高超声速风洞现代试验设计方法研究

尤文佳; 王慧杰; 韩仁坤; 陈刚

doi:10.11729/syltlx20210179

高超声速风洞现代试验设计方法研究

尤文佳^{1, 2,},
王慧杰^{1, 2, 3},
韩仁坤^{1, 2},
陈刚^{1, 2, ,}

1.
西安交通大学航天航空学院机械结构强度与振动国家重点实验室，西安　710049
2.
西安交通大学航天航空学院陕西省先进飞行器服役环境与控制重点实验室，西安　710049
3.
中国航天科工集团第三研究院创新研究院，北京　100074

详细信息

作者简介:
尤文佳: （1996—），女，山西长治人，硕士研究生。研究方向：现代风洞试验技术及数据融合。通信地址：陕西省西安市咸宁西路28号西安交通大学航天航空学院（710049）。E-mail：youwenjia2020@stu.xjtu.edu.cn

通讯作者:
陈刚: E-mail：aachengang@xjtu.edu.cn

中图分类号: V211.71
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出版历程
- 收稿日期: 2021-11-03
- 修回日期: 2022-04-05
- 录用日期: 2022-04-06
- 网络出版日期: 2022-07-11
- 刊出日期: 2022-07-03

Using modern design of experiments method for hypersonic wind tunnel test

YOU Wenjia^{1, 2,},
WANG Huijie^{1, 2, 3},
HAN Renkun^{1, 2},
CHEN Gang^{1, 2, ,}

1.
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China
2.
Shaanxi Key Laboratory of Environment and Control for Flight Vehicle, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an　710049, China
3.
Innovation Research Institute of HIWING Technology academy, Beijing 100074, China

摘要

摘要: 现代试验设计（Modern Design of Experiments，MDOE）方法是提升风洞试验效率的一种重要技术途径。基于拉丁超立方的现代试验设计方法尽管理论效率很高，但其设计的随机采样点在与风洞模型姿态自动控制系统配合时，实际效率会显著下降。根据现有风洞试验设备控制系统走刀特点，针对多变量风洞试验设计需求，提出一种基于分层拉丁超立方的现代风洞试验设计方法，并将其应用于马赫数6的风洞模型的二变量试验和三变量试验设计。在满足精度的情况下，将MDOE方法与传统试验设计（One Factor at A Time，OFAT）方法进行对比，结果表明：二变量试验中，MDOE方法仅需OFAT方法20%左右的样本量；三变量试验中，MDOE方法仅需OFAT方法30%左右的样本量。与经典拉丁超立方试验设计方法相比，本文所发展的分层拉丁超立方试验设计方法结合现有风洞试验设备，可有效减少试验车次，提高试验效率，缩短试验周期。
- 现代试验设计 /
- 风洞试验 /
- 分层拉丁超立方 /
- 高超声速风洞
Abstract: Modern Design of Experiments （MDOE） is an important technical approach to improve wind tunnel test efficiency. Although the modern design of experiment method based on Latin Hypercube Sampling has high theoretical efficiency, the practical efficiency of the random sampling points designed by it decreases significantly when the automatic attitude control system of the wind tunnel model is coordinated. In this paper, a modern design of experiment method based on the Stratified Latin Hypercube design is proposed to meet the requirements of the multi-variable wind tunnel test design in the automatic attitude control system. It is applied to the two-variable test and three-variable test design of the 6 Mach number wind tunnel model. The results which were compared with the One Factor at A Time （OFAT） method show that MDOE method only needs about 20% of the sample size of OFAT method in the two-variable test and only needs about 30% of the sample size of OFAT method in the three-variable test. Compared with the classical Latin Hypercube method, the Stratified Latin Hypercube method developed in this paper combined with the existing wind tunnel test equipment can effectively reduce the change of test runs, improve the test efficiency and shorten the test period.
- Modern Design of Experiment /
- wind tunnel test /
- Stratified Latin Hypercube /
- hypersonic wind tunnel

HTML全文

图 1 最大化最小距离准则的分层LHS设计

Fig. 1 Stratified LHS design of maximum and minimum distance

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图 2 最小化最大距离准则的分层LHS设计

Fig. 2 Stratified LHS design of minimum and maximum distance

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图 3 最小差异准则的分层LHS设计

Fig. 3 Stratified LHS design of minimize discrepancy

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图 4 相对理想累积分布最小均方根差异准则的分层LHS设计

Fig. 4 Stratified LHS design to minimize RMS variation from cumu-lative distribution function

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图 5 相对理想累积分布最小最大差异准则的分层LHS设计

Fig. 5 Stratified LHS design to minimize maximum variation from cumulative distribution function

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图 6 小迎角区间二变量试验的样本点分布及各纵向气动系数的响应面

Fig. 6 Sample point and response surface of each longitudinal aerodynamic coefficient for the two-variable test in small angle of attack

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图 7 大迎角区间二变量试验的样本点分布及各纵向气动系数的响应面

Fig. 7 Sample point and response surface of each longitudinal aerodynamic coefficient for the two-variable test in big angle of attack

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图 8 各纵向气动系数的置信区间

Fig. 8 Confidence intervals of longitudinal aerodynamic coefficients

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图 9 小迎角区间三变量试验俯仰力矩系数样本点分布及响应面

Fig. 9 Sample point and response surface of pitching moment coefficient for the three-variable test in small angle of attack

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图 10 大迎角区间三变量试验俯仰力矩系数样本点分布及响应面

Fig. 10 Sample point and response surface of pitching moment coefficient for the three-variable test in big angle of attack

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图 11 相同变量条件下的试验对比图

Fig. 11 Comparison of the same variables test

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表 1 二变量试验中OFAT方法所取的变量及水平值

Table 1 Variables and level values taken by OFAT method in the two-variable test

变量		水平值
α/（°）	小区间	–2，–1，0，1，2，3，4，5，6，7，8，9，10
α/（°）	大区间	10，12，13，14，16，17，18，19，21，22，23，25

β/（°）		–6，–4，–2，0，2，4，6

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表 2 三变量试验中OFAT方法所取的变量及水平值

Table 2 Variables and level values taken by OFAT method in the three-variable test

变量		水平值
α/（°）	小区间	–2，1，4，7，10
α/（°）	大区间	10，13，16，19，22，25

β/（°）		–6，–4，–2，0，2，4，6
δ/（°）		–7.5，–5.0，–2.5，0，2.5，5.0，7.5

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表 3 不同准则下的响应面检验结果

Table 3 Response surface test results of different criteria

不同准则下的分层LHS设计	均方误差	整体均方根误差	判定系数R²
最大化最小距离准则	3.1729×10^–9	5.6329×10^–5	0.999859
最小化最大距离准则	3.3033×10^–8	1.8175×10^–4	0.998444
最小差异准则	3.5695×10^–8	1.8893×10^–4	0.998424
相对理想累积分布最小均方根差异准则	1.4388×10^–8	1.1995×10^–4	0.999338
相对理想累积分布最小最大差异准则	1.5387×10^–8	1.2404×10^–4	0.999328

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表 4 小迎角区间响应面多项式的构成

Table 4 The formation of polynomials of response surface in small angle of attack interval

变量	α	β	α²	β²	αβ	α³	β³	αβ²	α²β
C_L	√		√			√
C_D			√			√		√
C_m			√			√	√	√

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表 5 大迎角区间响应面多项式的构成

Table 5 The formation of polynomials of response surface in big angle of attack interval

变量	α	β	α²	β²	αβ	α³	β³	αβ²	α²β
C_L			√			√
C_D	√	√	√		√		√	√	√
C_m	√	√	√	√	√		√	√	√

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