基于代理模型的双路燃气组合热试验参数优化

阿嵘; 齐玢; 陈鑫; 王日; 董素君; 周印佳

doi:10.13224/j.cnki.jasp.20210658

基于代理模型的双路燃气组合热试验参数优化

doi: 10.13224/j.cnki.jasp.20210658

阿嵘¹,
齐玢^1,*, ,,
陈鑫²,
王日³,
董素君³,
周印佳¹

1.
中国空间技术研究院钱学森空间技术实验室，北京 100094
2.
中国运载火箭技术研究院空间物理重点实验室，北京 100076
3.
北京航空航天大学航空科学与工程学院，北京 100191

基金项目: 国家自然科学基金（11902026，12102056）

详细信息

作者简介:
阿嵘（1991-），女，工程师，博士，主要从事飞行器热管理及热试验技术研究

通讯作者:
齐玢（1986-），男，高级工程师，博士，主要从事飞行器热管理及热试验技术研究。E-mail：qionline@163.com

中图分类号: V216.5
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- 被引次数: 0
出版历程
- 收稿日期: 2021-11-19
- 网络出版日期: 2023-07-07

Parameter optimization of dual gas flow combined thermal test based on surrogate model

A Rong¹,
QI Bin^{1,*
, ,},
CHEN Xin²,
WANG Ri³,
DONG Sujun³,
ZHOU Yinjia¹

1.
Qian Xuesen Laboratory of Space Technology， China Academy of Space Technology，Beijing 100094，China
2.
Science and Technology on Space Physics Laboratory， China Academy of Launch Vehicle Technology，Beijing 100076，China
3.
School of Aeronautics Science and Engineering，Beihang University，Beijing 100191，China

摘要

摘要:
为确保双路燃气组合热试验过程中试件表面热流与高超声速气动热流的吻合性，对试验参数进行了优化设计。针对典型尖楔结构建立了双路燃气组合加热的数值计算模型，通过拉丁超立方采样及基于模糊聚类的加点策略获取了128个样本点，开展了数值模拟，并采用Kriging代理模型以及带精英策略的非支配排序遗传优化算法，以燃气加热热流与气动热流的吻合度为优化目标，完成了多目标优化。结果表明，通过增加样本点，显著减小了代理模型误差；8个测试样本点下试件表面热流密度平均相对误差最大约为7%，大部分区域平均误差不超过5%，方均根误差的均值为1.72%，最大值误差的最大值为13.6%，表明Kriging代理模型具有较高的预测精度；通过优化，试件表面燃气加热热流分布与气动加热热流分布吻合较好，驻点处热流密度相对误差小于1%，平板区域相对误差不超过10%，表明了基于Kriging代理模型的双路燃气组合热试验参数优化方法的有效性。
- 高温燃气 /
- 热试验 /
- 优化设计 /
- 代理模型 /
- 尖楔结构
Abstract:
In order to ensure the coincidence between heat flux on the surface of the specimen during the dual gas flow combined thermal test and hypersonic aerodynamic heat flow, the test parameters were optimized. Numerical model of the dual gas flow combined heating for typical tip wedge structure was built, 128 samples were selected via the Latin Hypercube sampling method and the adding-point strategy based on fuzzy clustering, and numerical simulation was carried out. Then, Kriging surrogate model and elitist non-dominated sorting generic algorithm were applied in multi-objective optimization, which aimed at minimizing the difference between gas flow heating and hypersonic aerodynamic heating. The results showed that the error of surrogate model was significantly reduced by increasing samples. The maximum of mean relative errors of surface heat flux of 8 test samples was about 7%, and less than 5% in most areas, while the mean value of root mean square errors and the peak value of maximum errors were 1.72% and 13.6%, respectively, indicating that the Kriging surrogate model had high prediction accuracy. What’s more, through optimization, the distribution of surface heat flux by gas flow heating was in good agreement with that of hypersonic aerodynamic heat flow. The relative error of heat flux at stagnation was less than 1%, and no more than 10% at the flat plate area, which showed the effectiveness of parameters optimization of dual gas flow combined thermal test based on Kriging surrogate model.
- high temperature gas flow /
- thermal test /
- optimization design /
- surrogate model /
- tip wedge structure

HTML

图 1 双路气流组合热试验方案示意图

Figure 1. Schematic of dual gas flow combined heating method

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图 2 计算网格模型

Figure 2. Mesh structure of computational model

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图 3 不同尺寸网格计算的试件表面热流密度分布

Figure 3. Heat flux distribution on specimen wall with different mesh sizes

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图 4 某工况对称面温度分布云图

Figure 4. Contour of temperature distribution on symmetry plane at some condition

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图 5 某工况试件表面热流密度分布云图

Figure 5. Contour of heat flux distribution on specimen wall at some condition

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图 6 基于代理模型的参数优化流程

Figure 6. Flow chart of parameter optimization based on surrogate model

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图 7 NSGA-Ⅱ算法流程图

Figure 7. Flow chart of NSGA-Ⅱ algorithm

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图 8 样本点设计变量取值分布

Figure 8. Design variable distribution of samples

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图 9 平均驻点相对误差随样本点数量变化曲线

Figure 9. Average relative error at stagnation for different sample quantity

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图 10 测试工况下试件表面热流预测值

Figure 10. Prediction value of surface heat flux at test condition

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图 11 测试样本点下试件表面热流密度平均相对误差分布云图

Figure 11. Contour of average relative error of surface heat flux of test samples

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图 12 可行解的目标值空间

Figure 12. Objective space of feasible solution

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图 13 最优状态下试件表面热流预测值

Figure 13. Prediction value of surface heat flux at optimum condition

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图 14 最优状态下试件表面热流密度相对误差分布云图

Figure 14. Contour of average relative error of surface heat flux at optimum condition

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图 15 最优状态下试件表面热流密度与目标值对比

Figure 15. Comparison between surface heat flux and target value at optimum condition

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表 1 设计变量取值范围

Table 1. Value range of design variables

设计变量	取值范围
设计变量	下限	上限
Ma₁	0.1	0.5
Ma₂	0.1	0.5
d/mm	1	8
l/mm	5	20

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表 2 NSGA-Ⅱ算法参数设定值

Table 2. Parameter settings of NSGA-Ⅱ algorithm

参数	设定值
种群个数	10
种群代数	100
交叉概率	0.9
实数向量变异概率	1.0
二进制字符串变异概率	1.0
实数交叉分配指数	20
实数变异分配指数	20

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表 3 测试样本取值

Table 3. Value of test samples

序号	Ma₁	Ma₂	d/mm	l/mm
1	0.39	0.28	6.16	7.37
2	0.28	0.22	7.88	14.26
3	0.34	0.40	1.73	9.01
4	0.20	0.41	6.58	10.75
5	0.10	0.32	4.00	5.03
6	0.23	0.16	2.70	18.39
7	0.44	0.48	4.56	14.78
8	0.48	0.13	2.99	17.16

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表 4 测试样本点下表面热流密度误差

Table 4. Errors of surface heat flux of test samples

序号	$ {e_{{\text{NRMSE}}}} $/%	$ {L_\infty } $/%
1	1.47	11.98
2	2.40	13.60
3	2.94	12.94
4	0.89	5.43
5	2.18	11.81
6	1.55	12.53
7	0.91	6.89
8	1.40	7.39
平均值	1.72
最大值		13.60

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表 5 Pareto最优解及其相对坐标原点的距离

Table 5. Pareto optimal solution and distance from coordinate origin

编号	Ma₁	Ma₂	d/mm	l/mm	δ₀/%	δ₁/%	Δ
No.966	0.410	0.110	1.73	10.04	13.4	17.0	0.22
No.758	0.413	0.113	2.14	8.87	6.5	21.9	0.23
No.738	0.412	0.113	2.18	10.08	8.9	21.3	0.23
No.920	0.410	0.110	2.15	10.04	9.8	20.9	0.23
No.879	0.410	0.113	2.18	10.04	9.7	21.2	0.23
No.808	0.415	0.105	2.13	8.05	4.3	23.4	0.24
No.946	0.410	0.110	2.16	8.08	6.0	23.0	0.24
No.508	0.403	0.105	1.01	8.69	19.9	14.2	0.25
No.504	0.401	0.109	1.28	8.89	19.0	16.0	0.25
No.882	0.405	0.108	1.01	10.32	22.0	12.0	0.25
No.832	0.405	0.102	1.01	10.70	22.6	11.9	0.26
No.982	0.416	0.102	2.35	8.38	3.0	25.4	0.26
No.452	0.403	0.128	1.02	11.47	25.7	11.3	0.28
No.916	0.424	0.104	2.35	7.96	1.3	31.3	0.31
No.941	0.425	0.102	2.35	7.96	1.3	32.9	0.33
No.267	0.395	0.128	1.02	12.92	32.2	10.1	0.34
No.192	0.393	0.142	1.02	12.90	33.8	9.4	0.35

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