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Extraction of Feature Points for Non-Uniform Rational B-Splines(NURBS)-Based Modeling of Human Legs
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作者 王玺 吴宗谦 李乔 《Journal of Donghua University(English Edition)》 CAS 2022年第4期299-303,共5页
Methods of digital human modeling have been developed and utilized to reflect human shape features.However,most of published works focused on dynamic visualization or fashion design,instead of high-accuracy modeling,w... Methods of digital human modeling have been developed and utilized to reflect human shape features.However,most of published works focused on dynamic visualization or fashion design,instead of high-accuracy modeling,which was strongly demanded by medical or rehabilitation scenarios.Prior to a high-accuracy modeling of human legs based on non-uniform rational B-splines(NURBS),the method of extracting the required quasi-grid network of feature points for human legs is presented in this work.Given the 3 D scanned human body,the leg is firstly segmented and put in standardized position.Then re-sampling of the leg is conducted via a set of equidistant cross sections.Through analysis of leg circumferences and circumferential curvature,the characteristic sections of the leg as well as the characteristic points on the sections are then identified according to the human anatomy and shape features.The obtained collection can be arranged to form a grid of data points for knots calculation and high-accuracy shape reconstruction in future work. 展开更多
关键词 3D scan digital human modeling non-uniform rational b-splines(NURBS) feature extraction
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THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES
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作者 HAN XI’AN AND HUANG XILI 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1998年第4期445-450,共6页
Abstract For two rational quadratic B spline curves with same control vertexes, the cross ratio of four collinear points are represented: which are any one of the vertexes, and the two points that the ray initialing f... Abstract For two rational quadratic B spline curves with same control vertexes, the cross ratio of four collinear points are represented: which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the two curves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Bézier curves, the value is generally related with the location of the ray, and the necessary and sufficient condition of the ratio being independent of the ray's location is showed. Also another cross ratio of the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initial vertex intersects respectively with the curve segment, the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only with the ray's location, but not with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments. 展开更多
关键词 Computer aided geometric design rational b-spline curve cross ratio weight
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Shape Control and Modification of Rational Cubic B-Spline Curves
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作者 Zhao Hongsheng Zhang Mandong(Department of Mechanical EngineeringTaiyuan University of Technology, Taiyuan 030024, P. R. China) 《Computer Aided Drafting,Design and Manufacturing》 1999年第1期17-23,共7页
This paper considers the construction of a rational cubic B-spline curve that willinterpolate a sequence of data points x'+ith specified tangent directions at those points. It is emphasisedthat the constraints are... This paper considers the construction of a rational cubic B-spline curve that willinterpolate a sequence of data points x'+ith specified tangent directions at those points. It is emphasisedthat the constraints are purely geometrical and that the pararnetric tangent magnitudes are notassigned as in many' curl'e manipulation methods. The knot vector is fixed and the unknowns are thecontrol points and x'eightsf in this respect the technique is fundamentally different from otherswhere knot insertion is allowed.First. the theoretical result3 for the uniform rational cubic B-spline are presented. Then. in theplanar case. the effect of changes to the tangent at a single point and the acceptable bounds for thechange are established so that all the weights and tangent magnitUdes remain positive. Finally, aninteractive procedure for controlling the shape of a planar rational cubic B-spline curve is presented. 展开更多
关键词 rational cubic b-spline shape control tangent modification
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Spline-based automatic path generation of welding robot
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作者 牛雪娟 李亮玉 《China Welding》 EI CAS 2007年第4期27-31,共5页
This paper presents a flexible method for the representation of welded seam based on spline interpolation. In this method, the tool path of welding robot can be generated automatically from a 3D CAD model. This techni... This paper presents a flexible method for the representation of welded seam based on spline interpolation. In this method, the tool path of welding robot can be generated automatically from a 3D CAD model. This technique has been implemented and demonstrated in the FANUC Arc Welding Robot Workstation. According to the method, a software system is developed using VBA of SolidWorks 2006. It offers an interface between SolidWorks and ROBOGUIDE, the off-line programming software of FANUC robot. It combines the strong modeling function of the former and the simulating function of the latter. It also has the capability of with on-line robot. The result data have shown its high accuracy and strong reliability in experiments. This method will improve the intelligence and the flexibility of the welding robot workstation. 展开更多
关键词 CAD rational b-spline curve welded seam
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Methods of configuration test and deformation analysis for large airship
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作者 ZHAI Yutao SHEN Yongzheng +1 位作者 YAN Xiangbin TAN Huifeng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2022年第4期951-960,共10页
In recent years, high-altitude aerostats have been increasingly developed in the direction of multi-functionality and large size. Due to the large size and the high flexibility, new challenges for large aerostats have... In recent years, high-altitude aerostats have been increasingly developed in the direction of multi-functionality and large size. Due to the large size and the high flexibility, new challenges for large aerostats have appeared in the configuration test and the deformation analysis. The methods of the configuration test and the deformation analysis for large airship have been researched and discussed. A tested method of the configuration,named internal scanning, is established to quickly obtain the spatial information of all surfaces for the large airship by the three-dimensional(3D) laser scanning technology. By using the surface wrap method, the configuration parameters of the large airship are calculated. According to the test data of the configuration, the structural dimensions such as the distances between the characteristic sections are measured. The method of the deformation analysis for the airship contains the algorithm of nonuniform rational B-splines(NURBS) and the finite element(FE)method. The algorithm of NURBS is used to obtain the reconfiguration model of the large airship. The seams are considered and the seam areas are divided. The FE model of the middle part of the large airship is established. The distributions of the stress and the strain for the large airship are obtained by the FE method. The position of the larger deformation for the airship is found. 展开更多
关键词 large airship deformation analysis three-dimensional(3D)laser scanning technology non-uniform rational b-splines(NURBS) system engineering
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隧道结构NURBS无网格弹塑性快速分析方法及其应用
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作者 苟宇丹 姜弘 毕金锋 《隧道建设(中英文)》 CSCD 北大核心 2023年第12期2114-2121,共8页
为解决异型隧道结构建模分析困难、各类弹塑性数值计算方法精度有限、鲁棒性较低等问题,研究发展一种快速稳定的NURBS-MF(nonuniform rational B-spline-based meshfree)弹塑性分析方法,并将其应用于马蹄型隧道结构的塑性区计算中。NURB... 为解决异型隧道结构建模分析困难、各类弹塑性数值计算方法精度有限、鲁棒性较低等问题,研究发展一种快速稳定的NURBS-MF(nonuniform rational B-spline-based meshfree)弹塑性分析方法,并将其应用于马蹄型隧道结构的塑性区计算中。NURBS-MF方法利用样条曲线参数化建模结构几何的优点,实现对异型结构的快速建模;通过规则参数空间的映射法则自动进行结点布设,合理地离散待分析区域,极大地降低了异型结构计算的前处理与分析难度。在此基础上推导基于NURBS映射的无网格弹塑性控制方程,提出改进的NURBS-MF弹塑性算法,以适用于异型断面结构的弹塑性快速分析。NURBS-MF弹塑性分析方法提出了一种全新的无网格结点与积分点生成方式,避免了边界积分单元被切割;没有多余的积分点且不产生额外的数值积分代价,能较为明显地降低无网格类数值方法在弹塑性分析中的计算代价、提高其鲁棒性。根据NURBS-MF弹塑性公式与Newton-Raphson迭代算法编写的弹塑性分析程序,可优化异型隧道结构的建模与计算过程。通过典型的弹塑性数值算例及某大断面异型隧道衬砌结构的数值试验表明,该方法具有简洁、稳定、精确等优点,且具有工程实用性。 展开更多
关键词 NURBS 无网格法 弹塑性 隧道结构
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闭合圆锥曲线的2次周期性NURBS表示 被引量:4
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作者 秦开怀 孙家广 王学福 《计算机学报》 EI CSCD 北大核心 1992年第8期572-581,共10页
本文探讨了用2次周期性NURBS表示闭合圆锥曲线的方法,导出了精确表示椭圆、抛物线和双曲线的条件,并给出了精确表示圆弧的充要条件;提出了用2次NURBS精确表示圆的新方法.和其它基于矩形控制多边形的同类方法相比,其控制点数最少.用2次... 本文探讨了用2次周期性NURBS表示闭合圆锥曲线的方法,导出了精确表示椭圆、抛物线和双曲线的条件,并给出了精确表示圆弧的充要条件;提出了用2次NURBS精确表示圆的新方法.和其它基于矩形控制多边形的同类方法相比,其控制点数最少.用2次非周期性NURBS(2次有理Bezier样条)和2次均匀有理B样条描述圆锥曲线的方法均是本文的一个特例. 展开更多
关键词 圆锥曲线 B样条 周期性 NURBS
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三次NURBS曲线的插值方法 被引量:14
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作者 秦开怀 孙家广 范刚 《计算机辅助设计与图形学学报》 EI CSCD 1993年第3期179-183,共5页
本文提出了一个用于3次NURBS曲线插值的新方法,该方法首先用二次规划算出控制顶点的权因子,然后反算出所有的控制顶点,它能确保由型值点的权W_i(>0)所算出的控制顶点的权也均大于0,插值曲线具有C^2连续性,当W_i均为一个大于0的常数时... 本文提出了一个用于3次NURBS曲线插值的新方法,该方法首先用二次规划算出控制顶点的权因子,然后反算出所有的控制顶点,它能确保由型值点的权W_i(>0)所算出的控制顶点的权也均大于0,插值曲线具有C^2连续性,当W_i均为一个大于0的常数时,插值曲线退化为非均匀B样条曲线。 展开更多
关键词 NURBS 曲线 插值法 CAD
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NURBS曲面的算法分析及实现 被引量:6
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作者 秦志光 张凤荔 刘锦德 《电子科技大学学报》 EI CAS CSCD 北大核心 1994年第4期411-415,共5页
讨论了NURBS曲线和节点矢量、控制点和基函数对曲面形状的影响,给出了NURBS的算法分析及其实现方案,最后,将NURBS曲面与老式曲面(如B样条、Bezier曲面等)进行了比较。
关键词 节点 曲面 NURBS曲面 算法分析
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结构型网格分块生成技术 被引量:8
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作者 张立东 李椿萱 《计算物理》 CSCD 北大核心 2001年第4期325-328,共4页
构造了一种适用于模拟具有复杂几何特征的流动问题的结构型网格生成方法 ,该方法应用CAD技术中非均匀有理B样条 (NURBS)曲面表达形式 ,根据给定物体的典型站位截面 ,首先对物体进行分片表面网格的构造与重构 ,同时根据物体几何特征及流... 构造了一种适用于模拟具有复杂几何特征的流动问题的结构型网格生成方法 ,该方法应用CAD技术中非均匀有理B样条 (NURBS)曲面表达形式 ,根据给定物体的典型站位截面 ,首先对物体进行分片表面网格的构造与重构 ,同时根据物体几何特征及流场特性对绕流流场进行区域分解并构造其块边界 ,在此基础上再采用数值方法进行相应的分块网格生成 ,并给出了应用所建立的方法生成的几种天地往返运输系统流场网格 . 展开更多
关键词 结构型网格分块生成技术 非均匀有理B样条 衔接式块网格 重叠式块网格 流场特性 计算空气动力学
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NURBS曲面造型与数控加工 被引量:2
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作者 邹晓范 黄金莹 吕同富 《佳木斯大学学报(自然科学版)》 CAS 2007年第2期264-267,共4页
以NURBS为数学模型,对曲面造型及加工系统进行了研究.在对各种算法分析、研究和改进的基础上,完成了一个集CAD/CAM于一体具有多种功能的曲面造型及加工系统,合理地将NURBS的主要核心配套技术和各种算法运用于NURBS造型系统中,通过交互... 以NURBS为数学模型,对曲面造型及加工系统进行了研究.在对各种算法分析、研究和改进的基础上,完成了一个集CAD/CAM于一体具有多种功能的曲面造型及加工系统,合理地将NURBS的主要核心配套技术和各种算法运用于NURBS造型系统中,通过交互方式成功实现了对多种曲线曲面(直线、圆弧、二次曲线、自由曲线、平面、二次曲面、旋转面、直纹面、雕塑曲面、截线面曲面、自由曲面、复杂组合曲面等)的造型生成. 展开更多
关键词 NURBS 插值 数控加工
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基于多边形转换函数与NURBS的雕刻型面建模 被引量:1
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作者 张潇云 陈宇拓 苏畅 《电脑与信息技术》 2007年第6期40-42,57,共4页
根据平面任意闭合图形的图像,用多边形到函数的转换方法确定雕刻型面的部分深度信息,并用非均匀有理B样条(NURBS)曲面对这些参数进行插值,实现了对雕刻型面的建模。
关键词 多边形逼近 多边形到函数的转换 非均匀有理B样条曲面插值
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电极损耗分层预变形补偿方法
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作者 陈健 王进 陆国栋 《浙江大学学报(工学版)》 EI CAS CSCD 北大核心 2017年第3期436-444,共9页
为了提高大损耗量条件下电火花成型加工(DEDM)的精度,提出一种基于初始形状预变形的电极损耗补偿方法.分析电极损耗预变形补偿基本原理,建立以相对体积损耗比为基础的电极损耗量模型.在非均匀有理B样条曲线(NURBS)三维表征的基础上进行... 为了提高大损耗量条件下电火花成型加工(DEDM)的精度,提出一种基于初始形状预变形的电极损耗补偿方法.分析电极损耗预变形补偿基本原理,建立以相对体积损耗比为基础的电极损耗量模型.在非均匀有理B样条曲线(NURBS)三维表征的基础上进行电极曲面的离散;根据单次放电损耗量与总损耗量的线性关系,提出基于放电间隙的等损耗非均匀的分层补偿方法;构建基于平均曲率的偏移长度和基于伺服进给的偏移方向的计算模型,得出补偿矢量.结合能量法和遗传算法进行曲面光顺,并建立电极损耗的预变形补偿流程模型,计算电极的预变形形状.算例和实验结果表明,采用该方法补偿后的电火花成型加工产生的平均几何误差小于30μm,有助于实现精密加工. 展开更多
关键词 电火花成型加工(DEDM) 电极损耗 预变形 非均匀有理B样条曲线(NURBS) 分层补偿
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组合NURBS曲面转化Catmull-Clark曲面的多分辨率算法
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作者 吴维勇 王英惠 《机械设计》 CSCD 北大核心 2008年第4期53-56,共4页
为了将多分辨率造型技术应用于NURBS形体,基于小波重构技术给出了组合NURBS曲面转化为Catmull-Clark曲面的多分辨率算法,可以实现NURBS形体的小波分解与重构等多分辨率操作。首先利用Catmull-Clark曲面求值公式计算出初始控制网格,通过... 为了将多分辨率造型技术应用于NURBS形体,基于小波重构技术给出了组合NURBS曲面转化为Catmull-Clark曲面的多分辨率算法,可以实现NURBS形体的小波分解与重构等多分辨率操作。首先利用Catmull-Clark曲面求值公式计算出初始控制网格,通过计算拟合误差,利用局部插值算法计算小波系数,在此基础上,利用提升B样条小波重构公式构造出Catmull-Clark曲面,提出一种自适应算法,加快了曲面重构速度,运行实例验证了算法的有效性。 展开更多
关键词 非均匀有理B样条 细分曲面 小波 多分辨率分析
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A NEW METHOD FOR REPRESENTING THE CIRCLE BY NURBS
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作者 Qin Kaihuai Sun Jiaguang Dept. of Computer Science and Technology Tsinghua University, Beijing 100084, P. R. China 《Computer Aided Drafting,Design and Manufacturing》 1992年第2期1-9,共9页
In this paper, a new algorithm for representing conics precisely is presented using NURBS of degree two. The algorithm requires only four control vertices, which is the minimum number of control vertices compared with... In this paper, a new algorithm for representing conics precisely is presented using NURBS of degree two. The algorithm requires only four control vertices, which is the minimum number of control vertices compared with the other algorithms using the square control vertice configuration, to represent a full circle using the full circumscribing square based representation. This paper also derives a new con- dition for NURBS to precisely represent conics and shows the necessary and sufficient condition of rep- resentation of a circular arc. 展开更多
关键词 CONIC circle nonuniform rational b-spline (NURBS)
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电磁散射目标的NURBS建模 被引量:1
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作者 陈玲玲 万国宾 刘冲 《计算机辅助工程》 2005年第3期71-73,共3页
采用非均匀有理B样条(NURBS)对复杂目标进行建模,利用Cox-DeBoor算法将NURBS曲线曲面转化为更适合数值计算的有理Bézier曲线曲面,采用后向面判别法处理不同面元间的遮挡问题,并给出导弹雷达散射截面的计算结果。
关键词 非均匀有理B样条 BÉZIER曲面 后向面判别
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FREE-FORM SURFACE RECON-STRUCTION BASED ON NURBS TO SERIAL CROSS-SECTIONS 被引量:5
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作者 SunYuwen WangYuechao LiuWeijun 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2003年第4期420-423,共4页
A new method for recovering shape from cross-sectional contours with complexbranching structures is presented. First, each branching problem by providing an intermediatecontour using distance function and image proces... A new method for recovering shape from cross-sectional contours with complexbranching structures is presented. First, each branching problem by providing an intermediatecontour using distance function and image processing technology is solved. Then, all contours aredivided into several groups of simple contours. For each group, a NURBS curve is fitted to contourpoints in each section within a given accuracy on a common knot vector. Finally, the NURBS surfaceskinning of these contours is performed for providing a smooth geometric model. The method issuitable to reproduce the object by NC machining or rapid prototyping. Some results demonstrate itsusefulness and feasibility. 展开更多
关键词 Sectional contour Non-uniform rational b-splines Branching Surfacereconstruction
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PRACTICAL G^2 CONTINUITY ALGORITHMS BETWEEN ADJACENT NURBS PATCHES 被引量:1
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作者 Zhou Xijun Yang Haicbeng(Research Center for Computer Aided Design and Mannufacturing, NorthwesternPolytehnical University, Xi’an, 710072, China) 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 1997年第2期110-118,共9页
Non-uniform rationa1 B-spline (NURBS) curves and sdrices are becomingincreasingly widespread. ’The authors have explored G1 continuity condition between adja-cent NURBS surface patches along common boundary curve. Th... Non-uniform rationa1 B-spline (NURBS) curves and sdrices are becomingincreasingly widespread. ’The authors have explored G1 continuity condition between adja-cent NURBS surface patches along common boundary curve. This paper presents a G2continuity condition between adjacent NURBS patches along common quadratic boundarycurve and deduces a specific algorithm for control Points and weights of NURBS patch.For making another NURBS patch and one given NURBS patch to attain G2, according toalgorithms condition, one can adjust another patch control ponts and weights. It is muchmore convenient for engineers to apply. 展开更多
关键词 CONTOURS surfaces models nonuniform rational b-spline geometric CONTINUITY
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Offset approximation based on reparameterizing the path of a moving point along the base circle 被引量:2
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作者 ZHAO Hong-yan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第4期431-442,共12页
This paper presents a novel algorithm for planar curve offsetting. The basic idea is to regard the locus relative to initial base circle, which is formed by moving the unit normal vectors of the base curve, as a unit ... This paper presents a novel algorithm for planar curve offsetting. The basic idea is to regard the locus relative to initial base circle, which is formed by moving the unit normal vectors of the base curve, as a unit circular arc first, then accurately to represent it as a rational curve, and finally to reparameterize it in a particular way to approximate the offset. Examples illustrated that the algorithm yields fewer curve segments and control points as well as C^1 continuity, and so has much significance in terms of saving computing time, reducing the data storage and smoothing curves entirely. 展开更多
关键词 CAD/CAM OFFSET circle CONVOLUTION Bezier/b-spline curve rational curve
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基于核主成分分析的涡轮盘结构设计优化 被引量:2
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作者 罗丰 张立章 +1 位作者 米栋 钱正明 《推进技术》 EI CAS CSCD 北大核心 2022年第2期135-141,共7页
为解决轮盘形状优化过程中变量多且高度非线性的问题,建立了基于核主成分分析(Kernelized Principal Component Analysis,KPCA)技术的航空发动机轮盘优化方法。利用控制点形式的非均匀有理B样条(NURBS)曲线构造涡轮盘截面形状,以控制点... 为解决轮盘形状优化过程中变量多且高度非线性的问题,建立了基于核主成分分析(Kernelized Principal Component Analysis,KPCA)技术的航空发动机轮盘优化方法。利用控制点形式的非均匀有理B样条(NURBS)曲线构造涡轮盘截面形状,以控制点的坐标作为设计变量;利用实验设计(DOE)进行采样,从中选取60个较优样本,计算核矩阵K,应用核矩阵K的特征向量计算投影向量的系数矩阵,采用投影后的变量作为新的设计变量,重构设计空间;最后,在降维后的设计空间中优化涡轮盘。结果表明:优化后轮心当量应力降低4.21%,周向应力降低0.26%,轮背径向应力降低1.58%,子午截面平均周向应力降低2.57%,圆柱截面平均径向应力降低6.51%。 展开更多
关键词 涡轮盘 非均匀有理B样条 结构设计优化 核主成分分析 降维空间
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