摘要： 航空发动机叶片气动性能设计的改进要求叶片加工系统采用高精度、高效率的加工工艺，基于传统建模方法的叶片加工系统已难以满足当前的加工需求。提出一种基于改进麻雀搜索算法（SSA）的拟合方法，旨在利用最少控制点高效地达到曲线拟合的目标精度，进而提升传统建模方法的精度和效率，建立适用于数字孪生生产环境的高精度、高实时性的三维叶片模型，提高航空发动机叶片的加工合格率。启发式优化算法在B样条曲线拟合中存在收敛慢的问题，而SSA不断跃向最优解的特性使其能快速收敛。基于此，改进SSA的位置更新函数并给出内节点向量更新范围的概念，通过自动迭代内节点向量配置，利用最小二乘法计算最优控制点，依据局部和全局误差计算适应度值并参与下次迭代，多次迭代后得到符合目标精度的拟合曲线。此外，为提高SSA搜索最少控制点的效率，设计一种二分搜索方法。采用某型叶片截面数据进行拟合验证，结果表明，与传统定义节点向量方法和经典优化算法相比，该方法具有较高的拟合精度和收敛效率，在20和80个控制点下分别取得了1e-3 mm和1e-5 mm左右的拟合精度，在5e-3 mm目标精度下，收敛效率较粒子群优化算法、标准SSA分别提升了14.5%~97.8%和35.8%~70.1%，搜索最少控制点的效率较传统方法提升了34.7%~49.6%。

关键词: 数字孪生, B样条曲线拟合, 麻雀搜索算法, 节点向量, 二分搜索

Abstract: For blade processing systems, the improvement of aero-engine blade aerodynamic performance design requires high-precision and high-efficiency processing technology.Blade machining systems based on traditional modeling methods have difficulty meeting today's machining requirements.Therefore, a B-spline curve fitting method based on the improved Sparrow Search Algorithm(SSA) is proposed, which efficiently achieves the target accuracy of curve fitting using the fewest control points.The method improves the accuracy and efficiency of traditional modeling methods, establishes a three-dimensional blade model suitable for digital twin production environments, and improves the processing qualification rate of aero-engine blades.The heuristic optimization algorithm has the problem of slow convergence in B-spline curve fitting, and SSA's ability to continuously leap to the optimal solution enables it to converge quickly.Accordingly, this study improves the position update function of the SSA and proposes the concept of updating range of the inner node vector. In addition, the internal node vector configuration is automatically iterated, and the least squares method is used to calculate the optimal control point.The fitness value is next calculated based on local and global errors, the next iteration is performed, and finally a fitting curve that meets the target accuracy is obtained.To improve the efficiency of SSA searching for the least control points, a binary search method is also designed.Blade cross-section data of a certain type are used for fitting verification.Compared with classical optimization algorithms and the traditional method of defining node vectors, the results show that the fitting accuracy and convergence efficiency of this method are superior, and the efficiency of searching for the least control points is greatly improved.With 20 and 80 control points, this method achieves a fitting accuracy of approximately 1e-3 mm and 1e-5 mm, respectively.Under the target accuracy of 5e-3 mm, the convergence efficiency is improved by 14.5%-97.8% and 35.8%-70.1% as compared with the Particle Swarm Optimization(PSO) algorithm and standard SSA, respectively.Compared with the traditional method, the efficiency of searching for the least control points is improved by 34.7%-49.6%.

Key words: digital twin, B-spline curve fitting, Sparrow Search Algorithm(SSA), node vector, binary search

中图分类号: 

• TP391.72