三次样条插值——三转角方程的算法设计

三次样条插值是数值分析中插值问题的一个重要算法,主要解决的问题是已知原曲线上一些离散的点处函数值及端点处导函数值,从而得到曲线方程数值解的过程。该算法根据已知条件不同而分为三转角方程和三弯矩方程两种方法,文章主要讨论三转角方程算法原理及实现。

框架剪力墙的内力分析——三转角方程法

1 基本方程式图1（b）为框架剪力墙的计算简图,其中相交于同层结点 x 和 x′处各剪力墙和框架梁柱杆件的杆端转角位移方程为Mx,x+1=ix+1(4θx+2θx+1-6_

II型插值条件下三次样条函数误差分析

样条函数是函数逼近理论一个非常活跃的分支,促使了研究人员需要深刻认识样条函数的本质及性质。本文介绍了基于Hermite两点三次公式的三转角插值算法。三转角以插值节点的一阶导数为未知量构建样条函数,在此基础上,研究插值节点均匀分布时,在第二类边界条件下,即II型插值条件下,当边界初值发生扰动时,对应的三次样条函数在插值节点的一阶导数值如何随第二边界初值的扰动而变化,基于Doolittle分解和Crout分解性质,推导出2个定理,即误差估计的表达式,这些定理为三次样条函数在二阶导数边界初值变化时的误差分析提供了可行的方法。Spline function is a very active branch of function approximation theory, which makes researchers need to deeply understand the essence and properties of spline function. This paper introduces the three-angle interpolation algorithm based on Hermite two-point cubic formula. The three-angle spline function is constructed with the first derivative of the interpolating node as an unknown quantity. On this basis, when interpolating nodes are evenly distributed, under the second type of boundary condition, that is, under the type II interpolation condition, when the initial value of the boundary is disturbed, the corresponding cubic spline function in the interpolating node’s first derivative value changes with the disturbance of the initial value of the second boundary. Based on the properties of Doolittle decomposition and Crout decomposition, two theorems, namely the expression of error estimation, are derived. These theorems provide a feasible method for error analysis of cubic spline function when the initial value of the second derivative boundary changes.

220kV三回路转角塔设计与真型试验

对三回路杆塔进行研究,设计了新型的三回路转角塔,选择2DSJ622型转角塔进行真型试验,验证了其安全性和可靠性。

加速试验缺失数据的样条插值分析

加速试验是研究高可靠性长寿命产品的有效手段,试验中性能退化数据是产品可靠性分析的基础。但由于试验过程中的各种不确定性,造成数据缺失、未按计划采样。提出基于三次样条和B样条的插值法,根据退化数据的特点,对缺失数据进行插补。三次样条插值采用不同边界条件,通过求解方程组得到插值函数。B样条插值法通过求解控制顶点和de Boor⁃Cox递推定义的B样条基函数得到插值函数。实验表明,该方法具有可操作性和有效性。

螺旋曲面廓型的数值拟合方法研究

通过对不同的曲线拟合方法的比较、研究,提出了采用三次样条插值函数来逼近螺杆转子截面型线的方法,推导出了各系数表达式,给出了拟合的方程,并用实例验证了拟合效果,同时解决了拟合过程中的一些关键问题.该方法为精确的刀具轨迹生成提供了光滑的型线.

连续梁的简便计算

利用三转角方程，对连续梁的内力进行精确的计算．该方法简捷明了，便于应用．

RC柱弯曲破坏骨架曲线简化算法及试验验证

为了满足基于性能的抗震设计和非线性动力分析的需要,有必要研究弯曲破坏钢筋混凝土(reinforced concrete,RC)柱弯矩-转角骨架曲线的简化计算方法.首先,将其骨架曲线简化为以屈服点、峰值点、开裂点为特征点的三折线弯矩-转角骨架曲线;其次,在考虑弯曲、剪力及钢筋黏结滑移对柱转角影响的基础上,基于RC柱弯曲理论和平截面假定,用迭代方法求出截面应力与应变的分布,并根据截面弯矩-曲率关系求得各特征点的弯矩和转角,进而提出RC柱弯矩-转角骨架曲线的简化算法;最后,分别对6组试件各特征点的计算值与试验值进行分析,计算其比值S.研究结果表明,各特征点S值的变异系数均不大于15%,计算值与试验值吻合较好,验证了弯矩-转角骨架曲线简化算法的准确性.

STUDY OF NON-CONTACT MEASUREMENT OF FREE-FORM SURFACES

A non contact three dimensional measurement method is presented in this paper.This system consists of a laser triangulation probe,a probe head and a coordinate measuring machine (CMM).The measurement principle of the system is discussed,and a system calibration method employing a reference ball is proposed.The geometric model involving four frames is established to calculate the data points based on the reading of the laser probe and position information from the CMM.A measuring experiment for gesso free form surface using this system is carried out.

The research on signal-obtaining pattern for a new type of gyroscope

In this paper, a photoelectric signal obtained scheme via equator triangle pattern engraved on rotor is discussed and the mathematic model is deduced in the case which is deflexion between rotor axis and the coordinate frame of case. The deflexion error and coupling error under the situation are analyzed. Finally, three methods of engraving based on the spherical triangle pattern are presented. The error models of various methods are built up and the simulation curves are provided respectively. We have done the primary experiments on the surface of rotor using this method. It can be seen from the enlarged figures that the rim of the pattern is smooth and the demand of sensor resolution is satisfied by and large. The results of study supply reference for signal obtaining.

Analysis and Discussion of Fiber Motion in the Spinning Triangle of Ring Spinning

In order to analyze the effect of the spinning triangle on yarn structure,a shape model of the spinning triangle is established.The fiber motion in the spinning triangle can be divided into three stages,and the relationship between yarn structure and fiber duration as well as the force acting on the fibers in the three stages is analyzed.The fiber elongation in different location of the spinning triangle is variational.The difference is that the elongation of fiber in the middle spinning triangle is bigger than that in the edge of it and the difference will be amplified with the increase of spinning triangle width,which has an effect on the characteristic of yarns structure.Research results for further study on compact yarn structure and improving spinning frame structure provide theory basis.

Linear Support Vector Machine Based Inter-harmonic Modeling and Parameter Estimation

There are often system. The high measure many inter-harmonics in power t accuracy of inter-harmonics order, amplitude and initial phase is needed. A new approach is presented for inter-harmonic modeling and parameter estimation based on linear support vector machine （SVM）. Firstly, parameter estimation of linear model is realized based on standard linear SVM. Then, interharmonic model is transformed to a linear model according to trigonometric functions. The approach obtains order of inter-harmonic model with windowed Blackman-Tukey （BT） spectrum analysis, and gets number and frequency of harmonics. Finally, the linear SVM is applied to estimate the inter-harmonic parameters, amplitude and initial phase. The simulation results show that the proposed approach has high precision and good antinoise. The accuracy of three parameters are all higher than 98%.

Rotated block triangular preconditioning based on PMHSS

Based on the PMHSS preconditioning matrix, we construct a class of rotated block triangular preconditioners for block two-by-two matrices of real square blocks, and analyze the eigen-properties of the corresponding preconditioned matrices. Numerical experiments show that these rotated block triangular pre- conditioners can be competitive to and even more efficient than the PMHSS preconditioner when they are used to accelerate Krylov subspeme iteration methods for solving block two-by-two linear systems with coefficient matrices possibly of nonsymmetric sub-blocks.

Aerodynamics Design of Two-stage Vane-less Counter-rotating Turbinec

It is one of the most efficient ways to greatly improve aero-engines' performance by utilizing vaneless counterrotating turbine(VCRT) technology.To supply sufficient power,VCRT turns to be high Mach number,large flow angle at high-pressure turbine(HPT) rotor exit,and low blade camber angle,which increase difficulties to turbine design.As the axial velocity ratio of HPT rotor is much larger than the conventional ones,the optimal selection of VCRT velocity triangles based on theoretical analysis is developed,and how the efficiency varied by HPT stator/rotor exit flow angle is also figured out.The key points to design a high efficient practicable VCRT are to select velocity triangles that are characterized by low flow coefficient,high outlet flow angle and large axial velocity ratio of HPT rotor.Meanwhile,performance comparison between convergent blade and convergent-divergent blade shows the latter is more appropriate for VCRT.

Spatial distribution, seasonal variation and regionalization of PM_(2.5) concentrations in China

In order to provide scientific support to policy makers in the regulation of PM2.5 pollution in China, it is important to accurately assess the current status, spatiotemporal characteristics and regionalization data for this air pollutant. An analysis of the pollution status of PM2.5 was conducted using daily averaged mass concentration data recorded in 74 cities in 2013 and 161 cities in 2014. The rotated empirical orthogonal function(REOF) method was applied to analyze this data. Results showed that the average annual PM2.5 concentration in urban areas of China is 62.2±21.5 ?g/m3, and that the distribution is spatially heterogeneous. The North China Plain, middle and lower Yangtze River Plain, Sichuan Basin and Guanzhong Plain had relatively high annual PM2.5 concentrations compared with the southeast coastal region, the Tibetan Plateau and the Yungui Plateau. PM2.5 mass concentrations tended to be higher in winter than in summer, however, the data for many cities showed a small peak in concentrations from May to July. An analysis of the spatial correlation of PM2.5 indicated a significant influence of topographic conditions. A lower correlation was observed where terrain features varied greatly. Based on the results of the REOF analysis and topographic characteristics, ten regions were identified in mid-eastern China, which could be considered as basic pollution prevention divisions for PM2.5; these include the North China Plain region, Pearl River Delta region, Jianghuai Plain region, middle Yangtze River Plain region, Northeast Plain region, Jiangnan coastal region, Sichuan Basin region, Qiantao Plain region, Guanzhong-Central Plain region and Yungui Plateau region. Seasonal variations in the regionalization data were observed, especially for the North China Plain and Pearl River Delta regions. Among the ten regions identified in this study, the North China Plain, Guanzhong-Central Plain, middle Yangtze River Plain and Jianghuai Plain had relatively high PM2.5 mass concentrations in comparison with the others. Therefore, these regions should be considered as the key regions to target in developing PM2.5 pollution prevention strategies. This study improves the present understanding of the spatial distribution, seasonal changes and regional status of PM2.5 pollution in China and helps establish possible control strategies for the reduction of this air pollutant.

Application of Novel Rotation Angular Model for 3D Mouse System Based on MEMS Accelerometers

A new scheme is proposed to model 3D angular motion of a revolving regular object with miniature, low-cost micro electro mechanical systems(MEMS) accelerometers(instead of gyroscope),which is employed in 3D mouse system.To sense 3D angular motion,the static property of MEMS accelerometer,sensitive to gravity acceleration,is exploited.With the three outputs of configured accelerometers,the proposed model is implemented to get the rotary motion of the rigid object.In order to validate the effectiveness of the proposed model,an input device is developed with the configuration of the scheme.Experimental results show that a simulated 3D cube can accurately track the rotation of the input device.The result indicates the feasibility and effectiveness of the proposed model in the 3D mouse system.