The fuzzy C-means clustering algorithm(FCM) to the fuzzy kernel C-means clustering algorithm(FKCM) to effectively perform cluster analysis on the diversiform structures are extended, such as non-hyperspherical data, d...The fuzzy C-means clustering algorithm(FCM) to the fuzzy kernel C-means clustering algorithm(FKCM) to effectively perform cluster analysis on the diversiform structures are extended, such as non-hyperspherical data, data with noise, data with mixture of heterogeneous cluster prototypes, asymmetric data, etc. Based on the Mercer kernel, FKCM clustering algorithm is derived from FCM algorithm united with kernel method. The results of experiments with the synthetic and real data show that the FKCM clustering algorithm is universality and can effectively unsupervised analyze datasets with variform structures in contrast to FCM algorithm. It is can be imagined that kernel-based clustering algorithm is one of important research direction of fuzzy clustering analysis.展开更多
A support vector machine time series forecasting model based on rough set data preprocessing was proposed by combining rough set attribute reduction and support vector machine regression algorithm. First, remove the r...A support vector machine time series forecasting model based on rough set data preprocessing was proposed by combining rough set attribute reduction and support vector machine regression algorithm. First, remove the redundant attribute for forecasting from condition attribute by rough set method; then use the minimum condition attribute set obtained after the reduction and the corresponding initial data, reform a new training sample set which only retain the important attributes influencing the forecasting accuracy; study and train the support vector machine with the training sample obtained after reduction, and then input the reformed testing sample set according to the minimum condition attribute and corresponding initial data. The model was tested and the mapping relation was got between the condition attribute and forecasting variable. Eventually, power supply and demand were forecasted in this model. The average absolute error rates of power consumption of the whole society and yearly maximum load are respectively 14.21% and 13.23%. It shows that RS-SVM time series forecasting model has high forecasting accuracy.展开更多
The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the ...The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.展开更多
An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes(SNN) and local-Delaunay-trian...An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes(SNN) and local-Delaunay-triangulation(LDT) tech-niques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h-adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h-adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.展开更多
The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the p...The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.展开更多
The meshless method is a new numerical technology presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The w...The meshless method is a new numerical technology presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The process of cylinder compression was analyzed by using rigid-plastic meshless variational principle and programming reproducing kernel partial method(RKPM),the influence of node number,weight functions and size factor on the solution was discussed and the suitable range of size factor was obtained.Compared with the finite element method(FEM),the feasibility and validity of the method were verified,which proves a good supplement of FEM in this field and provides a good guidance for the application of meshless in actual engineering.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
虚拟电厂(virtual power plant,VPP)通过先进的控制技术高效聚合容量小、数量多的分布式能源(distributed energy resource,DER)参与电力市场交易。随着DER数量的增加,其出力的波动性以及聚合后的收益问题需要解决。基于此,提出一种在...虚拟电厂(virtual power plant,VPP)通过先进的控制技术高效聚合容量小、数量多的分布式能源(distributed energy resource,DER)参与电力市场交易。随着DER数量的增加,其出力的波动性以及聚合后的收益问题需要解决。基于此,提出一种在日前电力市场下,多类型DER聚合于VPP的协同博弈调度模型。首先,提出多类型DER聚合于VPP的运营框架。其次,由于风光出力的不确定性严重影响系统的运行,建立基于变分模态分解(variational modal decomposition,VMD)和改进的双向多门控长短期记忆(bidirectional multi gated long short-term memory,Bi-MGLSTM)网络的组合预测模型。然后,同类型DER形成联盟,并以售电收益最大化为目标,构建VPP多联盟的合作博弈调度模型,为实现联盟及成员间收益分配的公平性,设计多因素改进shapley值法和基于奇偶循环核仁法的两阶段细化收益分配方案。最后,算例结果表明,所提方法能有效提高风光功率的预测精度,实现VPP内联盟间合作互补运行,保证了多个主体间收益分配的公平性与合理性。展开更多
Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is...Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.展开更多
文摘The fuzzy C-means clustering algorithm(FCM) to the fuzzy kernel C-means clustering algorithm(FKCM) to effectively perform cluster analysis on the diversiform structures are extended, such as non-hyperspherical data, data with noise, data with mixture of heterogeneous cluster prototypes, asymmetric data, etc. Based on the Mercer kernel, FKCM clustering algorithm is derived from FCM algorithm united with kernel method. The results of experiments with the synthetic and real data show that the FKCM clustering algorithm is universality and can effectively unsupervised analyze datasets with variform structures in contrast to FCM algorithm. It is can be imagined that kernel-based clustering algorithm is one of important research direction of fuzzy clustering analysis.
基金Project(70373017) supported by the National Natural Science Foundation of China
文摘A support vector machine time series forecasting model based on rough set data preprocessing was proposed by combining rough set attribute reduction and support vector machine regression algorithm. First, remove the redundant attribute for forecasting from condition attribute by rough set method; then use the minimum condition attribute set obtained after the reduction and the corresponding initial data, reform a new training sample set which only retain the important attributes influencing the forecasting accuracy; study and train the support vector machine with the training sample obtained after reduction, and then input the reformed testing sample set according to the minimum condition attribute and corresponding initial data. The model was tested and the mapping relation was got between the condition attribute and forecasting variable. Eventually, power supply and demand were forecasted in this model. The average absolute error rates of power consumption of the whole society and yearly maximum load are respectively 14.21% and 13.23%. It shows that RS-SVM time series forecasting model has high forecasting accuracy.
基金supported by the National Natural Science Foundation of China under Grant No.12072090.
文摘The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods.However,reentry flight is accompanied by complex flight environments,which brings to the uncertain,complex,and strongly coupled non-Gaussian detection noise.As a result,there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application.To address these issues,a new iterated rational quadratic(RQ)kernel high-order unscented Kalman filtering(IRQHUKF)algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed.Firstly,the characteristic analysis of the RQ kernel is investigated in detail,which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing highorder moments of the RQ kernel.Subsequently,the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion,termed the iterated RQ kernel-UKF(RQ-UKF)algorithm by derived analytically,which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing highorder moments and heavy-tailed characteristics.Meanwhile,to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems,the high-order Sigma Points(SP)as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF.Finally,to further improve the flexibility of the IRQ-HUKF algorithm in practical application,an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence(KLD)method and parametric sensitivity analysis of the RQ kernel.The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.
基金Project supported by the National Natural Science Foundation of China (No.10202018)
文摘An h-adaptivity analysis scheme based on multiple scale reproducing kernel particle method was proposed, and two node refinement strategies were constructed using searching-neighbor-nodes(SNN) and local-Delaunay-triangulation(LDT) tech-niques, which were suitable and effective for h-adaptivity analysis on 2-D problems with the regular or irregular distribution of the nodes. The results of multiresolution and h-adaptivity analyses on 2-D linear elastostatics and bending plate problems demonstrate that the improper high-gradient indicator will reduce the convergence property of the h-adaptivity analysis, and that the efficiency of the LDT node refinement strategy is better than SNN, and that the presented h-adaptivity analysis scheme is provided with the validity, stability and good convergence property.
文摘The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.
基金Project(02103) supported by the National Education Department of ChinaProject(200509) supported by the Central South University of Forestry and Technology+1 种基金Project(07031B) supported by Scientific Research Fund of Central South University of Forestry and TechnologyProject supported by the Rewarding Project for Excellent PhD Thesis of Hunan Province,China
文摘The meshless method is a new numerical technology presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The process of cylinder compression was analyzed by using rigid-plastic meshless variational principle and programming reproducing kernel partial method(RKPM),the influence of node number,weight functions and size factor on the solution was discussed and the suitable range of size factor was obtained.Compared with the finite element method(FEM),the feasibility and validity of the method were verified,which proves a good supplement of FEM in this field and provides a good guidance for the application of meshless in actual engineering.
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。
文摘虚拟电厂(virtual power plant,VPP)通过先进的控制技术高效聚合容量小、数量多的分布式能源(distributed energy resource,DER)参与电力市场交易。随着DER数量的增加,其出力的波动性以及聚合后的收益问题需要解决。基于此,提出一种在日前电力市场下,多类型DER聚合于VPP的协同博弈调度模型。首先,提出多类型DER聚合于VPP的运营框架。其次,由于风光出力的不确定性严重影响系统的运行,建立基于变分模态分解(variational modal decomposition,VMD)和改进的双向多门控长短期记忆(bidirectional multi gated long short-term memory,Bi-MGLSTM)网络的组合预测模型。然后,同类型DER形成联盟,并以售电收益最大化为目标,构建VPP多联盟的合作博弈调度模型,为实现联盟及成员间收益分配的公平性,设计多因素改进shapley值法和基于奇偶循环核仁法的两阶段细化收益分配方案。最后,算例结果表明,所提方法能有效提高风光功率的预测精度,实现VPP内联盟间合作互补运行,保证了多个主体间收益分配的公平性与合理性。
基金supported by the National Natural Science Fundation of China (60736021)the Joint Funds of NSFC-Guangdong Province(U0735003)
文摘Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.
