基于NURBS的翼型参数化方法研究

RESEARCH ON AIRFOIL PARAMETERIZATION USING NONUNIFORM RATIONAL B-SPLINE

鲁子豪

11649092

硕士

力学

单肖文

2018-06-05

2018-07-02

哈尔滨工业大学

深圳

本文对离散翼型的 NURBS 表达做了详细的研究。NURBS 方法理论复杂，计算繁琐，种类多样，但具有十分良好的几何性质，本文希望通过研究结果，定量的描述出 NURBS 在进行翼型参数化时，各个变量对拟合效率的影响，依此开发出一种最佳的 NURBS（此处的 NURBS 包含一类曲线而并非单指非均匀有理 B 样条曲线）参数选择策略。翼型拟合作为一种优化问题，初值选取十分重要，本文对初值选取进行了详细的研究，在对应用较为广泛的余弦取点法进行微调后，制定出了一种在给定 NURBS 曲线控制点个数后的取点策略，并将这数据点进行 B 样条插值后反求得到的参数作为优化问题的初值。在优化算法的选取上，本文采用Nelder-Mead 单纯形法，一种高效的不依赖于梯度信息的直接优化算法。本文详细地对比了：1. 只将控制点作为设计变量，2. 将控制点和权因子作为设计变量，3.将控制点，权因子，节点区间一起作为设计变量，这三种设计变量选取形式的拟合效率，得出在一般情况下 (设计变量个数小于 30 个)，1 和 2 的效率比 3 高，但由于仅将控制点作为设计变量利于编程实现，且便于二维翼型插值生成三维机翼，故在一般情况下只将控制点作为设计变量是最佳选择；但当设计变量个数大于 30时，将控制点，节点区间和权因子都选作设计变量进行优化是最佳策略。同时，结果表明，采用本文的初值选取方式和优化算法，对绝大部分翼型而言，将控制点和权因子作为设计变量时，十个控制点足以达到 8 × 10∗5 的最大误差需求，这与相关文献采用方法所需的十三个控制点相比，效率提升了 23%。

In this thesis, the application of non-uniform rational B-spline method in the field of airfoil representation has been investigated in detail. The NURBS method is complex in theory, complicated in calculation, and diverse in variety, but it has very good geometric properties. This thesis hopes to formulate an optimal parameter selection strategy when using NURBS for airfoil optimization. Airfoil fitting is strictly an optimization problem. As we all know, the initial value of the optimization problem is very important. In this thesis, the initial value selection is studied in detail. After a fine tuning of the cosine points selection method, which is widely used, a strategy of choosing points after the number of control points of a NURBS curve is fixed is formulated. These points are used as B-spline interpolation points. After performing B-spline interpolation, the parameters obtained by inverse calculation are used as the initial value of the optimization problem. In the selection of optimization algorithm, the study uses Nelder-Mead simplex method, an efficient direct optimization algorithm that does not depend on gradient information. This study compares the efficiency of three design variable selecting methods, 1.Control points only, 2. Control points with weights, 3. Control points, weights and knot vector together when performing airfoil fitting, and concludes that, under normal circumstances, choosing control points alone is best, since this is easy for programming and generating 3D wing by 2D airfoil by interpolation; but when the fitting accuracy is very demanding,over 30 design variables have to be used, it is best to use control points, knot vector and weights together as design variables. At the same time, the results show that using the initial value selection method and optimization algorithm in this thesis, for most airfoils, when the control points and weights are both chosen as design variables, ten control points are sufficient to meet the maximum error requirement. Compared with the thirteen control points required for the method used in the relevant literature, the efficiency has increased by 23%.

优化 非均匀有理B样条 翼型 拟合 Nelder-Mead单纯形法

optimization NURBS airfoil fitting Nelder-Mead simplex method

中文

联合培养

南方科技大学

鲁子豪. 基于NURBS的翼型参数化方法研究[D]. 深圳. 哈尔滨工业大学,2018.