Third-order temporal discrete scheme for the non-stationary Navier–Stokes equations

In this article, we suggest a new third-order time discrete scheme for the two-dimensional non-stationary Navier–Stokes equations. After presenting the Galerkin finite element approximation for the spatial discretization, we consider an implicit/explicit time discrete scheme for the problem, which is based on the two-step Adams–Moulton scheme (implicit scheme) for the linear term and the three-step Adams–Bashforth scheme (explicit scheme) for the nonlinear term. In this method, we only need to solve a linearized discrete system at each time step, so the scheme can converge fast and the computational cost can be reduced. Moreover, under some assumptions, we deduce the stability and optimal error estimate for the velocity in L ²-norm.     

Attribute Selection Based on Rough Set Theory for Electromagnetic Interference (EMI) Fault Diagnosis

Electromagnetic emissions are radiated from every part of a personal computer motherboard, thus producing electromagnetic interference (EMI). EMI has an adverse effect on the surrounding environment because EMI could cause malfunctions or fatal problems in other digital devices. EMI engineers diagnose motherboard EMI problems using the electromagnetic noise data measured by the spectrum analyzer. Finding the sources (e.g., PS2, USB, VGA) of electromagnetic noise is a time-consuming process. The attribute selection and fault diagnosis was developed based on the advantage of rough set theory (RST). RST is a novel data mining approach for dealing with vagueness and uncertainty. It can be used to find hidden patterns in data sets. In this study, the basic rough set theory concepts are introduced. The rough set approach enables one to discover the minimal subsets of condition attributes associated with the motherboard EMI fault diagnosis problem. The operating sequence includes data collection, data preprocessing, discretization, attribute reduction, reduction filtering, rule generation, and classification accuracy. Historical EMI noise data, colleted from a famous motherboard company in Taiwan, were used to generate diagnostic rules. Our research result (average diagnostic accuracy of 80% above) shows that the RST model is a promising approach for EMI diagnostic support systems.     

一种基于改进粗糙集模型的归纳学习方法

对传统的粗糙集理论进行了扩展,提出了一种改进的粗糙集归纳学习方法。一方面,针对连续属性离散化,利用模糊集理论对连续属性进行模糊化,再根据模糊贴近度构造模糊相似矩阵,并用k-w方法粗略评估各连续属性的重要度,建立基于模糊相似关系的划分,最终生成相容的决策表。另一方面,针对解决最优属性的选择问题,提出一种加权求和的属性重要度定义。基于以上模型开发了一个原型系统,并以一个工程实例验证了此方法的有效性。     

Behavior of pre-stress group anchors——Theory approach and model

First of all the pre-stress group anchor ropes are resolved into twosub-systems: the stable rock stand lateral resistance load and inner bonding sectionstand lateral resistance load and pre-stress load. Then, discretization of everysub-system was carried on and it is assumed that different micro-sections possessuniform distribution side resistance. On the basis of Mindlin stress solution, stress overlay principle, modified layered-summation method as well as the load transfer method, westudy the anchor group effect and present a theory model which calculates the anchorgroup effect and establishes the relevant iterate standard.     

快速计算抛物线的一种新算法

分析了孙家广先生于１９８６年提出的计算抛物线的方法，提出了一种新的快速计算方法，使常数计算量减少了６６％，循环体计算量减少２Ｎ（Ｎ是一条抛物线的采样点数）．如果Ｎ很大（一般采样上百个点或几百个点），调用次数多，则减少很多计算量．新的计算方法简单，软件实现容易，实用价值较大．     

Block constrained versus generalized Jacobi preconditioners for iterative solution of large-scale Biot’s FEM equations

Generalized Jacobi (GJ) diagonal preconditioner coupled with symmetric quasi-minimal residual (SQMR) method has been demonstrated to be efficient for solving the 2 × 2 block linear system of equations arising from discretized Biot’s consolidation equations. However, one may further improve the performance by employing a more sophisticated non-diagonal preconditioner. This paper proposes to employ a block constrained preconditioner P_c that uses the same 2 × 2 block matrix but its (1, 1) block is replaced by a diagonal approximation. Numerical results on a series of 3-D footing problems show that the SQMR method preconditioned by P_c is about 55% more efficient time-wise than the counterpart preconditioned by GJ when the problem size increases to about 180,000 degrees of freedom. Over the range of problem sizes studied, the P_c-preconditioned SQMR method incurs about 20% more memory than the GJ-preconditioned counterpart. The paper also addresses crucial computational and storage issues in constructing and storing P_c efficiently to achieve superior performance over GJ on the commonly available PC platforms.     

对象跟踪任意阶参考模型的离散MRAC证明

证明了用Ｐｏｐｏｖ超稳定性理论构成的自适应控制系统，其对象可以跟踪任意阶参考模型，从而简化和统一了自适应控制系统的设计     

基于数据分区的连续属性整体离散化方法研究

实际问题中经常涉及连续的数值属性,然而许多归纳学习算法却是针对离散属性空间的.因此,对数据进行预处理的离散化算法一直受到人们的重视.兼顾所有属性间关系的整体离散化是一个重要方法,该文提出基于数据分区的整体离散化算法,它首先对例子集合在各个连续属性上的取值进行统一的放大处理,选出包含最多聚类信息的属性,将整个例子集合粗略的划分为多个分区;然后在各个分区中分别进行聚类、合并.该方法改进了基本的整体离散化算法,并利用农业专家系统中的土壤分类数据对算法进行了验证.     

Perona-Malik模型离散格式的改进

Perona和Malik给出的离散格式是原Perona-Malik模型的近似模型的离散形式.这个离散格式用差商代替梯度,并略去了原模型的一项,本文通过理论分析发现这些简化影响了平滑的速度和效果.文中将省略的一项也加以离散,并将差商绝对值替换为梯度模,最终得到一个隐式的离散格式.实验结果表明,本文的离散格式提高了平滑速度,改进了平滑效果.     

决策树算法的优化研究

针对决策树C4.5/5.0分类算法及改进的算法在创建决策树时训练误差率和校验误差率相对较高的缺点,提出一些改进策略,即利用属性相关性进行属性约简与度量以达到解决属性集合中的冗余属性,采用一定置信度值进行决策树的修剪,采用优化的Chi2算法更合理更准确地对连续属性进行离散化,基于改进策略设计并实现一个分类器,将改进的算法应用于Breast-cancer实例,实验结果证明改进的算法生成的决策树具有较高的分类正确率。