In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling met...In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.展开更多
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth o...It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation, which is completely based on data samples, is a long-term issue that has not been well settled so far. There exist analytic formulae of optimal kernel bandwidth, but they cannot be applied directly to data samples,since they depend on the unknown underlying density functions from which the samples are drawn. In this work, we devise an approach to pick out the totally data-based optimal bandwidth. First, we derive correction formulae for the analytic formulae of optimal bandwidth to compute the roughness of the sample's density function. Then substitute the correction formulae into the analytic formulae for optimal bandwidth, and through iteration we obtain the sample's optimal bandwidth. Compared with analytic formulae, our approach gives very good results, with relative differences from the analytic formulae being only 2%～3% for sample size larger than 10~4. This approach can also be generalized easily to cases of variable kernel estimations.展开更多
A new algorithm for linear instantaneous independent component analysis is proposed based on maximizing the log-likelihood contrast function which can be changed into a gradient equation.An iterative method is introdu...A new algorithm for linear instantaneous independent component analysis is proposed based on maximizing the log-likelihood contrast function which can be changed into a gradient equation.An iterative method is introduced to solve this equation efficiently.The unknown probability density functions as well as their first and second derivatives in the gradient equation are estimated by kernel density method.Computer simulations on artificially generated signals and gray scale natural scene images confirm the efficiency and accuracy of the proposed algorithm.展开更多
交叉熵法可显著加速电网可靠性评估,但往往聚焦于独立随机变量,若将其拓展至相关性变量可进一步提升加速性能。为有效获取相关性变量的重要抽样密度函数以实现其重要抽样,针对相关性建模中广泛使用的核密度估计模型(kernel density esti...交叉熵法可显著加速电网可靠性评估,但往往聚焦于独立随机变量,若将其拓展至相关性变量可进一步提升加速性能。为有效获取相关性变量的重要抽样密度函数以实现其重要抽样,针对相关性建模中广泛使用的核密度估计模型(kernel density estimation,KDE)开展了交叉熵优化研究。因KDE模型不属于指数分布家族,传统交叉熵优化难以实施,故利用复合抽样算法特点提出了新颖的直接交叉熵优化方法,推导出KDE模型最优权重参数的解析表达式。因权重参数数量级较小,直接优化易导致准确性退化,故基于子集模拟思想进一步提出间接交叉熵优化方法,将较小的权重参数优化转换成较大的条件概率优化,提升了优化准确性。通过MRTS79和MRTS96可靠性测试系统的评估分析,验证了所提方法在含相关性变量电网可靠性评估中的高效加速性能。展开更多
In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to...In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .展开更多
单木分割在森林结构分析、林木参数提取以及森林生物量反演中具有重要作用。激光雷达(Light Detection and Ranging,LiDAR)作为一种低成本、高效率的数据源,为森林单木分割研究提供了坚实的数据基础。目前的单木分割研究主要集中在结构...单木分割在森林结构分析、林木参数提取以及森林生物量反演中具有重要作用。激光雷达(Light Detection and Ranging,LiDAR)作为一种低成本、高效率的数据源,为森林单木分割研究提供了坚实的数据基础。目前的单木分割研究主要集中在结构较为简单的森林区域,通常通过考虑点云之间的空间关系,制定合适的判别准则来实现单木的分割。然而,针对结构复杂的森林,现有的单木分割算法研究相对较少。提出了一种融合核密度估计、数字表面模型和K-means聚类等方法的单木分割算法。研究结果表明:以甘肃省甘南藏族自治区为研究区,对西北云杉林进行单木分割时,该方法能够显著提高人工云杉林与天然云杉林的分割精度。与传统的K-means聚类单木分割算法相比,该方法的整体棵数查全率分别提高了32%和15%,查准率分别提高了51%和27%,分别达到了83%和89%的查全率,以及92%和55%的查准率。这一方法为机载LiDAR在森林生态应用中的进一步应用提供了新的技术支持,特别为复杂林型结构中的单木分割问题提供了一种高效、简便的解决方案。展开更多
基金supported by Science and Technology project of the State Grid Corporation of China“Research on Active Development Planning Technology and Comprehensive Benefit Analysis Method for Regional Smart Grid Comprehensive Demonstration Zone”National Natural Science Foundation of China(51607104)
文摘In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.
基金Supported by the National Science Foundation of China under Grant No.11273013by the Natural Science Foundation of Jilin Province under Grant No.20180101228JC
文摘It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation, which is completely based on data samples, is a long-term issue that has not been well settled so far. There exist analytic formulae of optimal kernel bandwidth, but they cannot be applied directly to data samples,since they depend on the unknown underlying density functions from which the samples are drawn. In this work, we devise an approach to pick out the totally data-based optimal bandwidth. First, we derive correction formulae for the analytic formulae of optimal bandwidth to compute the roughness of the sample's density function. Then substitute the correction formulae into the analytic formulae for optimal bandwidth, and through iteration we obtain the sample's optimal bandwidth. Compared with analytic formulae, our approach gives very good results, with relative differences from the analytic formulae being only 2%～3% for sample size larger than 10~4. This approach can also be generalized easily to cases of variable kernel estimations.
文摘A new algorithm for linear instantaneous independent component analysis is proposed based on maximizing the log-likelihood contrast function which can be changed into a gradient equation.An iterative method is introduced to solve this equation efficiently.The unknown probability density functions as well as their first and second derivatives in the gradient equation are estimated by kernel density method.Computer simulations on artificially generated signals and gray scale natural scene images confirm the efficiency and accuracy of the proposed algorithm.
文摘交叉熵法可显著加速电网可靠性评估,但往往聚焦于独立随机变量,若将其拓展至相关性变量可进一步提升加速性能。为有效获取相关性变量的重要抽样密度函数以实现其重要抽样,针对相关性建模中广泛使用的核密度估计模型(kernel density estimation,KDE)开展了交叉熵优化研究。因KDE模型不属于指数分布家族,传统交叉熵优化难以实施,故利用复合抽样算法特点提出了新颖的直接交叉熵优化方法,推导出KDE模型最优权重参数的解析表达式。因权重参数数量级较小,直接优化易导致准确性退化,故基于子集模拟思想进一步提出间接交叉熵优化方法,将较小的权重参数优化转换成较大的条件概率优化,提升了优化准确性。通过MRTS79和MRTS96可靠性测试系统的评估分析,验证了所提方法在含相关性变量电网可靠性评估中的高效加速性能。
基金Supported by Natural Science Foundation of Beijing City and National Natural Science Foundation ofChina(2 2 30 4 1 0 0 1 30 1
文摘In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .
文摘单木分割在森林结构分析、林木参数提取以及森林生物量反演中具有重要作用。激光雷达(Light Detection and Ranging,LiDAR)作为一种低成本、高效率的数据源,为森林单木分割研究提供了坚实的数据基础。目前的单木分割研究主要集中在结构较为简单的森林区域,通常通过考虑点云之间的空间关系,制定合适的判别准则来实现单木的分割。然而,针对结构复杂的森林,现有的单木分割算法研究相对较少。提出了一种融合核密度估计、数字表面模型和K-means聚类等方法的单木分割算法。研究结果表明:以甘肃省甘南藏族自治区为研究区,对西北云杉林进行单木分割时,该方法能够显著提高人工云杉林与天然云杉林的分割精度。与传统的K-means聚类单木分割算法相比,该方法的整体棵数查全率分别提高了32%和15%,查准率分别提高了51%和27%,分别达到了83%和89%的查全率,以及92%和55%的查准率。这一方法为机载LiDAR在森林生态应用中的进一步应用提供了新的技术支持,特别为复杂林型结构中的单木分割问题提供了一种高效、简便的解决方案。
