保形光顺的样条曲线

给出了一种对给定平面上的数据点进行保形的最小二乘逼近的算法,并且得到的逼近曲线是光顺的。本文利用拉格朗日乘数法对带约束条件的参数曲线进行了优化设计。     

涡轮平面叶栅非轴对称端壁优化设计

开发了一套造型灵活直观、网格生成速度快的涡轮平面叶栅非轴对称端壁优化设计工具,该工具的核心技术是非均匀有理B样条(NURBS)曲面造型和网格变形.在此基础上以商业软件Isight为优化驱动器,以CFX为求解器,搭建了非轴对称端壁优化设计流程.以Pack B涡轮平面叶栅为例,对其进行了非轴对称端壁优化设计.优化后涡轮平面叶栅总压损失系数减小了12.96%.结果表明:涡轮平面叶栅端部的静压分布改变削弱了涡轮平面叶栅通道中马蹄涡、通道涡的强度,提高了涡轮平面叶栅的气动性能.      

B-样条曲线奇点的几个定理

根据B-样条曲线控制多边形的剖分理论和B-样条曲线及其基函数的性质,分别给出B-样条曲线出现奇点的两个充分必要条件。     

B样条快速求值算法及其在曲线拟合中的应用

B样条方法是数据插值、拟合与平滑的重要方法。通过对de Boor-Cox算法计算路径的分析,给出了一种基于向量扩展的B样条基函数求值运算方法。分析表明,该方法具有并行计算结构和递推计算结构,利于计算机实现。同de Boor-Cox递推运算方法比,它能够同步计算出k次B样条的所有k＋1个非零函数值,运算效率提高了2k＋1倍。在最小二乘法B样条曲线拟合算法中的应用验证了本文算法的有效性。     

Rapid local ionosphere modeling based on Precise Point Positioning over Iran: A case study under 2014 solar maximum

Presently, the ionosphere effect is the main source of the error in the Global Positioning System (GPS) observations. This effect can largely be removed by using the two-frequency measurements, while to obtain the reasonable results in the single-frequency applications, an accurate ionosphere model is required. Since the global ionosphere models do not meet our needs everywhere, the local ionosphere models are developed. In this paper, a rapid local ionosphere model over Iran is presented. For this purpose, the GPS observations obtained from 40 GPS stations of the Iranian Permanent GPS Network (IPGN) and 16 other GPS stations around Iran have been used. The observations have been selected under 2014 solar maximum, from the days 058, 107, 188 and 271 of the year 2014 with different geomagnetic activities. Moreover, ionospheric observables based on the precise point positioning (PPP) have been applied to model the ionosphere. To represent our ionosphere model, the B-spline basis functions have been employed and the variance component estimation (VCE) method has been used to regularize the problem.To show the efficiency our PPP-derived local ionosphere model with respect to the International GNSS Service (IGS) global models, these models are applied on the single point positioning using single-frequency observations and their results are compared with the precise coordinates obtained from the double-differenced solution using dual-frequency observations. The results show that the 95th percentile of horizontal and vertical positioning errors of the single-frequency point positioning are about 3.1 and 13.6?m, respectively, when any ionosphere model are not applied. These values significantly improve when the ionosphere models are applied in the solutions. Applying CODE’s Rapid Global ionosphere map (CORG), improvements of 59% and 81% in horizontal and vertical components are observed. These values for the IGS Global ionosphere map (IGSG) are 70% and 82%, respectively. The best results are obtained from our local ionosphere model, where 84% and 87% improvements in horizontal and vertical components are observed. These results confirm the efficiency of our local ionosphere model over Iran with respect to the global models. As a by-product, the Differential Code Biases (DCBs) of the receivers are also estimated. In this line, we found that the intra-day variations of the receiver DCBs could be significant. Therefore, these variations must be taken into account for the precise ionosphere modeling.     

Non-parametric regional VTEC modeling with Multivariate Adaptive Regression B-Splines

In this work Multivariate Adaptive Regression B-Splines (BMARS) is applied to regional spatio-temporal mapping of the Vertical Total Electron Content (VTEC) using ground based Global Positioning System (GPS) observations. BMARS is a non-parametric regression technique that utilizes compactly supported tensor product B-splines as basis functions, which are automatically obtained from the observations. The algorithm uses a scale-by-scale model building strategy that searches for B-splines at each scale fitting adequately to the data and provides smoother approximations than the original Multivariate Adaptive Regression Splines (MARS). It is capable to process high dimensional problems with large amounts of data and can easily be parallelized. The real test data is collected from 32 ground based GPS stations located in North America. The results are compared numerically and visually with both the regional VTEC modeling generated via original MARS using piecewise-linear basis functions and another regional VTEC modeling based on B-splines.     

星箭连接界面处环形分布动载荷识别

提出一种基于卫星结构响应的环形分布动载荷识别方法。首先基于脉冲响应函数,在时域内构建激励与响应之间的传递关系;进一步,利用B样条函数表示动载荷的环形分布函数,并结合卫星结构有限元模型和结构测点加速度响应,识别了动载荷的分布函数及其时间历程。以某卫星模型开展数值仿真研究,结果表明：在不同噪声水平,响应测点数以及B样条控制点数的情况下,本文所提出的方法能够准确识别卫星结构所受分布动载荷。本文方法能够为实际飞行情况下卫星载荷环境评估提供理论支撑。     

A new error-controllable method for smoothing the G01 commands

In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.     

基于B样条的平流层飞艇外形优化设计

为改善飞艇气动性能,提高推进系统的效率,增加飞艇承受有效负载的能力并延长其运行时间,将飞艇艇体气动阻力和艇体表面积两个主要因素引入到平流层飞艇外形优化设计中,建立了复合目标函数,在飞艇体积不变的前提下,采用EXTREM数值优化算法,对平流层飞艇外形基于B样条曲线参数化方法在体积和长度不变的限制条件下,进行了双目标优化设计,优化后,外形的气动阻力减小了7.12%,同时飞艇艇体表面积也减少了1.76%。文章的研究结果实现了减阻和减重的双重目标,证明了该方法是合理可行的,可为平流层飞艇总体设计提供相关参考。     

汽车车身局部复杂曲面造型的计算方法

本文结合汽车车身复杂外形设计的实际，运用重节点型B样条曲线曲面理论，研究了汽车车身局部复杂曲面的造型方法，阐述了汽车车身局部复杂曲面造型的具体计算方法，为汽车车身复杂曲面的处理提供了一种有效的手段。