基于Copula函数法推求分期设计洪水和汛限水位

采用3-维非对称型Frank Copula函数结构,构建汛期分期为三分期、边缘分布为P-Ⅲ型分布的分期洪水联合分布.在假定分期设计洪水值的联合重现期等于防洪标准T的前提下,推导基于Frank Copula函数的分期设计洪水频率和防洪标准的关系,解决了分期设计洪水达不到防洪标准和分期频率与年频率不一致的问题,为分期设计洪水、分期汛限水位优化设计提供了一条新思路.     

基于Copula的ERCS系统软硬件综合可靠性建模与分析

在现代的电子业、制造业和工业控制等系统中,系统的可靠性越来越重要,而嵌入式实时控制系统(Embedded Real-time Control System,ERCS)大部分是控制系统的核心部分,其系统可靠性尤为重要。首先对嵌入式实时控制系统软硬件进行形式化抽象定义;然后对不可再分的软件模块和IP硬核进行可靠性建模,应用Copula函数对软件子系统和硬件子系统分别进行建模,并建立了ERCS系统的软硬件综合可靠性Copula模型;最后应用建立的模型,对具体的系统进行了软硬件综合可靠性计算。通过实例计算可知,用Copula建立的ERCS软硬件综合可靠性模型考虑了软件各个模块间、硬件各个IP硬核间和软硬件间的相依性,使得ERCS软硬件综合可靠性比独立时有所提高。     

Smooth semiparametric and nonparametric Bayesian estimation of bivariate densities from bivariate histogram data

Penalized B-splines combined with the composite link model are used to estimate a bivariate density from a histogram with wide bins. The goals are multiple: they include the visualization of the dependence between the two variates, but also the estimation of derived quantities like Kendall’s tau, conditional moments and quantiles. Two strategies are proposed: the first one is semiparametric with flexible margins modeled using B-splines and a parametric copula for the dependence structure; the second one is nonparametric and is based on Kronecker products of the marginal B-spline bases. Frequentist and Bayesian estimations are described. A large simulation study quantifies the performances of the two methods under different dependence structures and for varying strengths of dependence, sample sizes and amounts of grouping. It suggests that Schwarz’s BIC is a good tool for classifying the competing models. The density estimates are used to evaluate conditional quantiles in two applications in social and in medical sciences.     

Time-delay estimation for SISO systems using SWσ

This paper addresses the time-delay estimation problem of SISO systems using uniformly sampled input-output data. A dependence measure known as Schweizer and Wolff's σ (SWσ) from the copula theory is employed to measure the dependence of the input-output data. The quantitative relation between the time-delay and SWσ is studied, and the time-delay is estimated given that the SWσ of the input-output data reaches its maximum value when the time-delay is removed. The major advantage of our work is that no other parameters of the system must be estimated before or during the time-delay estimation process. Experiments and comparisons are used to verify the feasibility and effectiveness of the proposed method.     

Application of copula method and neural networks for predicting peak outflow from breached embankments

The limited number of available data is a common problem in most hydrologic and hydraulic studies, typically dam breach analysis. Construction of a probabilistic model is a key step in most decision making analyses to overcome such limitation. To analyze peak outflow from breached embankments, this paper has utilized two sets of data, original and synthetic datasets. Original datasets were collected from numerous historical dam failures and synthetic datasets were generated by copula method after incorporating the dependence structure among effective variables (height and volume of water behind the dam at failure and peak outflow discharge). The databases were separately employed to train two artificial neural networks (ANNs) as well as two statistical relations. Analyzing the results showed that the ANN model trained with synthetic datasets was the most competitive model for predicting peak outflows having R² of 0.96 and 0.95 for calibration and testing steps, respectively. The other ANN model was also better than statistical relations with R² of 0.94 and 0.87 respectively for calibration and testing steps.     

Modelling the Dynamic Dependence Structure in Multivariate Financial Time Series

Abstract. The dependence structure in multivariate financial time series is of great importance in portfolio management. By studying daily return histories of 17 exchange‐traded index funds, we identify important features of the data, and we propose two new models to capture these features. The first is an extension of the multivariate BEKK (Baba, Engle, Kraft, Kroner) model, which includes a multivariate t‐type error distribution with different degrees of freedom. We demonstrate that this error distribution is able to accommodate different levels of heavy‐tailed behaviour and thus provides a better fit than models based on a multivariate t‐with a common degree of freedom. The second model is copula based, and can be regarded as an extension of the standard and the generalized dynamic conditional correlation model [Engle, Journal of Business and Economics Statistics (2002) Vol. 17, 425–446; Cappiello et al. (2003) Working paper, UCSD] to a Student copula. Model comparison is carried out using criteria including the Akaike information criteria and Bayesian information criteria. We also evaluate the two models from an asset‐allocation perspective using a three‐asset portfolio as an example, constructing optimal portfolios based on the Markowitz theory. Our results indicate that, for our data, the proposed models both outperform the standard BEKK model, with the copula model performing better than the extension of the BEKK model.     

Data-driven reliability assessment with scarce samples considering multidimensional dependence

This study proposes a data-driven method for assessing reliability, based on the scarce input dataset with multidimensional correlation. Since considering the distribution parameters estimated from the scarce dataset as those of the population may lead to epistemic uncertainty, the bootstrap resampling algorithm is adopted to infer the distribution parameters as interval parameters. To account for the variable dependence, vine copula theory is utilized to construct the joint probability density function (PDF) of input variables, and maximum likelihood estimation (MLE) and Akaike information criterion (AIC) analysis are employed to select optimal copulas based on the samples for the vine structure. Subsequently, the failure probability bounds of a response function are calculated based on the constructed joint PDF with interval distribution parameters by the active learning Kriging (AK) method combining the sparse grid integration (SGI) method. Finally, several examples are provided to demonstrate the feasibility and efficiency of the proposed method.     

基于Copula理论的序列型地震动随机模型

通过考虑序列型地震动中主震和余震间的空间相关性,将已有地震动物理随机模型推广至序列型地震动随机模型。依据序列型地震动的产生与传播机制,将其表示为包含16个随机变量的Fourier模型。考虑主震与余震的空间相关性,基于Copula理论,将模型更准确地表示为6个二维随机变量和2个一维随机变量;为描述地震动在局部场地上传播的过程,建立了序列型地震动的随机场模型;根据1038组实测序列型地震动及5组地震动台阵数据,对模型中的物理随机变量进行参数识别和统计分析,结合Copula函数,给出了各参数的概率分布。与实测地震动对比表明:该文提出的序列型地震动随机模型,能够较为真实地再现序列型地震动的空间相关性以及地震动在局部场地的行波效应。     

基于多元Copula函数的桥梁体系地震易损性分析方法研究

为了考虑桥墩、支座等构件地震需求之间相关性,引入多元Copula函数对构件地震需求之间的相关结构进行描述,提出了桥梁体系易损性分析的新方法。基于增量动力分析结果建立了单个构件的易损性,采用核光滑方法对各构件的边缘分布函数进行估计;基于离差平方和最小准则和最小距离法对多元Copula函数进行了参数估计及优选;结合单个构件的易损性及多元Copula函数,建立了桥梁体系的易损性曲线,分析了构件地震需求之间相关性对桥梁体系易损性的影响。结果表明:桥墩、支座等构件地震需求之间的相关性对桥梁体系易损性影响显著;基于离差平方和最小准则构造的多元Copula函数,能够准确描述构件地震需求之间的相关结构,有效降低桥梁体系易损性分析的难度。