Probe measurement correction method based on genetic algorithm-optimized BP neural network
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摘要:
针对探针在航空发动机复杂流场中因多种因素导致的总压测量误差的问题，采用了一种基于遗传算法优化反向传播 （GA-BP）神经网络的误差修正方法。基于数值模拟得到的多组样本数据集，采用GA-BP神经网络：确定隐藏层为6节点结构；logsig和purelin分别为隐藏层、输出层的激活函数，trainlm为训练函数；优化初始种群规模为45，交叉概率0.8与变异分布指数为5的组合使方均根误差降至
0.37591 。实验结果表明：GA-BP测试集的方均根误差较标准BP模型降低66.7%，平均相对误差降幅为72.4%，决定系数高于0.999；90%样本误差低于2×10−3且在零均值对称分布，显著提升了模型的修正精度与泛化能力，为航空发动机气动性能测试提供了参考方案。Abstract:To address total pressure measurement errors caused by multiple factors in complex aero-engine flow fields, an error correction method based on a genetic algorithm-optimized backpropagation (GA-BP) neural network was proposed. Utilizing multi-sample datasets from numerical simulations, the GA-BP neural network was adopted: a 6-node hidden layer structure was determined, with logsig and purelin served as activation functions for the hidden and output layers respectively, and trainlm as the training function. An optimized combination of initial population size of 45, crossover probability of 0.8, and mutation distribution index of 5 reduced the root mean square error to
0.37591 . Experimental results demonstrate that, compared with the standard BP model, the GA-BP model reduced root mean square error by 66.7% and the mean relative error by 72.4% on the test set, while achieving a coefficient of determination above 0.999; errors of 90% samples were below 2×10−3 and symmetrically distributed around zero. This proposed approach significantly enhances correction accuracy and generalization capability, providing a reference solution for aero-engine aerodynamic performance testing.-
Key words:
- probe /
- total pressure measurement /
- error correction /
- neural network /
- genetic algorithm
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图 6 不同临壁距离下的总压测量误差实验值与数值模拟结果对比
Figure 6. Comparison of experimental and numerical simulation results of total pressure measurement error at different wall distances
表 1 隐藏层不同节点数时的方均根误差
Table 1. Root mean squared error with different numbers of hidden layer nodes
隐藏层节点数 实验次数 平均值 1 2 3 4 5 6 7 3 1.1366 1.4693 1.7792 1.8433 1.4663 1.6276 0.9604 1.4690 4 0.8855 0.8052 1.8485 1.7460 0.9017 0.3784 0.5373 1.0147 5 0.3388 0.3491 0.8929 1.3562 0.9728 1.5196 1.2238 0.9505 6 1.5242 1.4524 0.4547 0.7616 0.3197 0.5855 0.2074 0.7580 7 0.6133 1.4029 0.5860 0.8684 0.3670 1.5094 0.7643 0.8730 8 1.3411 0.4445 1.6633 0.3749 1.0680 1.2330 0.6140 0.9627 9 1.2894 0.6478 0.8781 0.8180 0.9074 0.9928 1.0802 0.9448 10 1.4148 0.7764 0.627 1.3779 0.5524 1.1857 0.8677 0.9717 
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表 2 不同激活函数的方均根误差对比表
Table 2. Comparison table of root mean squared errors for different activation functions
隐藏层 输出层 方均根误差 logsig logsig 16.883 purelin logsig 15.933 tansig logsig 16.122 logsig purelin 0.710 purelin purelin 3.958 tansig purelin 0.766 logsig tansig 1.447 purelin tansig 3.376 tansig tansig 0.881
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表 3 不同训练函数的方均根误差对比表
Table 3. Comparison table of root mean squared errors for different training functions
训练函数 训练步数 方均根误差 trainlm 50 0.553 trainbr 290 0.503 trainrp 36 2.272 traingdx 156 4.422
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表 4 不同初始种群的方均根误差
Table 4. Root mean squared error with different initial populations
初始种群数量 训练步数 方均根误差 10 34 0.455546 15 42 0.448802 20 22 0.767064 25 24 0.711038 30 42 0.856368 35 32 0.704458 40 27 0.455836 45 31 0.337510 50 24 0.637122 55 30 0.578608 60 24 0.75814 65 24 0.390754 70 38 0.472082
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表 5 不同交叉概率和变异分布指数的方均根误差
Table 5. Root mean squared error for different crossover probabilities and mutation distribution indices
变异分布指数 方均根误差 Pc=0.4 Pc=0.5 Pc=0.6 Pc=0.7 Pc=0.8 Pc=0.9 2 0.41737 0.599393 0.449535 0.607968 0.848658 1.13681 3 0.417895 0.560195 0.669135 0.585493 0.37986 0.398423 4 0.435128 0.65001 0.84736 0.775194 1.048908 0.775638 5 0.514388 0.731993 0.403785 0.407817 0.37591 1.016433 6 0.572373 0.89844 0.727013 0.53635 0.67243 0.381245
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表 6 模型评价
Table 6. Model evaluation
评价指标 BP GA-BP 训练集 测试集 训练集 测试集 $ {e}_{{\mathrm{rms}}} $ 0.70242 1.0162 0.34214 0.33854 $ {{{R}^{2}}} $ 0.99851 0.9969 0.99986 0.99969 $ {e}_{{\mathrm{ma}}} $ 0.48448 0.72881 0.12507 0.20089 $ {e}_{{\mathrm{mr}}} $ 0.0038 0.0058 0.0010 0.0016
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