Computation of maximal turning points to nonlinear equations by nonsmooth optimization

We develop a new approach to finding bifurcations of solutions of nonlinear equation systems, which is based on the detection of extreme values of a new type of variational functional associated with the considered problems. The variational functional is obtained constructively by the extended functional method which can be applied to a wide class of parametric problems including nonlinear partial differential equations. Sufficient and necessary conditions for the existence of a maximal turning point by the approach are proved. Based on these, an algorithm of the quasi-direction of steepest ascent is introduced. Simulation experiments are used to illustrate the behaviour of the method and to discuss its advantages and disadvantages in comparison with the alternatives.     

Fitted mesh numerical method for singularly perturbed delay differential turning point problems exhibiting boundary layers

This paper is concerned with the numerical study of singularly perturbed boundary value problems for delay differential equations with a turning point. The fitted mesh technique is employed to generate a piecewise uniform mesh, condensed in the neighbourhood of the boundary layers. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Some numerical experiments are carried out to illustrate, in practice, the result of convergence proved theoretically and demonstrate the effect of the delay argument and the coefficient of the delay term on the layer behaviour of the solution.     

基于最小方差的股市拐点预测方法

预测股市拐点对指导股市投资具有重要意义,而股市拐点的预测是不平衡分类问题,针对SVM在解决此类不平衡问题时存在偏斜性的问题,提出了一种选取惩罚因子的方法。该方法以训练集交叉验证后所有类别样本的查全率与查准率的方差的乘积做为判断标准,将最小方差乘积对应的惩罚因子作为各类的最优惩罚因子,并将此Biased-SVM模型应用于股市拐点预测。在实验中,选取了常用股票技术指标作为输入向量,与其他几种解决不平衡问题的方法相比。实验结果表明最小方差法在保证非拐点的多数类样本识别精度的同时,提高了两类拐点样本的识别精度,为投资决策提供了佐证与帮助。     

A numerical method for quasilinear singular perturbation problems with turning points

In this paper we consider a quasilinear singular perturbation problem with turning points. First derivatives of the exact solution are estimated. Then an approximate problem is constructed. Finally we give an algorithm whose accuracy is good for arbitrary ?>0.     

基于拓扑法的与时间相关二维矢量场的可视化

分析与时间相关二维矢量场可视化的拓扑法,并针对其在检测封闭流线时依赖网格以及不能对封闭流线精确定位的问题,进行改进。通过运用特征流场对临界点跟踪以及鞍状连接符对流面积分,提出一种检测封闭流线的方法。该方法不依赖于网格,解决了封闭流线精确定位的问题。实验结果表明本文提出的算法为与参数相关二维矢量场可视化提供一个基本框架。     

基于时间序列趋势转折点的分段线性表示*

在充分利用时间序列时变特征的基础上,以有效地提取序列中的趋势和压缩原始数据为目标,提出了基于时间序列趋势转折点的分段线性表示方法。该方法在有效地提取序列中的趋势和压缩原始数据的同时,能够随着时间序列长度的增长对序列进行划分,具有高效、实现方法简便、效果直观的优点,对于不同领域的数据适应性良好。     

A uniform numerical method for quasilinear singular perturbation problems without turning points

A numerical method for singularly perturbed quasilinear boundary value problems without turning points is proposed: the continuous problem is transformed by introducing a special new independent variable and then finite-difference schemes are applied. The first order convergence uniform in the perturbation parameter is proved in the discreteL ¹-norm. The numerical results show the pointwise convergence, too.     

基于关键点的轮廓描述方法

为了有效表达图像的轮廓,给出了一种新颖的关键点描述轮廓方法。首先采用一种快速的点弦累加距离技术(chord-to-point distance accumulation,CPDA)用来提取角点;然后用椭圆模型找到相邻角点间的平面曲线的极值点,这样可以更好地表达轮廓的结构,通过相邻点间的曲线拟合出图像的轮廓。通过理论的推导和实验结果验证了所提出的方法比前人的工作有了更准确的模拟。     

求解根轨迹分离点数值解法的研究

在多年教学经验基础上总结出一种求解根轨迹分离点的二分试探数值解法,经验证明此法有助于对根轨迹本质含义的理解,同时将此法从理论和仿真结果上与经典的牛顿迭代法进行了对比研究,结果表明二分迭代法具有运算速度快、易于精度控制等优点。     

Relaxing instance boundaries for the search of splitting points of numerical attributes in classification trees

We propose a simple heuristic partition method (HPM) of classification tree to improve efficiency in the search for splitting points of numerical attributes. The proposal is motivated by the idea that the selection process of candidates in the splitting point selection can be made more flexible as to achieve a faster computation while retaining classification accuracy. We compare the performance of the HPM against Fayyad’s method, as the latter is the improved version of the standard C4.5 algorithm on the search of splitting points. We demonstrate that HPM is more efficient, in some cases by as much as 50%, while producing essentially the same classification for six different data sets. Our result supports the relaxation of instance boundaries (RIB) as a valid approach that can be explored to achieve more efficient computations.     

The optimum lift angle for the culinary spatula (turning shovel)

A culinary spatula (turning shovel) is one of the common cooking tools used in the Oriental kitchen. Since the use of a turning shovel may cause cumulative trauma to the wrist, the spatula angle for food frying, food turning, and food shovelling was investigated. The subjects were eight female students who were experienced cooks. Handle angle significantly affected both performance and subjective rating. The optimum angle is 25°.     

Automatic generation of a fuzzy rule base for constant turning force

An automatic fuzzy rule base generation method is proposed to control nonlinear and timevarying turning processes with constant cutting forces. Based on this study, the optimum fuzzy rule base for the control of turning processes can be self-organized without the need for experienced manufacturing engineers. A fuzzy logic controller based on these fuzzy rules can adjust feed rate on line to achieve an optimal production rate in turning operations.     

电容探测器理论分析及数值计算

利用电荷镜像法建立了电容探测器球形电极对地目标探测方程,与某迫弹电容近炸引信电容探测器的有限元数值分析结果比较,在互电容、自电容对地变化趋势和变化率方面有很好的一致性。通过理论分析和有限元计算可以看出:电容近炸引信电容探测器对地电容探测方程可以用等效球电极的探测电容方程来建立。     

红外测温仪在车削工件温度场监测中的应用

介绍红外测温仪在线监测精密加工过程中车削工件的温度场，对在线监测温度系统进行设计，并针对车削工件温度监测准确度进行分析。     

非线性偏微分方程数值求解的自适应方法研究

对小波理论在偏微分方程数值求解中的应用进行深入研究的基础上,提出了一种自适应求解非线性偏微分方程的算法——小波最优有限差分法。并以非线性Burgers方程为例,分别用小波最优有限差分法和直线法对它进行数值求解,显示了小波最优有限差分法在数值求解非线性问题时的自适应性、高效性和可行性。     

Optimization of multi-task turning operations under minimal tool waste consideration

Most of the literatures on machining economics problems tend to focus on single cutting operations. However, in reality most parts that need to be machined require more than one operation. In addition, machining technology has been developed to the point that a single computer numerical control (CNC) machine is capable of performing multiple operations, even simultaneously, employing multiple spindles and cutting tools. When several operations are performed on a CNC turning machine, various tools are required for the cutting operations. Determining the life of these cutting tools under different machining conditions is an arduous task for the operators. They usually replace the tools based on their experience or according to the specific cutting tool handbook. Frequent tool replacements may result in wasted tools and tool utilization, while infrequent tool replacements may result in poorly machined parts. In this study we propose a mathematical model in which several different turning operations (turning, drilling, and parting) with proper constraints are performed. The issue of tool replacement is taken into account in the proposed cutting model. In addition, an evolutionary strategy (ES)-based optimization approach is developed to optimize the cutting conditions of the multiple turning-related operations while taking into account the minimizing unit cost criteria under the economical tool replacement strategy.     

A parameter-uniform method for singularly perturbed turning point problems exhibiting interior or twin boundary layers

A numerical scheme for a class of two-point singularly perturbed boundary value problems with an interior turning point having an interior layer or twin boundary layers is proposed. The solution of this type of problem exhibits a transition region between rapid oscillations and the exponential behaviour. The problem with interior turning point represents a one-dimensional version of stationary convection–diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin. To solve these problems numerically, we consider a scheme which comprises quintic B-spline collocation method on an appropriate piecewise-uniform mesh, which is dense in the neighbourhood of the interior/boundary layer(s). The method is shown to be parameter-uniform with respect to the singular perturbation parameter ?. Some relevant numerical examples are illustrated to verify the theoretical aspects computationally. The results compared with other existing methods show that the proposed method provides more accurate solutions.     

航空发动机转子系统的动态响应计算

利用有限元方法建立了航空发动机双转子系统耦合非线性动力学模型,采用MATLAB计算了系统的临界转速和振型;研究了双转子结构的稳态不平衡响应,给出了双转子-机匣系统在不同转速下的运动规律,为工程中双转子系统的设计提供了一定的理论支持.     

一种计算机图形曲线转戾点的数值计算方法

文章提供了一种利用计算机图形处理技术对二维曲线转戾点进行采样的数值计算方法,并对计算过程中的一些具体问题提出了针对性的解决方案,包括对奇异点和不同轴向曲线的处理方法。