基于Copula函数的CFG桩复合地基载荷-变形曲线的概率分析

CFG桩(cement-fly ash-gravel pile)复合地基是一种重要的地基处理形式,在日益增加的大面积住宅和商业开发中作用越来越突出,然而该种桩型的加卸荷-沉降变形特性仍然需深入研究,尤其在概率评估方面。根据北京星光影视股份有限公司生产科研基地项目工地中的21根CFG桩单桩静载试验和32个复合地基静载试验的原位加卸载测试成果,采用两参数的双曲线或幂曲线回归拟合了每一条加荷-变形曲线。由于土体的内在各向异性和其强度的变异性,评估整个场地的加荷-变形曲线时,其回归参数表现出了较大的离散性。将一个场地的多组回归参数组成一个随机向量,其加载-位移曲线的不确定性可由简单的两变量随机向量体现,引入双变量联结函数（Copula）描述随机回归参数间的相依性。最后,考虑正常使用极限状态,采用基于Copula函数的模拟模型计算了CFG桩复合地基的可靠度指标。研究结果有助于改进CFG桩复合地基的概率设计与评估。     

Archimedean族Copulas函数在多变量干旱特征分析中的应用

以甘肃省陇西站月降水资料为例,应用9种3维Archimedean Copulas函数构造了干旱历时、干旱烈度和烈度峰值的联合概率分布,并进行了多变量的拟合优度评价,利用优选出的3维非对称型M12 Copula函数,计算联合分布的重现期以及不同组合下的条件概率与条件重现期。结果表明,M12Copula函数可以描述干旱历时、干旱烈度和烈度峰值间的联合分布。由于Copula函数能够用来构建不同边缘分布的联合分布,可以获得变量间不同组合下的重现期,因而能够更全面客观地反映干旱的特征,是描述干旱多变量分布的一种有效途径。     

基于Copulas函数的二维干旱变量联合分布

通过构建干旱变量的联合分布揭示干旱演变规律,可作为干旱分析的重要手段。基于8种单参数族的Copulas函数进行新疆乌鲁木齐和石河子气象站二维干旱变量的联合分布。经拟合优度评价:Frank Copula对干旱历时和干旱烈度、干旱历时和烈度峰值的拟合度最好;Clayton Copula对于干旱烈度和烈度峰值的拟合效果最好。二维变量联合超越概率值随单变量值的减小而增大;单变量的重现期介于二维变量联合重现期与同现重现期之间。表明Copulas函数能够描述二维干旱特征变量的联合分布。     

区域气象干旱评估分析模式

为应对全球范围内日益严重的干旱问题,对区域气象干旱相对完整的评估分析模式开展了探讨。提出了从区域气象干旱识别到干旱特征值计算,再到干旱特征多变量分析的3个分析评估步骤。并以渭河流域为例,对研究区域进行了矩形干旱评估单元划分,选取了RDI（Reconnaissance Drought Index）为评估指标对区域内各单元各时段的干旱状态进行了识别,结果与历史记载的干旱年份吻合较好。分别采用了分布拟合、相关系数和Copula函数等统计学方法对区域干旱的干旱特征值（干旱历时、干旱面积、干旱强度和干旱频率）进行了特征分析,得出了一系列的单变量、双变量及多变量特征分析对比结果。通过对各类分布函数的计算和绘图,得到了渭河流域干旱事件发生的条件概率和重现期,形成了一套相对完整的区域干旱评估分析模式。     

水系连通变异下荆南三口河系水文干旱识别与特征分析

为揭示水系连通变异下荆南三口河系水文干旱演变特征,运用荆南三口河系五站1956-2016年的月径流量数据,采用游程理论识别该河系水文干旱特征变量,并运用Kolmogorow-Smirnov优度检验法选出干旱历时、干旱强度和峰值的概率分布函数,构建出水文干旱特征联合分布Copula函数,对水系连通变异下该河系水文干旱特征进行深入研究。结果表明：① 1989年为荆南三口河系（1956-2016年）水系连通变异分割点;② 该河系连通性变异前后水文干旱特征均发生显著变化,水文干旱事件发生的次数增多,干旱历时增长,干旱强度增大,峰值增高;③ 各站点的相同单变量重现期下二维联合重现期在水系连通变异前基本上均比水系连通变异后长,二维同现重现期在水系连通变异前均比水系连通变异后短;④ 水系连通变异后,该河系水文干旱历时、干旱强度和峰值呈现增加趋势,且在相同单变量重现期的情况下,干旱历时更长,干旱强度更大,峰值更高;⑤ 水系连通变异后水文干旱特征的变化幅度与变异前存在差异,不同河系其水文干旱特征的变化幅度不同。     

Impact of sample size on geotechnical probabilistic model identification

This paper aims to investigate the impact of sample size on geotechnical probabilistic model identification. First, the copula approach is presented to model the bivariate distribution of geotechnical parameters. Thereafter, the AIC scores are adopted to identify the best-fit marginal distribution and copula. Second, the variation of AIC scores because of small sample size is investigated using simulated data. Finally, the impact of the variation of AIC scores on identification of the best-fit marginal distribution and copula is examined. The minimum sample sizes for geotechnical data are also suggested to obtain a correct identification of the probabilistic models. The results indicate that the AIC scores estimated from a small sample exhibit large variation. The variation of the AIC scores has a significant impact on probabilistic model identification. The marginal distributions and copulas have a low percentage of correct identification when sample size is small. The percentages of correct identification for the marginal distributions and copulas increase with increasing sample size. The correlation coefficient between geotechnical parameters has a much larger impact on probabilistic model identification than the COV of geotechnical parameters. The suggested minimum sample sizes for geotechnical data are useful for guiding practical geotechnical site investigation.     

Assessment of uncertainty in environmental contours due to parametric uncertainty in models of the dependence structure between metocean variables

A key factor for computing environmental contours is the appropriate modeling of the dependence structure among the environmental variables. It is known that all the information on the dependence structure of a set of random variables is contained in the copulas that define their multivariate probability distribution. Provided that copula parameters are estimated by means of statistical inference using observations, recordings, numerical or historical data, uncertainty is unavoidably introduced in their estimates. Parametric uncertainty in the copulas parameters then introduces uncertainty in the environmental contours. This study deals with the assessment of uncertainty in environmental contours due to parametric uncertainty in the copula models that define the dependence structure of the environmental variables. A point estimation approach is adopted to estimate the statistics of the uncertain coordinates of the environmental contours considering they are given in terms of inverse functions of conditional copulas. A case study is reported using copulas models estimated from storm hindcast data for the Gulf of Mexico. Uncertainty in environmental contours of significant wave height, peak period and wind speed is assessed. The accuracy of the point estimation of the mean and variance of the contour coordinates is validated based on Monte Carlo simulations. A parametric study shows the manner in which greater parametric uncertainty induces larger variability in the environmental contours. The influence of parametric uncertainty for different degrees of association is also analyzed. The results indicate that variability between contours considering parametric uncertainty can be meaningful.     

Statistical characterization of temporal structure of storms

The authors present a statistical procedure to estimate the probability distributions of storm characteristics. The approach uses recent advances in stochastic hydrological modeling. The temporal dynamics of rainfall are modeled via a reward alternating renewal process that describes wet and dry phases of storms. In particular, the wet phase is modeled as a rectangular pulse process with dependent random duration and intensity; the global dependence structure is described using multidimensional copulas. The marginal distributions are described by Generalized Pareto laws. The authors derive both the storm volume statistics and the rainfall volume distribution within a fixed temporal window preceding a storm. Based on these results, they calculate the antecedent moisture conditions. The paper includes a thorough discussion of the validity of the assumptions and approximations introduced, and an application to actual rainfall data. The models presented here have important implications for improved design procedures of water resources and hydrologic systems.     

基于非对称Archimedean Copula的三变量洪水风险评估

分析洪峰、洪量和历时三变量联合分布与风险概率及其设计分位数,为水利工程规划设计和风险评估提供参考依据。以珠江流域西江高要站52年洪水数据为例,采用非对称阿基米德M6 Copula函数与Kendall分布函数计算三变量洪水联合分布的“或”重现期、“且”重现期和二次重现期及其最可能的设计分位数。结果表明:“或”重现期的风险率偏高,“且”重现期的风险率偏低,二次重现期更准确地反映了特定设计频率情况下三变量洪水要素遭遇的风险率;按三变量“或”重现期或三变量同频率设计值推算的洪水设计值偏高,以最大可能概率推算的三变量洪水要素的二次重现期设计值可为防洪工程安全与风险管理提供新的选择。     

Wave energy assessment based on trivariate distribution of significant wave height,mean period and direction

Based on the Vine copula theory, a trivariate statistical model of significant wave height, characterized wave period and mean wave direction was constructed. To maintain the properties of the different types of variables, a special copula function was derived from the model developed by Johnson and Wehrly based on the maximum entropy principle. It was then combined with the Archimedean copulas to construct the proposed model. An effective algorithm for generating corresponding joint pseudo-random numbers was also developed. Statistical analysis of hindcast data for the significant wave height, mean wave period, and direction, which were collected from an observation point in the North Atlantic every three hours from 1997 to 2001, was performed. The marginal distributions of the significant wave height and mean wave period were fitted by a modified maximum entropy distribution, and the mean wave direction was fitted by a mixture of von Mises distributions. It was shown that the proposed model is a good fit for the data. The seasonal wave energy resources in the target area were assessed using the model estimates. Histograms of the directional wave energy, wave energy roses, and scatter and energy diagrams were presented.