基于Copula函数的洪水峰量联合设计方法研究

为明晰洪水峰量联合设计的特点,以岗南水库洪水为例,基于Gumbel Copula函数,分析了AND、OR、Kendall、生存Kendall 4种重现期的优缺点,采用极大似然法、同频率法、条件最可能组合法3种方法计算了联合设计值。结果表明: ①AND和OR重现期在危险域和安全域的识别上存在局限性;相对而言,Kendall重现期更合理,但其安全域是无界的,这与实际不符;生存Kendall重现期则界定了有界的安全域,使得重现期的概念在逻辑上更科学合理。② 3种设计值计算方法的差别不大,但从简单实用角度出发,推荐采用同频率法计算设计值。③不同重现期标准的设计值差别比较明显,基于OR重现期计算的设计值总是最大的,生存Kendall、Kendall重现期设计值次之,AND重现期设计值最小。④推荐采用生存Kendall重现期进行两变量洪水设计,因其有比较严谨的理论基础,且设计结果兼顾了安全性与经济性。⑤两变量联合设计值与单变量设计值的差异受变量间相关性的影响较大,且变量相关性越弱,差异越大。研究显示,基于生存Kendall重现期、采用同频率法计算设计值是目前较为科学合理的洪水峰量联合设计途径。     

Dependence tree structure estimation via copula

We propose an approach for dependence tree structure learning via copula. A nonparametric algorithm for copula estimation is presented. Then a Chow-Liu like method based on dependence measure via copula is proposed to estimate maximum spanning bivariate copula associated with bivariate dependence relations. The main advantage of the approach is that learning with empirical copula focuses on dependence relations among random variables, without the need to know the properties of individual variables as well as without the requirement to specify parametric family of entire underlying distribution for individual variables. Experiments on two real-application data sets show the effectiveness of the proposed method.     

Bayesian bivariate generalized Lindley model for survival data with a cure fraction

The cure fraction models have been widely used to analyze survival data in which a proportion of the individuals is not susceptible to the event of interest. In this article, we introduce a bivariate model for survival data with a cure fraction based on the three-parameter generalized Lindley distribution. The joint distribution of the survival times is obtained by using copula functions. We consider three types of copula function models, the Farlie–Gumbel–Morgenstern (FGM), Clayton and Gumbel–Barnett copulas. The model is implemented under a Bayesian framework, where the parameter estimation is based on Markov Chain Monte Carlo (MCMC) techniques. To illustrate the utility of the model, we consider an application to a real data set related to an invasive cervical cancer study.     

Pair-copula based mixture models and their application in clustering

Finite mixtures are often used to perform model based clustering of multivariate data sets. In real life applications, such data may exhibit complex nonlinear form of dependence among the variables. Also, the individual variables (margins) may follow different families of distributions. Most of the existing mixture models are unable to accommodate these two aspects of the data. This paper presents a finite mixture model that involves a pair-copula based construction of a multivariate distribution. Such a model de-couples the margins and the dependence structures. Hence, the margins can be modeled using different families. Again, many possible dependence structures can also be studied using different copulas. The resulting mixture model (called DVMM) is then capable of capturing a broad family of distributions including non-Gaussian models. Here we study DVMM in the context of clustering of multivariate data. We design an expectation maximization procedure for estimating the mixture parameters. We perform extensive experiments on the basis of a number of well-known data sets. A detailed evaluation of the clustering quality obtained by DVMM in comparison to other mixture models is presented. The experimental results show that the performance of DVMM is quite satisfactory.     

感潮地区暴雨和潮水位遭遇组合的涝灾风险

采用Copula函数建立感潮地区暴雨和外江(海)潮水位遭遇的联合分布,提出了设计组合下涝灾风险的分析方法,并定义和分析了暴雨和潮水位的联合风险率和同现风险率.通过研究中山市坦洲镇涝区的暴雨和潮水位的遭遇表明,AMH Copula函数能够较好地模拟暴雨与潮水位的联合分布;若设计暴雨为20年一遇,则与多年平均潮位或5年一遇潮位组合的排涝风险率分别不超过6.39%、9.58%;若设计暴雨为10年一遇,则与多年平均潮位或5年一遇潮位组合的排涝风险率分别不超过10.39%、7.04%;20年一遇暴雨、10年一遇暴雨分别与多年平均潮位或5年一遇潮位的同现风险率分别为0.086%、0.279%和0.173%、0.56%.     

上海市不同历时暴雨组合概率研究

基于上海市徐家汇站1960—2011年的日降雨资料,分析上海市年最大1d和3d降水量年际变化和年代际变化特性;择优选择GH Copula函数构建了年最大1 d与3 d降水量的联合分布模型,并推算它们的同现重现期和组合风险概率。结果表明:年最大1 d和3 d降水随时间呈增加趋势,自20世纪70年代开始其均值随年代增加;年最大1 d和3 d设计暴雨同频遭遇风险率在75%~85%之间,且同现风险率随年最大1 d设计暴雨值增大而增加。在设计上海市防洪排涝标准时若考虑最大1 d和3 d降水量的遭遇组合,有利于提升防洪排涝能力,保障防洪安全。     

Graphical causal inference and copula regression model for apple keywords by text mining

Apple is a leading company of technological evolution and innovation. This company founded and produced the Apple I computer in 1976. Since then, based on its innovative technologies, Apple has launched creative and innovative products and services such as the iPod, iTunes, the iPhone, the Apple app store, and the iPad. In many fields of academia and business, diverse studies of Apple’s technological innovation strategy have been performed. In this paper, we analyze Apple’s patents to better understand its technological innovation. We collected all applied patents by Apple until now, and applied statistics and text mining for patent analysis. By using graphical causal inference method, we created the causal relations among Apple keywords preprocessed by text mining, and then we carried out the semiparametric Gaussian copula regression model to see how the target response keyword and the predictor keywords are relating to each other. Furthermore, Gaussian copula partial correlation was applied to Apple keywords to find out the detailed dependence structure. By performing these methods, this paper shows the technological trends and relations between Apple’s technologies. This research could make contributions in finding vacant technology areas and central technologies for Apple’s R&D planning.     

变化环境下治涝效益估算方法研究

治涝工程建设前后涝区内状况往往会发生变化,承灾体的种类、数量和空间分布也会有所改变,因此,变化环境下治涝工程效益应为有治涝工程情况下比假设无该治涝工程情况下减少的涝灾损失;且各频率的暴雨导致的涝灾损失应为与承泄区各种水位组合下的涝灾损失的数学期望值。本文基于Copula函数和GIS构建的变化环境下治涝效益分析计算模型,用Copula函数构建涝区暴雨和承泄区水位的联合分布,借助GIS技术构建涝区数字高程模型。根据涝区暴雨和承泄区水位遭遇组合下的积水过程估算其涝灾损失,进而计算有治涝工程和假设无该治涝工程两种工况时所有组合下的涝灾损失期望值,从而得到治涝工程效益。以广州市南沙区的一个涝区为例简要说明了治涝效益的分析过程,结果表明,本文构建的治涝效益分析模型能分析涝区内状况和承灾体均发生改变、同时考虑涝区暴雨和承泄区水位全体组合下的治涝效益,可为治涝工程建设的合理决策提供科学依据。     

考虑风电不确定性的交直流配电网低碳分布鲁棒优化调度

为增加配电网风电的消纳能力,减少碳排放,建立了一种交直流配电网低碳分布鲁棒优化调度模型。分析风电预测误差和预测出力历史数据之间的正相关性,采用混合Copula函数,建立它们之间的联合概率分布,得到风电预测误差的条件概率分布。将交直流配电网解耦为交流和直流子网,以各自综合运行成本最小为优化目标,在交流子网优化模型中引入碳交易机制,建立交直流配电网分散协调优化模型。以得到的风电预测误差的条件概率分布为参考,构建了基于K-L散度的分布鲁棒模糊集。利用拉格朗日对偶理论,将优化模型转化为单层优化目标模型,并利用交替方向乘子法进行分散协调优化求解。基于修改后33节点交直流配电网模型的仿真结果表明所提模型能有效减少配电网侧碳排放量,显著提高风电消纳能力。     

基于Vine Copula的短期径流预报不确定性分析

定量分析短期径流预报序列的不确定性特征,对于提高水库短期运行计划的可靠性具有重要意义。针对常用多元椭圆Copula或阿基米德Copula难以有效刻画短期径流预报不确定性特征的问题,本文引入了Vine Copula对不同径流量级及不同预见期下预报不确定性进行定量评估,进而分析了先验信息对于后续时段预报不确定性的影响。以雅砻江流域锦西水库为例进行验证,结果表明：相较于传统多元Copula函数,Vine Copula构建的相对预报误差联合分布均能通过假设检验且拟合效果最好,模拟结果的统计量与实测数据相差较小;通过利用调度期内已经发生的相对预报误差信息,可以有效减小后续时段相对预报误差期望值及90%置信水平分位距,降低预报的不确定性。