THE DOMAIN DECOMPOSITION TECHNIQUES FOR THE FINITE ELEMENT PROBABILITY COMPUTATIONAL METHODS

1. IntroductionWe have discussed probability computational methods of finite element methods in [1,2,3,4].Probability computational methods have many advalltages. The advantages are more obviousin three dimensions for finite element problems. In probability model, the time that the particlemoves from one place to the boundary of the domain and is absorbed by the boundary (whichis called the time of running up to the boundary for short) is only dependent on the averagedistance between the start…     

EMD新算法及其应用

经验模态分解（ENID）算法是Hilbert-Huang变换（HHT）的核心算法，它的分解效果依赖于包络线的生成算法和端点延拓算法。采用分段幂函数插值算法求包络成。结合一种改进的端点延拓算法。得到了一种新的EMD算法。分析了分段幂函数插值算法的收敛精度。从数学角度解释了选取该插值算法的原因．最后，结合一个股票模型的仿真结果说明新的EMD算法效果更好。     

基于并行计算的盾构机刀盘三维切削仿真

针对盾构机工作时刀盘切削土体的数值仿真，建立了细致分析模型，并利用任意拉格朗日欧（ALE）和流固耦合（FSI）理论及方法未解决传统有限元方法进行切削仿真时易引发的网格大变形问题；在国产曙光4000A超级计算机上利用LS-DYNAMPP970完成了并行计算，采用了传统递归坐标对分、以夏根据仿真模型特点提出的基于耦合均衡坐标对分等两种区域分解策略。结果表明，ALE-FSI方法能有效处理刀盘切割土体仿真时的网格大变形，仿真数据与试验数据对比也比较一致：通过促进负载均衡，在计算时CBCB法比RCB法体现出了更好的加速比和并行效率。     

Parametric adaptive time-frequency representation based on time-sheared Gabor atoms

A localized parametric time-sheared Gabor atom is derived by convolving a linear frequency modulated factor, modulating in frequency and translating in time to a dilated Gaussian function, which is the generalization of Gabor atom and is more delicate for matching most of the signals encountered in practice, especially for those having frequency dispersion characteristics. The time-frequency distribution of this atom concentrates in its time center and frequency center along energy curve, with the curve being oblique to a certain extent along the time axis. A novel parametric adaptive time-frequency distribution based on a set of the derived atoms is then proposed using a adaptive signal subspace decomposition method in frequency domain, which is non-negative time-frequency energy distribution and free of cross-term interference for multicomponent signals. The results of numerical simulation manifest the effectiveness of the approach in time-frequency representation and signal de-noising processing.     

基于集中式模型的我国各地区及三大产业的DEA效率评价

基于集中式模型, 首先在考虑地区内部三大产业的情况下, 对2010年我国31个地区展开DEA效率评价, 然后在保持各地区整体效率不变的前提下进行效率分解, 确定各产业的效率值和相对重要程度. 此外, 对各地区三大产业的规模收益问行了研究. 实证分析结果表明, 各地区的整体效率值偏低, 第一产业的效率重要程度偏低, 第二产业和第三产业的效率均值相差不大, 但大部分地区的产业比第二产业的相对重要程度高. 此外, 从规模收益角度来看, 大部分地区整体处于规模收益递减阶段, 大多数地区的第一和第三产业均处于规模收益递增阶段, 绝大多数地区的第二产业已处于规模收益递减阶段.     

The runt test for multimodality

Single linkage clusters on a set of points are the maximal connected sets in a graph constructed by connecting all points closer than a given threshold distance. The complete set of single linkage clusters is obtained from all the graphs constructed using different threshold distances. The set of clusters forms a hierarchical tree, in which each non-singleton cluster divides into two or more subclusters; the runt size for each single linkage cluster is the number of points in its smallest subcluster. The maximum runt size over all single linkage clusters is our proposed test statistic for assessing multimodality. We give significance levels of the test for two null hypotheses, and consider its power against some bimodal alternatives. Research partially supported by NSF Grant No. DMS-8617919.     

一类o-对称矩阵的3种分解

给出o-对称矩阵概念及结构,研究其中一类o-对称矩阵的LDU分解和Cholesky分解及三对角分解,给出了分解公式,得到一些新结果,据此可大大减少这类矩阵的LDU分解和Cholesky分解及三对角分解的计算量和存储量.     

广义系统多传感器分布式融合降阶Kalman滤波器

对于带多传感器的广义线性离散随机系统,应用奇异值分解,将其变换为等价的两个降阶多传感器子系统,提出了基于变换后的状态融合器构造原始状态融合器的新的融合方法。应用Kalman滤波方法,在线性最小方差按矩阵加权、按对角阵加权和按标量加权融合准则下,分别提出了三种最优加权融合降阶广义Kalman滤波器。可统一处理融合滤波、平滑和预报问题。可减少计算负担和改善局部滤波精度。证明了三种融合器和局部估值器之间的精度关系。为了计算最优加权。提出了局部滤波误差协方差阵的计算公式。一个Monte Carlo仿真例子说明了其有效性。     

An extended Lagrangian support vector machine for classifications

Lagrangian support vector machine (LSVM) cannot solve large problems for nonlinear kernel classifiers. In order to extend the LSVM to solve very large problems, an extended Lagrangian support vector machine (ELSVM) for classifications based on LSVM and SVMlight is presented in this paper. Our idea for the ELSVM is to divide a large quadratic programming problem into a series of subproblems with small size and to solve them via LSVM. Since the LSVM can solve small and medium problems for nonlinear kernel classifiers, the proposed ELSVM can be used to handle large problems very efficiently. Numerical experiments on different types of problems are performed to demonstrate the high efficiency of the ELSVM.     

基于VMD-LSTM-IPSO-GRU的电力负荷预测

为了挖掘电力负荷数据中的潜藏信息,提高负荷预测的精度,针对电力负荷强非线性、非平稳性等特点,提出一种基于变分模态分解(variational mode decomposition,VMD)、优化长短期神经网络(long-term and short-term memory network,LSTM)、改进的粒子群算法(improve particle swarm optimization,IPSO)优化门控循环单元(gated recurrent unit neural network,GRU)的混合预测模型。首先,使用相关性分析确定确定输入因素,再将负荷数据运用VMD算法结合样本熵分解为一系列本征模态分量(intrinsic mode fuction,IMF)和残差量,更加合理地确定分解层数和惩罚因子;其次,根据过零率将这些量划分为低频和高频,低频分量使用LSTM网络,高频分量利用IPSO-GRU网络分别进行预测;最后,将预测结果重构得到电力负荷的最终结果。仿真结果表明,相对于其它常规模型,该混合模型可有效的提取模态特征,具有更高的预测精度。