基于自适应遗传算法响应面优化模型的MDOE方法研究

程起有; 李春华; 江嘉伟; 胡磊; 陈卫星

doi:10.13224/j.cnki.jasp.20240844

基于自适应遗传算法响应面优化模型的MDOE方法研究

doi: 10.13224/j.cnki.jasp.20240844

中国航空工业集团有限公司中国直升机设计研究所，江西景德镇 333001

基金项目: 直升机旋翼动力学国家重点实验室基金（61422202206）

详细信息

作者简介:
程起有（1980-），男，研究员，博士，主要从事直升机风洞试验技术研究。E-mail：chengqy@avic.com

通讯作者:
江嘉伟（1998-），男，工程师，硕士，主要从事直升机风洞试验气动特性研究。E-mail：jiangjw018@avic.com

中图分类号: V211.52
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出版历程
- 收稿日期: 2024-12-18
- 网络出版日期: 2025-05-19

Research on MDOE methods based on response surface optimization model with adaptive genetic algorithm

China Helicopter Research and Development Institute，Aviation Industry Corporation of China，Limited，Jingdezhen Jiangxi 333001，China

摘要

摘要:
多项式响应面模型（PRSM）具有建模简单、计算量较小的特点，在基于现代试验设计（MDOE）方法的风洞试验中得到广泛应用。然而，多项式响应面模型无法对模型拟合后的残差进行处理，会丢失部分模型矩阵信息而导致参数预测误差增加。因此，通过预测值和实测值的差值，构造模型残差目标函数，并根据轮盘赌计算个体适应度值，对遗传算法（GA）的交叉概率和变异概率进行改进，建立一种基于改进自适应遗传算法（IAGA）优化多项式响应面模型的MDOE方法，并应用于飞行器风洞试验。结果表明：MDOE方法仅需传统单变量（OFAT）方法35%左右的试验点，基于改进自适应遗传算法优化后的MDOE方法较基于传统遗传算法的MDOE方法，响应面模型预测误差降低了1.263%，平均迭代速度提高了3.76倍，有效提升风洞试验效率。
- 现代试验设计（MDOE）方法 /
- 多项式响应面模型（PRSM） /
- 遗传算法（GA） /
- 风洞试验 /
- 气动系数
Abstract:
The polynomial response surface model (PRSM) was characterized by its simplicity in modeling and low computational cost, making it widely used in wind tunnel tests based on the modern design of experiments (MDOE) method. However, PRSM cannot process residuals after model fitting, leading to a loss of some model matrix information and increased parameter prediction error. To address this, a residual objective function based on the difference between predicted and measured values was constructed. Then, the crossover and mutation probabilities of the genetic algorithm (GA) were improved by calculating individual fitness values using a roulette wheel selection method. This contributed to the establishment of an MDOE method optimized by an improved adaptive genetic algorithm (IAGA) for PRSM, which was applied to aircraft wind tunnel tests. The results showed that the MDOE method required only about 35% of the experimental points needed by the one factor according to OFAT method. Compared with the traditional GA-based MDOE method, the IAGA-based MDOE method decreased the prediction error of the response surface model by 1.263% and increased the average iteration speed by 3.76 times, which effectively improved the efficiency of wind tunnel tests.
- modern design of experiments (MDOE) /
- polynomial response surface model (PRSM) /
- genetic algorithm (GA) /
- wind tunnel experiment /
- aerodynamic coefficient

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图 1 OFAT方法风洞试验样本点分布

Figure 1. Distribution of sample points for wind tunnel experiments using the OFAT method

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图 2 MDOE方法风洞试验样本点分布

Figure 2. Distribution of sample points for wind tunnel experiment using the MDOE method

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图 3 整机风洞试验模型示意图

Figure 3. Schematic diagram of the full-scale wind tunnel experiment model

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图 4 开口直流式低速风洞

Figure 4. Open-jet low-speed wind tunnel

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图 5 天平测量结构图

Figure 5. Structural balance measurement diagram

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图 6 LXI采集器示意图

Figure 6. Diagram of LXI data acquisition unit

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图 7 MDOE方法气动系数响应面模型

Figure 7. Response surface model for aerodynamic coefficient based on MDOE method

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图 8 基于IAGA的参数优化流程图

Figure 8. Flowchart for parameter optimization based on IAGA

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图 9 基于GA优化的阻力系数极小值迭代收敛图

Figure 9. Iteration convergence diagram for minimizing drag coefficient based on GA optimization

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图 10 基于IAGA优化的阻力系数极小值迭代收敛图

Figure 10. Iteration convergence diagram for minimizing drag coefficient based on IAGA optimization

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图 11 基于GA优化的垂向力系数极小值迭代收敛图

Figure 11. Iteration convergence diagram for minimizing vertical force coefficient based on GA optimization

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图 12 基于IAGA优化的垂向力系数极小值迭代收敛图

Figure 12. Iteration convergence diagram for minimizing vertical force coefficient based on IAGA optimization

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图 13 基于GA优化的滚转力矩系数极小值迭代收敛图

Figure 13. Iteration convergence diagram for minimizing rolling moment coefficient based on GA optimization

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图 14 基于IAGA优化的滚转力矩系数极小值迭代收敛图

Figure 14. Iteration convergence diagram for minimizing rolling moment coefficient based on IAGA optimization

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图 15 基于GA优化的俯仰力矩系数极小值迭代收敛图

Figure 15. Iteration convergence diagram for minimizing pitching moment coefficient based on GA optimization

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图 16 基于IAGA优化的俯仰力矩系数极小值迭代收敛图

Figure 16. Iteration convergence diagram for minimizing pitching moment coefficient based on IAGA optimization

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图 17 基于IAGA优化后的MDOE方法气动系数响应面模型

Figure 17. Response surface model for aerodynamic coefficient based on MDOE method optimized by IAGA

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表 1 待定系数与模型形式关系表

Table 1. Relationships between undetermined coefficients and model forms

多项式响应面模型形式	待定系数个数
一元二次多项式	3
二元三次多项式	10
三元四次多项式	35
四元五次多项式	126

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表 2 OFAT方法所取的自变量及试验值

Table 2. Variables and experiment values by OFAT method

自变量	试验值
风速V/（m/s）	5，8，10，12，15，20，25
迎角α/（°）	−6，−4，−2，0，2，4，6

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表 3 阻力系数响应面模型插值数据对比

Table 3. Comparison of interpolation data for drag coefficient response surface model

序号	迎角/（°）	风速/（m/s）	OFAT方法阻力系数	GA-MDOE方法		IAGA-MDOE方法
序号	迎角/（°）	风速/（m/s）	OFAT方法阻力系数	阻力系数	相对误差/%	阻力系数	相对误差/%
1	−6	5	−0.09298	−0.09468	1.828	−0.09361	0.678
2	−6	25	−1.35134	−1.37615	1.836	−1.36049	0.677
3	−2	5	−0.08756	−0.08918	1.850	−0.08816	0.685
4	2	8	−0.16701	−0.17007	1.832	−0.16814	0.677
5	4	18	−0.63941	−0.65111	1.830	−0.64372	0.674
6	6	12	−0.27897	−0.28409	1.835	−0.28086	0.677
7	6	25	−1.127	−1.14765	1.836	−1.13459	0.677

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表 4 垂向力系数响应面模型插值数据对比

Table 4. Comparison of interpolation data for vertical force coefficient response surface model

序号	迎角/（°）	风速/（m/s）	OFAT方法垂向力系数	GA-MDOE方法		IAGA-MDOE方法
序号	迎角/（°）	风速/（m/s）	OFAT方法垂向力系数	垂向力系数	相对误差/%	垂向力系数	相对误差/%
1	−6	5	0.05699	0.058	1.772	0.0574	0.719
2	−6	25	1.1805	1.20088	1.726	1.18797	0.633
3	−2	5	0.05553	0.0565	1.747	0.05585	0.576
4	2	8	0.25867	0.26311	1.716	0.26031	0.634
5	4	18	1.51499	1.54103	1.719	1.52453	0.630
6	6	12	0.70202	0.71413	1.725	0.70643	0.628
7	6	25	3.23964	3.29514	1.713	3.25988	0.625

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表 5 滚转力矩系数响应面模型插值数据对比

Table 5. Comparison of interpolation data for rolling moment coefficient response surface model

序号	迎角/（°）	风速/（m/s）	OFAT方法滚转力矩系数	GA-MDOE方法		IAGA-MDOE方法
序号	迎角/（°）	风速/（m/s）	OFAT方法滚转力矩系数	滚转力矩系数	相对误差/%	滚转力矩系数	相对误差/%
1	−6	5	0.05267	0.05349	1.557	0.05304	0.702
2	−6	25	−0.0199	−0.02021	1.558	−0.02004	0.704
3	−2	5	0.00846	0.0086	1.655	0.00852	0.709
4	2	8	−0.00635	−0.00645	1.575	−0.0064	0.787
5	4	18	−0.0408	−0.04144	1.569	−0.04109	0.711
6	6	12	0.08562	0.08694	1.542	0.08622	0.701
7	6	25	−0.01384	−0.01405	1.517	−0.01394	0.723

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表 6 俯仰力矩系数响应面模型插值数据对比

Table 6. Comparison of interpolation data for pitching moment coefficient response surface model

序号	迎角/（°）	风速/（m/s）	OFAT方法俯仰力矩系数	GA-MDOE方法		IAGA-MDOE方法
序号	迎角/（°）	风速/（m/s）	OFAT方法俯仰力矩系数	俯仰力矩系数	相对误差/%	俯仰力矩系数	相对误差/%
1	−6	5	0.0066	0.00672	1.818	0.00665	0.758
2	−6	25	−0.30989	−0.31538	1.772	−0.31184	0.629
3	−2	5	0.00836	0.00851	1.794	0.00841	0.598
4	2	8	−0.00539	−0.00548	1.670	−0.00542	0.557
5	4	18	0.05038	−0.05128	1.786	−0.0507	0.635
6	6	12	−0.00396	−0.00403	1.768	−0.00398	0.505
7	6	25	−0.01989	−0.02025	1.810	−0.02002	0.654

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