值模式SWAN对中国海海区进行风浪场的数值模拟,并利用浮标资料对驱动风场和计算有效波高进行验证。根据模拟的结果分别采用广义帕雷托分布(GPD)和常用的广义极值分布(GEV)拟合累积频率曲线并进行效果检验,进而分析和比较2种分布的优缺点,并运用广义帕雷托分布(GPD)模型进行重现期波要素的推算,分析GPD模型的应用前景。     

极值波高Weibull分布的参数估计方法对比分析

介绍了三参数威布尔分布及其4种参数估计方法：极大似然估计法、相关系数优化法、灰色估计法和概率权重矩法。利用蒙特卡罗法对以上参数估计方法进行不同样本尺度的模拟,通过偏差、标准差和均方误差对比分析各种方法的特点、精度和适用性。运用上述方法结合涠洲站34a实测年极值波高,推算涠洲岛的设计波高,从相关系数、均方根误差和Q统计值分析各种方法的差异及优劣性。结果表明,小样本情况下各估计法的差别较大,而大样本时差别较小,极大似然估计法能较好拟合各种大小的样本,相关系数优化法次之;选取合适的经验频率会提高参数估计精度;各种参数估计方法计算而得的设计波高相差不大,其中极大似然估计法的精度最高     

年极值波高的分布特点及其频率曲线的选配

对海岸工程或海洋工程结构物必须考虑防御波浪的能力,因为它关系到工程的安全和造价.为了防止最大波浪的破坏,就要给出某一重现期的单个极值波浪.重现期波高的推算,许多学者做过探讨.尽管讨论的方法不同,但一致的观点是选取拟合资料最好的分布函数.     

设计波高分布函数比较

利用澳大利亚悉尼观测站连续16年的实测资料,并结合波高阈值法以及年N大波法两种新的采样方法,利用最小二乘法原理,对对数正态分布、Gumbel第一型极值分布、Weibull分布、指数分布和皮尔逊Ⅲ型曲线五种分布函数进行分析和比较,从而选出一种适用的分布函数。同时,文章介绍了一种最新的估计三参数Weibull分布参数的方法。结果表明:三参数Weibull分布函数的相关系数较大,拟合较好,而且均方误也都较小。从而得出结论,三参数Weibull分布函数得到的结果较好,并建议使用该分布函数进行设计波高的计算。     

基于WW3的南海北部有效波高时空变化及其极值重现期估算方法分析

本文基于第3代海浪模式WAVEWATCH III （WW3）模拟的1996–2015年海浪后报数据,分析了南海北部有效波高及其极值的时空变化特征,并采用Pearson-III和Gumbel两种极值分布方法对该区极值波高重现期进行了估算。结果表明,南海北部有效波高的季节变化和空间分布与季风风场基本一致,呈现秋冬高春夏低,并自吕宋海峡西侧向西南降低的特征,与ERA5再分析数据结果高度相似。有效波高极值（简称极值波高）的时空分布特征受时间分辨率强烈影响,采用极值数据的分辨率越高（如逐小时）,所展现的台风型波浪特征越显著。扣除季节变化信号后的有效波高和年极值波高均体现出较强的线性增高趋势,近20年升高的比例分别为7.7%和31.6%,值得警惕和关注。该区多年一遇极值波高存在若干个大值区,且与台风的路径、强度有直接联系,表明台风是引发该区域极端大浪的最主要机制。对比Pearson-III和Gumbel极值分布估算结果发现：若极值波高较低,频率随极值波高升高缓慢降低,此时两种极值分布的估算都比较准确,差异极小,可忽略不计;但当研究时间范围内,某年极值波高远超其他年份时,Pearson-III极值分布估算结果明显高于Gumbel极值分布估算结果,且更接近实际极值波高,即Pearson-III极值分布在此情况下表现更好。本研究表明对于特定海区,在出现超强台风引发极值波高远超出其他年份时,不同计算方法对极值波高的估算差异较大,会显著影响重现期的评估。此外,南海北部年极值波高的强烈增高趋势,也可能给计算未来极值波高重现期和海上工程防护带来不可忽视的影响。     

基于现场实测数据的半潜式平台运动响应分析和极值预测研究

浮式平台承受风浪流等多种海洋环境载荷作用,呈现出复杂的运动学响应状态.通过对"南海挑战号"半潜式平台的实测六自由度响应数据进行分析,采用广义极值分布建立六自由度响应的概率密度和分布模型,并通过K-S(Kolmogorov-Smirnov)检验验证了分布模型的合理性,进而开展了对该平台多年一遇重现期的六自由度响应极值预测研究.通过与平台的初始设计指标进行对比,发现平台的横荡、纵荡等五个自由度表现良好,而垂荡的响应极值超出设计指标,在现场作业中应予以注意研究成果对平台的安全作业具有辅助指导意义,可将预测结果作为极端恶劣海况下,人员提前撤离的辅助决策支持.通过更新平台的监测数据进行极值分析和预测研究可评估平台的性能变化行为.     

A maximum-entropy compound distribution model for extreme wave heights of typhoon-affected sea areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle.The new model is formed by nesting a discrete distribution in a continuous one,having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper.The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea,and the predicted results are compared with those predicted by use of some other compound distribution models.Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.     

基于最大熵原理的非瑞利海浪波高的统计分布

本论文在最大熵原理的基础上,通过解一个条件变分问题导出一种适用于描述非瑞利海浪波高H统计分布的概率密度函数fn(H)=αHre-βHn,用实验室风浪槽中不同风速下和不同风区处实测的36组风浪波高数据对上述概率密度函数进行验证,并与至今仍被广泛应用的瑞利波高概率密度函数加以比较.结果显示瑞利概率密度函数显著地偏离实验数据,而上述概率密度函数则与各组实测波高分布均符合良好.     

Increasing wave heights and extreme value projections: The wave climate of the U.S. Pacific Northwest

Deep-water wave buoy data offshore from the U.S. Pacific Northwest (Oregon and Washington) document that the annual averages of deep-water significant wave heights (SWHs) have increased at a rate of approximately 0.015 m/yr since the mid-1970s, while averages of the five highest SWHs per year have increased at the appreciably greater rate of 0.071 m/yr. Histograms of the hourly-measured SWHs more fully document this shift toward higher values over the decades, demonstrating that both the relatively low waves of the summer and the highest SWHs generated by winter storms have increased. Wave heights associated with higher percentiles in the SWH cumulative distribution function are shown to be increasing at progressively faster rates than those associated with lower percentiles. This property is demonstrated to be a direct result of the probability distributions for annual wave climates having lognormal- or Weibull-like forms in that a moderate increase in the mean SWH produces significantly greater increases in the tail of the distribution. Both the linear regressions of increasing annual averages and the evolving probability distribution of the SWH climate, demonstrating the non-stationarity of the Pacific Northwest wave climate, translate into substantial increases in extreme value projections, important in coastal engineering design and in quantifying coastal hazards. Buoy data have been analyzed to assess this response in the wave climate by employing various time-dependent extreme value models that directly compute the progressive increases in the 25- to 100-year projections. The results depend somewhat on the assumptions made in the statistical procedures, on the numbers of storm-generated SWHs included, and on the threshold value for inclusion in the analyses, but the results are consistent with the linear regressions of annual averages and the observed shifts in the histograms.     

基于随机集合的非传统型有效波极值模型

The analysis and design of offshore structures necessitates the consideration of wave loads. Realistic modeling of wave loads is particularly important to ensure reliable performance of these structures. Among the available methods for the modeling of the extreme significant wave height on a statistical basis, the peak over threshold method has attracted most attention. This method employs Poisson process to character- ize time-varying properties in the parameters of an extreme value distribution. In this paper, the peak over threshold method is reviewed and extended to account for subjectivity in the modeling. The freedom in selecting the threshold and the time span to separate extremes from the original time series data is incorpo- rated as imprecision in the model. This leads to an extension from random variables to random sets in the probabilistic model for the extreme significant wave height. The extended model is also applied to different periods of the sampled data to evaluate the significance of the climatic conditions on the uncertainties of the parameters.     

运用SWAN数值模拟对渤海波浪极值参数的研究(英文)

本文以高分辨率后报风场资料为输入,采用SWAN波浪模式,模拟了渤海海域1985年至2004年共20年间的波浪场。通过有效波高数据的比较,可看出波浪数值结果与实测资料符合较好,可以用数值结果分析渤海海域的波浪特征。利用计算的年极值波要素,本文给出并分析了渤海海域不同重现期下的极值参数分布情况。     

极值波高建模中不确定性的模糊量化方法

A non-traditional fuzzy quantification method is presented in the modeling of an extreme significant wave height. First, a set of parametric models are selected to fit time series data for the significant wave height and the extrapolation for extremes are obtained based on high quantile estimations. The quality of these results is compared and discussed. Then, the proposed fuzzy model, which combines Poisson process and generalized Pareto distribution(GPD) model, is applied to characterizing the wave extremes in the time series data. The estimations for a long-term return value are considered as time-varying as a threshold is regarded as non-stationary. The estimated intervals coupled with the fuzzy theory are then introduced to construct the probability bounds for the return values. This nontraditional model is analyzed in comparison with the traditional model in the degree of conservatism for the long-term estimate. The impact on the fuzzy bounds of extreme estimations from the non stationary effect in the proposed model is also investigated.     

Seasonality and duration in extreme value distributions of significant wave height

This paper presents a statistical model to characterize the long-term extreme value distribution of significant wave height, conditioning to the duration of the storm and accounting for seasonality. A time-dependent version of the peak over threshold (POT) approach is used to build the model, which is then applied to specific reanalysis time series and NOAA buoy records. The model considers the annual and semiannual cycles which are parameterized in terms of harmonic functions. The inclusion of seasonal variabilities substantially reduces the residuals of the fitted model. The information obtained in this study can be useful to design maritime works, because (a) the model improves the understanding of the variability of extreme wave climate along a year and (b) the model accounts for the duration of the storm, which is a key parameter in several formulations for rubble mound breakwater design.