Generalization of the Gram-Charlier/Edgeworth Series and Application to Time-Frequency Analysis

We derive a general equation relating probability densities and as special cases we the obtain Gram-Charlier and Edgeworth series. This allows us to generalize these methods and clarify a number of issues pertaining to both probability theory and time-frequency analysis. In particular we show how the Gram-Charlier and Edgeworth series are related to the kernel method of time-frequency analysis. The approach allows us to construct densities that satisfy given constraints such as joint moments or conditional moments. Also, we show that the kernel has to be signal dependent and that to obtain a proper distribution it should be the ratio of two characteristic functions.     

计及信号随机延时的电力系统小干扰概率稳定性分析

为了研究随机延时对电力系统小干扰稳定性的影响,基于阻尼转矩分析法提出了一种计算特征根相对于延时的灵敏度的方法,进而通过Gram-Charlier级数展开的方法,得到随机延时下电力系统临界特征根实部的概率密度函数,该稳定性分析方法具有计算快速、简便的优点;然后,对计及广域信号随机延时的电力系统稳定器进行了参数鲁棒设计。在基于OPNET-MATLAB的信息物理融合电网系统联合仿真平台中搭建了两区四机系统模型,通过蒙特卡洛模拟验证了所提特征根概率密度函数计算方法的正确性,并分析了不同延时特性对系统小干扰稳定的影响,最后通过两区四机算例验证了所提电力系统稳定器鲁棒性设计方法的有效性。     

Modeling threshold conditional heteroscedasticity with regime-dependent skewness and kurtosis

Construction of nonlinear time series models with a flexible probabilistic structure is an important challenge for statisticians. Applications of such a time series model include ecology, economics and finance. In this paper we consider a threshold model for all the first four conditional moments of a time series. The nonlinear structure in the conditional mean is specified by a threshold autoregression and that of the conditional variance by a threshold generalized autoregressive conditional heteroscedastic (GARCH) model. There are many options for the conditional innovation density in the modeling of the skewness and kurtosis such as the Gram-Charlier (GC) density and the skewed-t density. The Gram-Charlier (GC) density allows explicit modeling of the skewness and kurtosis parameters and therefore is the main focus of this paper. However, its performance is compared with that of Hansen’s skewed-t distribution in the data analysis section of the paper. The regime-dependent feature for the first four conditional moments allows more flexibility in modeling and provides better insights into the structure of a time series. A Lagrange multiplier (LM) test is developed for testing for the presence of threshold structure. The test statistic is similar to the classical tests for the presence of a threshold structure but allowing for a more general regime-dependent structure. The new model and the LM test are illustrated using the Dow Jones Industrial Average, the Hong Kong Hang Seng Index and the Yen/US exchange rate.     

计及风险控制策略的含风电机组的输电系统规划

采用概率方法描述与风电机组相关的不确定性因素,并利用半不变量和Gram-Charlier级数展开理论计算支路概率潮流。在此基础上,通过在规划模型中引入风险控制策略,设置支路潮流不越限概率、系统潮流不越限概率和系统潮流裕度概率,以最大化系统抵御安全风险的能力;将系统潮流不越限概率和系统潮流裕度概率联合起来作为系统安全性风...     

基于镜面散射的雷达探测浅海水下地形研究

海面镜面散射建模及其应用方法是小入射角时雷达海洋遥感的关键问题.深入研究了基于格拉母一卡利尔(Gram-Charlier)分布的海面镜面散射建模方法,分析了其极化特性,将风速统一以海面上10 m高度为基准.通过与实测数据的比较,证明了其正确性和优越性.提出了采用Wu J方法估计海面均方斜率可改进其在中低风速时的性能,指...     

考虑随机性分布式电源的配电系统潮流计算简

配电系统中风力发电以及光伏发电等具有随机性的分布式电源容量的不断增加,使配电系统潮流变化具有一定的随机性。根据风电系统以及光伏系统的变化规律建立了风电以及光伏的随机等效模型,利用三点估计法进行了含随机分布式电源的概率潮流计算,并利用Gram Charlier级数得到相关变量的概率密度分布函数,通过对IEEE33节点进行仿真说明了方法的可行性。     

基于邻域统计分布变化分析的UWB SAR隐蔽目标变化检测

该文针对载机不同航迹条件下所得多时相UWB SAR图像灰度值存在较大起伏,严重影响了基于像素灰度值差异的变化检测算法性能,提出了一种基于邻域统计分布变化分析的UWB SAR隐蔽目标变化检测方法。该方法将Gram-Charlier展开理论同秩序滤波器相结合对多时相图像中每个像素邻域的统计分布进行估计,进而借助K-L散度理论对多时相图像邻域统计分布变化进行定量分析以检测目标对应的变化区域。实验结果表明,该文方法能够更好地适应不同航迹UWB SAR图像间灰度起伏的影响,取得更好的检测结果。     

机组检修计划的最小累积风险度法

以等风险度原则为基础,以各检修时段风险度方差最小为目标函数,建立了发电机组检修计划模型,提出了最小累积风险度法。该启发式求解方法采用半不变量法结合Gram-Charlier级数展开法求解系统的风险度,通过寻找检修区间内累积风险度最小的区间确定待检修机组的检修位置。以IEEE-RTS系统为算例的机组检修计划结果验证了最小累积风险度法的有效性。     

考虑电网静态安全风险的随机潮流计算

随机潮流能够比较全面地反映系统运行状态,对电网安全性风险评估起到重要作用。现有的随机潮流计算方法中,结合半不变量和Gram-Charlier展开级数的方法可快速且准确地计算节点电压和支路潮流的概率密度函数(probability distribution function,PDF)以及累积分布函数(cumulative distribution function,CDF)。以受时域和地域不均匀分布影响的系统当前运行状态为基础构造预想事故集,将全概率理论与半不变量法随机潮流相结合,提出一种考虑电网静态安全风险的随机潮流算法。对IEEE RTS 96节点实验系统的计算表明,该算法可快速、准确地评估系统当前运行状态的静态安全风险,具有实际应用价值。