Research on layout optimization algorithm for high-aspect-ratio blades of aero-engines
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摘要:
为优化大展弦比转子叶片的动平衡布局，构建了以径向、轴向与切向质量矩为核心约束的多目标优化模型。针对传统遗传、蚁群和粒子群算法在收敛速度与寻优能力方面的不足，提出一种融合多维目标特性的改进优化策略。设计多维适应度函数以融合多方向力矩目标，增强算法对复杂约束的适应性；引入叶片对称性约束与权重控制机制提升解的结构合理性；改进种群初始化并引入局部搜索机制提升局部收敛精度与整体收敛速度。基于实际叶片数据的实验结果表明：改进遗传算法平均适应度由初始的28万降至2.8万，优化幅度超90%，相比其他算法优化效率提升约15%，最终解质量提高超过10%。
Abstract:To optimize the dynamic balance layout of high aspect ratio rotor blades, a multi-objective optimization model was established by incorporating radial, axial, and tangential mass moments as key constraints. To address the limitations of traditional genetic, ant colony, and particle swarm optimization algorithms in convergence speed and global search capability, an improved optimization strategy integrating multi-dimensional objective characteristics was proposed. A multi-dimensional fitness function was designed to accommodate multi-directional moment targets, while a symmetry constraint and weight control mechanism were introduced to enhance the structural rationality of the solution. Population initialization was improved, and a local search mechanism was integrated to boost both local convergence precision and global convergence efficiency. Experimental results based on actual blade mass moment data showed that the average fitness of the improved genetic algorithm decreased from approximately 280 000 to 28 000, achieving a reduction of over 90%. Compared to the other two algorithms, optimization efficiency improved by about 15%, and the final solution quality increased by more than 10%.
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图 3 某次排序3种算法收敛性能对比（算例1）
Figure 3. Comparison of convergence performance of three algorithms in a sorting instance （case 1）
图 4 某次排序3种算法收敛性能对比（算例2）
Figure 4. Comparison of convergence performance of three algorithms in a sorting instance （case 2）
图 5 3种算法平均收敛性能对比
Figure 5. Comparison of average convergence performance of three algorithms
表 1 改进启发式算法
Table 1. Improved heuristic algorithm
算法 传统 改进后 蚁群算法 依赖固定信息素更新，搜索路径单一 随机扰动、信息素动态调整、约束优化 遗传算法 固定变异概率、简单交叉 精英保留、动态变异、局部搜索 粒子群算法 静态权重更新、单纯位置调整 混合初始化、局部优化、动态参数调整 
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表 2 某套18转子叶片的质量矩数据
Table 2. Mass moment data of a set of 18 rotor blades
cm·g 叶片
编号径向
质量矩R轴向
质量矩A切向
质量矩T1 210161 − 22373 − 1627 2 208774 − 22468 −1874 3 208616 − 22136 − 2051 4 209493 − 22298 − 2053 5 209537 − 22324 − 2179 6 209866 − 22557 −1 986 7 209559 − 22330 −1 996 8 209362 − 22359 −1 966 9 207890 − 22210 −1 985 10 209800 − 22352 −1 984 11 208566 − 22178 − 2072 12 208397 − 22204 −2 023 13 209590 − 22310 −1 919 14 209919 − 22480 −2 027 15 209960 − 22373 −1 981 16 209502 − 22431 −1 967 17 209221 − 22079 − 2184 18 207496 − 21980 −2 035
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表 3 传统遗传算法和改进遗传算法参数对比
Table 3. Comparison of parameters between traditional genetic algorithm and improved genetic algorithm
算法 种群
大小交叉概率/
精英保留变异
概率最大迭代
次数传统遗传算法 20 0.6 0.01 100 改进遗传算法 50 0.8 0.1 200
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表 4 传统蚁群算法和改进蚁群算法参数对比
Table 4. Comparison of parameters between traditional ant colony algorithm and improved ant colony algorithm
算法 蚂蚁数量 信息素蒸发率 信息素重要程度因子 启发式信息重要程度因子 最大迭代次数 信息素增加强度系数 传统蚁群算法 50 0.1 1.0 1.0 200 1.0 改进蚁群算法 50 0.15 1.0 2.0 200 100
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表 5 传统粒子群算法和改进粒子群算法参数对比
Table 5. Comparison of parameters between traditional particle swarm algorithm and improved particle swarm algorithm
算法 粒子群规模 惯性权重 个体学习因子 社会学习因子 最大速度限制 迭代次数 传统粒子群算法 30 0.7 2.0 2.0 4.0 100 改进粒子群算法 50 0.9～0.4 2.5 2.5 6.0 300
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表 6 传统算法和改进后算法总适应度F结果对比
Table 6. Total fitness F result of the traditional algorithm and the improved algorithm
算法 迭代次数 1 2 3 4 5 传统遗传算法 2021333.38 1483170.72 310476.51 1740946.74 1096872.71 改进遗传算法 697.42 1099.72 1043.03 1250.86 1542.72 传统蚁群算法 846.19 1402.17 878.98 1005.79 1039.09 改进蚁群算法 839.55 1021.00 1005.79 1013.67 839.55 传统粒子群算法 47901674.28 72497527.38 152129883.46 52026871.19 51427324.77 改进粒子群算法 1006.52 1061.94 921.20 1149.79 797.06 算法 迭代次数 6 7 8 9 10 传统遗传算法 2253812.35 888052.17 2554866.31 620477.52 862996.94 改进遗传算法 1202.91 794.97 763.53 1363.90 1178.83 传统蚁群算法 839.55 906.15 885.44 655.62 1184.98 改进蚁群算法 906.15 1067.87 1029.37 906.15 528.93 传统粒子群算法 18354654.14 27041241.36 63972203.67 103311318.17 55884253.85 改进粒子群算法 1107.07 1091.89 1378.07 1085.93 860.52
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表 7 某次排序目标函数计算结果
Table 7. Objective function calculation results of a sorting instance
算法 C1 C2 C3 C4 改进遗传算法 336.38 525.96 340.57 394.00 改进蚁群算法 120.16 467.69 318.30 394.00 改进粒子群算法 31.76 761.81 313.50 426.00
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表 8 3种算法最佳适应度结果
Table 8. Best fitness results of three algorithms
算法 最佳适应度 改进蚁群算法 603.96 改进遗传算法 332.58 改进粒子群算法 990.01
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