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.     

A statistical analysis of typhoon frequency and application in design wave height

A typhoon leading is an important natural disaster to many disasters to China. A giant wave caused by it has brought large threat for an offshore project. Based on the maximum entropy principle,one new model which has 4 undetermined parameters is constructed,which is called the discrete maximum entropy probabilistic model. In practical applications,the design wave height is considered as soon as possible in a typhoon affected sea areas,the result fits the observed data well. Further more this model does not have the priority compared with other distributions as Poisson distribution. The model provides a theoretical basis for the engineering design more reasonable when considering typhoon factors comprehensively.     

Estimation of extreme wave heights using GEOSAT measurements

Satellite technology has yielded a large database of global ocean wave heights which may be used for engineering applications. However, the sampling protocol used by the satellite leads to some difficulties in making use of these data for practical applications. These difficulties and techniques to estimate extreme wave heights using satellite measurements are discussed. Significant wave heights for a 50-year return period are estimated using GEOSAT measurements for several regions around North America. Techniques described here may be used for estimation of wave heights associated with any specified return interval in regions where buoy data are not readily available.     

A probability distribution for depth-limited extreme wave heights in a sea state

A model for the depth-limited distribution of the highest wave in a sea state is presented. The distribution for the extreme wave height is based on a probability density function (pdf) for depth-limited wave height distribution for individual waves [Méndez, F.J., Losada, I.J., Medina, R. 2004. Transformation model of wave height distribution. Coastal Eng, Vol. 50, 97:115.] and considers the correlation between consecutive waves. The model is validated using field data showing a good representation of the extreme wave heights in the surf zone. Some important statistical wave heights are parameterized obtaining useful expressions that can be used in further calculations.     

A multi-distribution approach to POT methods for determining extreme wave heights

Determination of extreme wave heights using a Peaks-Over-Threshold (POT) approach is revisited. Firstly, the GPD-Poisson model is recalled. A double threshold is presented and justified, with objective tools for determining the high threshold. This model is then extended to other statistical distributions, namely the Weibull and Gamma distributions. Objective criteria (BIC and AIC) based upon likelihood are used to select the best-fitting distribution. This method is tested on two locations: the historical IAHR Haltenbanken dataset and a location at the entry of the Strait of Gibraltar. Finally, sensitivity analyses are carried out with respect to the high threshold and to the duration of the dataset to estimate the robustness of the approach presented.     

一种新的非线性波浪周期概率分布

在最大熵原则的基础上,通过解一条件变分问题,导出一种新的适用于描述非线性波浪周期T统计分布的概率密度函数.这种概率分布有如下的优越性:(1)该分布的参数是由无因次周期的m(m为正数)阶分布矩得出,从而周期的信息熵达到最大,故适用于描述波浪周期的非线性;(2)该分布有4个参数,从而更能符合最大熵原则;(3)该分布形式简单...     

基于广义极值分布的设计波高推算

简介了广义极值分布函数及其3种参数估计方法,包括极大似然(ML)、线性矩(LM)和间隔最大积(MPS)估计的计算方法。使用广义极值分布函数推算了北部湾涠洲岛海域3个波向的年波高极值序列设计波高,并与Weibull分布、Gumbel分布和皮尔逊Ⅲ型分布的推算结果加以对比。分析表明,涠洲岛海域极值波高服从于广义极值Ⅲ型分布,拟合优度检验结果表明广义极值分布能更好地拟合极值波高;MPS方法是一种优良的参数估计法,推算的设计波高可作为海岸环境工程设计的首要参考值。     

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.     

极值波高与历时联合分布的重现水平分析

使用美国北卡罗来纳州的 FRF 1985—2016 年的极值波高及其持续时间数据,采用最优的 Gumbel-Hougaard copula函数和 Kendall 分布函数构建极值波高和相应历时不同组合的联合概率分布模式,分析各个组合的遭遇概率、“或”重现期、“且”重现期和 Kendall 重现期,以出现最大可能概率的方法推算各组合联合设计值。结果表明：Kendall 重现期所对应的累积频率更准确地代表了特定设计频率下的风险率;重现期分别为 5 年、10 年、20 年、50 年、100 年、200 年推算的 Kendall重现期设计值介于“或”重现期和“且”重现期设计值之间,小于相应的边缘分布设计值;基于 Kendall 重现期的极值波高及其持续时间不同重现期组合推算的结果可为海洋工程构筑物设计与风险管理提供新的选择与参考。     

Validation of the Boccotti's generalized model for large nonlinear wave heights from laboratory mixed sea states

The presented work aims at validating the generalization of the asymptotic distribution model of Boccotti for large wave heights recently proposed by Tayfun [1] to laboratory generated mixed sea states with two-peak spectra. The input wave spectra are modelled as the sum of two JONSWAP spectra describing unidirectional wave systems with different or identical directions of propagation (crossing or following mixed seas). In order to account for the effect of the energetically dominant wave system on the largest observed waves, the Boccotti's parameters were calculated at the absolute minimum of the autocorrelation function which can differ from the first minimum for some cases of mixed seas, such as those dominated by the swell or seas with comparable contribution of the two spectral components. So far the proposed model has been validated elsewhere against samples of large wave heights exceeding the significant wave height in wind seas and in mechanically generated long-crested seas, both characterized by unimodal spectra and strong third-order nonlinearities. The present study demonstrates that it can predict equally well the tail of the distributions for mixed seas, irrespective of the type of the mixed sea, particularly when the third-order statistics is relatively large. Typically, the mixed seas from the considered offshore basin experiment display such conditions as the propagation distance from the wavemaker increases, though this effect is less pronounced for mixed following than for mixed crossing wave conditions. Moreover, the generalized model remains valid irrespective of the sign of the fourth-order sum Λ which is a key parameter of the distribution. Its good predictive ability is quantified here by the root-mean-square errors between observations and theory.     

湄洲湾波高和波周期的统计分布

本文探讨了福建湄洲湾海区的波高和波周期的一元分布和二元联合分布,并给出了该海区波浪的各种统计特征值,提出了波高和波周期的经验分布模式。     

A generalized approach for long-term modelling of extreme crest-to-trough wave heights

This paper deals with the long-term modelling of high sea waves. The solution is given for the return period of sea storms during which an arbitrary chosen number of waves, with crest-to-trough heights exceeding a fixed threshold, occur. This return period is derived starting from the Equivalent Triangular Storm (ETS) model, which associates a triangle to each actual storm and thus represents a significant wave height time series at a fixed location by means of a sequence of triangular storms. The short-term statistics is then applied to investigate the occurrence of large crest-to-trough wave heights during a given storm. Finally, by combining the statistical distribution of significant wave heights, the ETS model and the short-term wave statistics, the solution is given for the return periods R_N and R_N of a sea storm in which N or at least N waves higher than a fixed threshold occur. The values of R_N are then calculated, starting from data of two buoys moored in the Pacific Ocean and in the Mediterranean Sea.     

墨西哥湾波候统计特性分析

简要介绍了波候的概念,简述Ｗｅｉｂｕｌｌ分布及对数一正态分布的拟合方法,提出最大熵分布拟合有效波高、峰周期分布的新方法;选取半封闭海湾墨西哥湾内水深不同、地理位置不同的六个观测站一年的连续资料,以上述三种拟合方法对其有效波高,峰周期概率分布进行拟合,并与观测直方图进行比较检验,结果表明,在墨西哥海湾内,最大熵分布优于对数－正态分布,对数－正态分布优于Ｗｅｉｂｕｌｌ分布。     

Application of Maximum Entropy Principle to Studying the Distribution of Wave Heights in A Random Wave Field

Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh fonu, involves two parameters: the average wave height H^- and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.     

西太平洋8708号台风海面风、浪结构及其关系的遥感研究

本文以Geosat卫星高度计1987年8月11日在西太平洋海域上的-上升轨道测得的风、浪资料为基础,统计分析了8708号台风影响下的海面风速和海浪特征.结果显示,此次台风影响下的海面风速和海浪波高的空间分布具有相对台风中心近似对称的结构特征,但在台风内区,台风移动方向的右方风速较左方风速增加较快,同时在台风外围,右方风速较左方风速衰减也较快;有效波高没有明显的内、外区结构,且左、右方波高随距离变化也呈不同的衰减率;风速与有效波高的关系在台风中心左右也呈现明显的不同;本文给出了台风的风速及波高随相对台风中心距离变化的经验关系式,以及合风风速与波高的经验关系式等.     

A weakly non-gaussian model of wave height distribution for random wave train

The wave height distribution with Edgeworth’s form of a cumulative expansion of probability density function (PDF) of surface elevation are investigated. The results show that a non-Gaussian model of wave height distribution reasonably agrees with experimental data. It is discussed that the fourth order moment (kurtosis) of water surface elevation corresponds to the first order nonlinear correction of wave heights and is related with wave grouping.     

Application of MEP Method to the Study of Statistical Properties of Random Waves

—The maximum entropy principle(MEP)method and the corresponding probability evaluationmethod are introduced,and the maximum entropy probability distribution expression is deduced in mo-ment of the second order.Fully developed wave height distribution in deep water and wave height and peri-od distribution for different depths in wind wave channel experiment are obtained from the MEP method,and the results are compared with the distribution and the experimental histogram.The waveheight and period distribution for the Lianyungang port is also obtained by the MEP method,and the re-sults are compared with the Weibull distribution and the field histogram.     

Modified Weibull distribution for maximum and significant wave height simulation and prediction

Calibration coefficients incorporated in the modified Weibull distribution are more effective for maximum wave height simulation. The parametric relations are derived there from to estimate various wave height statistics including extreme wave heights. The characteristic function of the Weibull distribution is derived. The Weibull distribution is suggested for the newly defined significant wave height simulation by the method of characteristic function. The statistical tools suggested and developed here for predicting the required wave height statistics are validated against the wave data (both deep and shallow) of eastern Arabian Sea comprising rough monsoon conditions also, giving reasonable accuracy.     

最大熵原理应用于海浪波高分布的研究

利用最大熵原理从理论上推导出波高的最大熵分布,在此基础上研究了状态参量对波高分布和波高熵的影响。影响最大熵分布的因子是平均波高和状态参量,不同海况对应的状态参量是不同的。利用波高实测资料,得出3种不同海况下的最大熵分布,通过比较发现最大熵分布很好地符合实测数据。把最大熵分布与目前广泛应用的瑞利分布作了比较,结果表明,最大熵分布有2个优点：没有对波高作出任何限制性假定和能够描述不同海况下的波高分布。     

山东沿海台风浪数值模拟与统计分析

为了得到山东沿海台风浪的重现期波高分布场,以Jelesnianski-Ⅱ模型构建的风场作为模式驱动,利用SWAN模式建立了山东及其附近海域的台风浪数值模型。通过对典型台风过程"麦莎"和"梅花"的数值计算,将模拟的有效波高与观测数据作了对比分析,验证了模型在计算海域的适用性;基于建立的模型,对1960-2012年期间发生于山东沿海的50场台风进行模拟。选取计算海域10个点的模拟所得波高序列,寻求复合极值分布拟合最优的分布型式,根据所得分布进行重现期波高的统计分析;最终绘制计算海域50年一遇和100年一遇的台风浪波高分布图,为山东沿海的防灾减灾和海洋结构设计提供参考依据。