关于非中心X^2分布性质的研究

X^2分布是多元分析中重要的分布之一，在参数估计、假设检验、回归分析和判别分析等领域中有广泛的应用旨在证明非中心X^2分布的几个重要性质和结论，重点讨论经线性变换后的n维正态随机向量的二次型所构成的分布，给出其非中心参数的具体计算公式．简化变换后非中心X^2分布的计算，并说明了这些结论在多元分析中的作用．     

GM(2,1)模型预测公式的改进研究

从GM（2，1）模型的构造原理出发，认为其存在2个缺陷：Z^（1）和X^（1）预测公式混淆和强行定义边界条件：提出2种改进方案：用X^（0）直接预测法代替么Z^（1）和X^（1）预测后累减来预测X^（0）；用最小二乘的二次参数估计代替由边界条件确定白化微分方程的常数。计算示例表明，新方法具有更好的效果。     

飞行器结构疲劳寿命分散系数理论值确定的一种方法

提出了一种基于假设检验观点的确定疲劳寿命分散系数理论值的方法,针对疲劳寿命服从对数正态分布和威布尔分布的情况,分别推导了基假设检验观点的分散系数确定公式,算例表明在小子样容量条件下,与传统的参数估计概念的分散系数相比,假设检验观点的分散系数更趋近于实际统计值。     

Weibull分布工序控制图

Weibull分布是一种重要的非正态分布。本文导出了Weibull分布X^～R图控制限计算公式，列出了相应的控制图常数表。这些图使用起来非常方便。     

分布曲线拟合的R—检验方法——关于罗曼诺夫斯基R-检验方法的推证与补充

对工程上的某一类实际问题进行分布曲线拟合的假设检验中,其显著性水平α,一般可取为同一个常数。若用X~2—检验法,每一次检验都要根据得到自由度K去查相应的X~2分布表,以确定临界值。R—检验法的临界值不严格依赖自由度K,因此可以只根据问题要求的显著性水平α来确定,这为使用提供了方便。本文阐述了R—检验法的统计学原理,给出了用显著性水平α确定临界值的数值表,并通过实例详细讨论了R—检验法在分布曲线拟合中的应用。     

限制空间中的参数在平方损失下的容许估计

对限制空间中的参数的容许估计进行了讨论，得到了限制空间中的一般分布族参数在平方损失下为容许估计的一个充分条件，这一条件使得成平、陈希孺、陈桂景等人在《参数估计》一书中的结果成为它的一种特殊情况，并由此推出了一系列结构。     

UX（X=H，F，Cl，Br）的分子结构与势能函数

用密度泛函B3LYP方法对UX（X=H，F，Cl，Br）分子体系进行了理论研究，结果表明，这些分子的基态电子状态分别是X^4Ⅱ、X^6∑、X^2∑、X^6∑；势能函数为Murrell—Sorbie势函数，并得到了相应的几何性质、力学性质和光谱数据。     

Inverse Gaussian分布的假设检验

用一种新构造方法，实现了Inverse Gaussian分布的正态化，进而解决了一类长期遗留下来的Inverse Gaussian分布的假设检验问题。     

窑用多通道燃烧器回流区的三维数值模拟

在采用重整化群（RNG）k—ε模型对水泥窑用多通道燃烧器进行数值模拟的基础上，针对影响燃烧器性能的重要指标一回流区进行讨论，将三维条件下燃烧器的流场分布与传统燃烧器流场进行对比，提出了三维条件下燃烧器回流区分为中心回流区、内回流区、外回流区3个回流区的分布模型，并分析了影响回流区的直流风和旋流风2个重要因素。结果表明：旋流风的速度变化对回流区的影响比其他因素的影响更大，旋流风速度适当增大可以增大回流区的范围，而当旋流风速度过大时，外回流区消失。     

Linex损失下Burr分布参数的Bayes估计

讨论了Linex损失函数下Burr分布参数在不同先验分布下的Bayes估计,并且讨论了多层Bayes估计,给出了容许性估计的一般形式。     

粗糙模糊规划

提出了一种基于粗糙模糊集的数学规划模型,该模型利用粗糙模糊集中的上、下近似之差表示模糊规划模型中的容差,可得出系统的客观容差,为解决基于粗糙模糊信息系统的规划问题提供理论参考。     

笔式加工轨迹的B样条曲线逼近

提出一种新的节点矢量计算方法,应用于最小二乘法B样条曲线的逼近计算,通过实例验证,此算法生成的逼近曲线精度高,曲线更具有光顺性,能够很好抑制逼近曲线的扭摆现象,能够满足逼近精度要求。利用此算法对笔式加工轨迹进行B样条逼近,生成C²连续且光顺的刀位路径,大大缩短数控加工代码量,提高加工效率和加工精度。     

基于模糊相容关系的集值决策表的相对约简

从模糊粗糙集的角度讨论集值决策表的相对约简。首先,基于2个对象取相同值的可能性大小,在集值信息系统中定义了一个模糊相容关系,给出了模糊相容关系的上近似和下近似;其次,通过引入模糊近似质量,定义了集值决策表中条件属性的重要度与相对重要度,进而提出了一种计算相对约简的启发式算法;最后,通过实例说明该算法能够得到集值决策表的相对约简。     

多元正态总体情形下容许因子的近似计算

研究了容忍因子的几个重要近似计算公式，提出了修改方案。对容忍因子的近似方案做了计算比较。     

Global optimization of tool path for five-axis flank milling with a cylindrical cutter

In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed. interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach. Supported by the National Natural Science Foundation of China (Grant Nos. 50775147 and 50835004), the National Basic Research Program of China (“973” Project) (Grant No. 2005CB724103), and the Science & Technology Commission of Shanghai Municipality (Grant No. 07JC14028)     

An Approximation Method of NURBS Curves in NC Machining

An algorithm for approximating arbitrary NURBS curve with straight line is presented.Firstly,NURBS curve is acquired according to data points on the curve.Secondly,Approximating arbitrary NURBS curve is based on dichotomy.The resulting straight line approaches to the original curve with relatively fewer segments within the required tolerance.The example shows that the algorithm is simple and its approximation precision is high.The method is most useful in numerical control to drive the cutter along straight line or circular paths.     

一类机会约束规划的回溯逼近求解法

研究了一类机会约束随机规划的近似求解问题,提出了基于蒙特卡罗随机模拟的回溯逼近求解算法,该方法通过在迭代过程中逐步增加抽样次数和精确求解确定性数学规划,最终得到机会约束规划的最优解。文中讨论了最优解的计算方法及算法迭代终止条件。最后,通过算例验证了该方法的有效性。     

Dominant point detecting based non-uniform B-spline approximation for grain contour

Three-dimension reconstruction from serial sections has been used in the last decade to obtain information concerning three-dimensional microstructural ge-ometry. One of the crucial steps of three-dimension reconstruction is getting compact and fairing grain contours. Based on the achievement of closed raw con-tours of ceramic composite grains by using wavelet and level set, an adaptive method is adopted for the polygonal approximation of the digitized raw contours. Instead of setting a fixed length of support region in advance, the novel method computes the suitable length of support region for each point to find the best es-timated curvature. The dominant points are identified as the points with local maximum estimated curvatures. Periodic closed B-spline approximation is used to find the most compact B-spline grain boundary contours within the given tolerance. A flexible distance selection approach is adopted to obtain the common knot vector of serial contours consisting of less knots that contain enough degrees of freedom to guarantee the existence of a B-spline curve interpolating each contour. Finally, a B-spline surface interpolating the serial contours is generated via B-spline surface skinning.     

Modelling three dimensional dynamic problems using the four-node tetrahedral element with continuous nodal stress

A partition of unity (PU) based four-node tetrahedral element with continuous nodal stress (Tetr4-CNS) was recently proposed for static analysis of three-dimensional solids. By simply using the same mesh as the classical four-node tetrahedral (Tetr4) element, high order global approximation function in the Tetr4-CNS element can be easily constructed without extra nodes or nodal DOFs. In this paper, the Tetr4-CNS element is further applied in the analysis of three dimensional dynamic problems. A series of free vibration and forced vibration problems are solved using the Tetr4-CNS element. The numerical results show that, for regular meshes, accuracy obtained using the Tetr4-CNS element is superior to that obtained using the Tetr4 and eight-node hexahedral (Hexa8) elements. For distorted meshes, the Tetr4-CNS element has better mesh-distortion tolerance than both the Tetr4 and Hexa8 elements.     

A general,fast and robust B-spline fitting scheme for micro-line tool path under chord error constraint

The discontinuity of linear tool path(or G01 blocks) brings about unnecessary feedrate deceleration and fluctuation during machining. To improve the continuity, the linear tool path is usually smoothed by the local transition method or the global fitting method. For micro-line tool path, the transition method will significantly decrease the machining efficiency and introduce feedrate fluctuation. The global fitting method cannot be directly used in the NC interpolation because the indispensable chord error checking and iterative fitting processes are computation-intensive. This paper presents a general, fast and robust B-spline fitting scheme under chord error constraint for high speed interpolation of micro-line tool path. The proposed fitting method guarantees the chord error by utilizing the strong convex hull property of B-spline curves. The knot vector and control points are initially generated by a progressive iterative approximation method and locally refined to conform to the chord error constraint by using an analytical method. The analytical approximation and refining methods avoid solving a linear system of equations that is necessary in the standard B-spline fitting method. The feasibility and efficiency of the proposed scheme has been verified via simulations and experiments. Compared with the traditional fitting method, the proposed scheme can strictly constrain the chord error and can significantly decrease the computational load. Compared with the transition scheme, the proposed scheme can significantly increase the machining efficiency for the same micro-line tool path under the same chord error tolerance.