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面向InSAR的空气扰动影响机翼挠曲变形建模

朱庄生 张萌

朱庄生, 张萌. 面向InSAR的空气扰动影响机翼挠曲变形建模[J]. 北京航空航天大学学报, 2020, 46(1): 38-50. doi: 10.13700/j.bh.1001-5965.2019.0172
引用本文: 朱庄生, 张萌. 面向InSAR的空气扰动影响机翼挠曲变形建模[J]. 北京航空航天大学学报, 2020, 46(1): 38-50. doi: 10.13700/j.bh.1001-5965.2019.0172
ZHU Zhuangsheng, ZHANG Meng. Air disturbance affecting wing deflection deformation modeling for InSAR[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(1): 38-50. doi: 10.13700/j.bh.1001-5965.2019.0172(in Chinese)
Citation: ZHU Zhuangsheng, ZHANG Meng. Air disturbance affecting wing deflection deformation modeling for InSAR[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(1): 38-50. doi: 10.13700/j.bh.1001-5965.2019.0172(in Chinese)

面向InSAR的空气扰动影响机翼挠曲变形建模

doi: 10.13700/j.bh.1001-5965.2019.0172
基金项目: 

国家自然科学基金 61873019

国家自然科学基金 61573040

国家自然科学基金 61421063

国家自然科学基金 61661136007

国家自然科学基金 61703021

国家自然科学基金 61722103

国家自然科学基金 61571030

国家自然科学基金 61473020

航空科学基金 20170551004

详细信息
    作者简介:

    朱庄生  男, 博士, 副研究员。主要研究方向:惯性导航/组合导航、静动态变形GNSS/光学/惯性精密测量技术

    张萌  女, 硕士研究生。主要研究方向:静动态机翼变形测量、惯性导航/组合导航

    通讯作者:

    朱庄生, E-mail:zszhu@buaa.edu.cn

  • 中图分类号: V211.3;V212.11;TB125

Air disturbance affecting wing deflection deformation modeling for InSAR

Funds: 

National Natural Science Foundation of China 61873019

National Natural Science Foundation of China 61573040

National Natural Science Foundation of China 61421063

National Natural Science Foundation of China 61661136007

National Natural Science Foundation of China 61703021

National Natural Science Foundation of China 61722103

National Natural Science Foundation of China 61571030

National Natural Science Foundation of China 61473020

Aeronautical Science Foundation of China 20170551004

More Information
  • 摘要:

    针对多节点InSAR机翼挠曲变形误差问题,提出了一种基于机理模型综合参数辨识的方法对空气扰动影响机翼挠曲变形分层建模。首先,将大气湍流作为InSAR成像工作段的主要空气扰动,并基于Dryden模型分析得出了载机工作高度和速度是影响大气湍流的主要因素,将大气湍流影响机翼挠曲变形建模转换为载机在不同工作状态(高度变化、速度变化)的机翼挠曲变形分层建模。其次,基于空气动力学理论及悬臂梁变形理论建立机翼挠曲变形机理模型,借助计算流体力学与计算结构力学仿真分析获取实验数据辨识模型参数。最后,通过仿真实验验证,所提方法与模态叠加原理计算横向位移精度均优于0.6 mm(相对误差0.3%),轴向位移精度均优于0.015 mm(相对误差0.2%)。对实验室搭建的分布式光纤光栅测量系统进行测试,利用模态叠加原理计算变形量来验证所提方法,横向位移精度优于0.3 mm(相对误差1%),轴向位移精度优于0.06 mm(相对误差3%)。

     

  • 图 1  机载分布式InSAR系统

    Figure 1.  Airborne distributed InSAR system

    图 2  不同高度变化引起的垂直风切变

    Figure 2.  Vertical wind shear caused by different height changes

    图 3  1-cosine阵风模型

    Figure 3.  1-cosine gust model

    图 4  机翼模型

    Figure 4.  Wing model

    图 5  机翼飞行流场区域

    Figure 5.  Wing flight flow field area

    图 6  机翼所受气动载荷及湍流速度变化

    Figure 6.  Changes in aerodynamic loads and turbulent velocity on wing

    图 7  机翼结构Y向位移

    Figure 7.  Y-direction displacement of wing structure

    图 8  不同工作速度时的机翼挠曲变形

    Figure 8.  Deflection of wing at different working speeds

    图 9  不同工况下测点15的机翼挠曲变形

    Figure 9.  Wing deflection deformation at measuring point 15 under different conditions

    图 10  蒙皮表面气动载荷分布

    Figure 10.  Aerodynamic load distribution on skin surface

    图 11  机翼骨架结构变形示意图

    Figure 11.  Schematic diagram of wing skeleton structure deformation

    图 12  高度变化时的AYAZ系数

    Figure 12.  AY and AZ at different heights

    图 13  骨架结构的应变、位移模态

    Figure 13.  Skeleton structure strain and displacement mode

    图 14  实验室机翼结构

    Figure 14.  Wing structure in laboratory

    图 15  机翼加载实验

    Figure 15.  Loading experiment in wing

    图 16  模态值与拟合模型值对比

    Figure 16.  Comparison of modal and fitted values

    表  1  铝合金7075材料属性

    Table  1.   Aluminum alloy 7075 material properties

    参数 数值
    密度/(g·cm-3) 2.81
    极限抗拉强度/MPa 524
    极限屈服强度/MPa 455
    弹性模量/GPa 71
    泊松比 0.33
    下载: 导出CSV

    表  2  不同工作高度上的大气物理参数[22]

    Table  2.   Atmospheric physical parameters at different working altitudes [22]

    工作高度/km 压力/Pa 温度 密度/(g·cm-3)
    摄氏度 开尔文
    2.0 79 810 2.35 275.5 1.009
    3.0 70 510 -3.25 269.9 0.908 7
    3.5 66 100 -6.27 266.88 0.862 5
    4.0 61 950 -9.29 263.86 0.818 1
    4.5 58 070 -12.3 260.85 0.775 6
    5.0 54 420 -15.32 257.83 0.734 8
    5.5 51 000 -18.34 254.81 0.695 6
    6.0 47 680 -21.62 251.53 0.658 9
    6.5 44 520 -24.97 248.18 0.623 7
    7.0 41 580 -28.32 244.83 0.59
    7.5 38 770 -31.65 241.5 0.557 7
    8.0 36 080 -35.07 238.08 0.526 8
    下载: 导出CSV

    表  3  载机工作速度影响的参数辨识结果

    Table  3.   Parameter identification results of carrier speed

    测点 u=Av2 R2 SSE u=Av2.014 R2 SSE u=Av2.015 R2 SSE
    2 u=6.492×10-7v2 1.000 7.22×10-10 u=6.022×10-8v2.014 1.000 1.33×10-11 u=5.99×10-8v2.015 1.000 4.57×10-12
    7 u=1.001×10-6v2 1.000 1.57×10-7 u=9.284×10-7v2.014 1.000 1.52×10-9 u=9.234×10-7v2.015 1.000 3.34×10-11
    12 u=2.407×10-6v2 1.000 8.96×10-7 u=2.233×10-6v2.014 1.000 7.67×10-9 u=2.221×10-6v2.015 1.000 1.74×10-9
    15 u=3.424×10-6v2 1.000 1.82×10-6 u=3.176×10-6v2.014 1.000 1.52×10-8 u=3.159×10-6v2.015 1.000 2.98×10-9
    下载: 导出CSV

    表  4  载机工作高度影响的参数辨识结果

    Table  4.   Parameter identification results of carrier's working height

    测点 指数函数u=aebP R2 SSE 线性模型u=aP+b R2 SSE 幂函数u=aP0.833 R2 SSE
    2 u=2.286×10-8e1.368×10-5P 0.996 1.42×10-18 u=7.27P×10-13+8.696×10-9 1.000 5.08×10-20 u=5.484×10-12P0.833 1.000 8.60×10-21
    7 u=3.522×10-7e1.368×10-5P 0.996 3.52×10-16 u=1.121P×10-11+1.339×10-7 1.000 1.51×10-17 u=8.454×10-11P0.833 1.000 2.82×10-18
    12 u=8.467×10-7e1.369×10-5P 0.996 2.05×10-15 u=2.696P×10-11+3.215×10-7 1.000 9.16×10-17 u=2.033×10-10P0.833 1.000 1.80×10-17
    15 u=1.205×10-6e1.368×10-5P 0.996 4.16×10-15 u=3.834P×10-11+4.585×10-7 1.000 1.89×10-16 u=2.892×10-10P0.833 1.000 3.74×10-17
    下载: 导出CSV

    表  5  本文模型预测Y向变形

    Table  5.   Y-direction deformation predicted by proposed model

    工作速度/(m·s-1) 工作高度/km ANSYS Workbench
    Y向变形量/mm
    本文模型
    Y向变形量/mm
    测点7 测点12 测点15 测点7 测点12 测点15
    250 1.5 3.85 4.38 4.30 3.85 4.37 4.31
    200 1.5 2.45 2.79 2.74 2.46 2.79 2.75
    2.0 2.33 2.65 2.60 2.33 2.65 2.61
    6.5 1.44 1.63 1.61 1.43 1.63 1.61
    7.0 1.36 1.54 1.52 1.35 1.54 1.52
    7.5 1.28 1.46 1.44 1.28 1.45 1.43
    8.0 1.21 1.38 1.36 1.20 1.37 1.35
    185 2.5 1.89 2.15 2.12 1.89 2.15 2.12
    235 2.5 3.07 3.48 3.44 3.06 3.48 3.44
    285 2.5 4.52 5.14 5.07 4.52 5.14 5.07
    下载: 导出CSV

    表  6  本文模型预测Z向变形

    Table  6.   Z-direction deformation predicted by proposed model

    工作速度/(m·s-1) 工作高度/km ANSYS Workbench
    Z向变形量/mm
    本文模型
    Z向变形量/mm
    测点7 测点12 测点15 测点7 测点12 测点15
    250 1.5 73.36 176.36 250.83 73.24 176.14 250.56
    200 1.5 46.80 112.48 159.97 46.72 112.35 159.82
    2.0 44.44 106.81 151.91 44.37 106.69 151.77
    6.5 27.31 65.67 93.41 27.28 65.61 93.33
    7.0 25.81 62.08 88.31 25.77 61.98 88.17
    7.5 24.38 58.64 83.43 24.31 58.47 83.17
    8.0 23.01 55.35 78.75 22.90 55.07 78.34
    185 2.5 36.04 86.66 123.28 36.01 86.60 123.19
    235 2.5 58.36 140.34 199.63 58.32 140.24 199.49
    285 2.5 86.05 206.92 294.36 86.02 206.86 294.26
    下载: 导出CSV

    表  7  Y向变形模态叠加原理计算结果

    Table  7.   Y-direction deformation calculated by modal superposition principle

    工作速度/(m·s-1) 工作高度/km ANSYS Workbench
    Y向变形量/mm
    模态叠加原理
    Y向变形量/mm
    测点7 测点12 测点15 测点7 测点12 测点15
    250 1.5 3.85 4.38 4.30 3.85 4.37 4.30
    200 1.5 2.45 2.79 2.74 2.45 2.79 2.74
    2.0 2.33 2.65 2.60 2.33 2.65 2.60
    6.5 1.44 1.63 1.61 1.44 1.63 1.61
    7.0 1.36 1.54 1.52 1.36 1.54 1.52
    7.5 1.28 1.46 1.44 1.28 1.46 1.44
    8.0 1.21 1.38 1.36 1.21 1.38 1.36
    185 2.5 1.89 2.15 2.12 1.89 2.15 2.12
    235 2.5 3.07 3.48 3.44 3.07 3.49 3.43
    285 2.5 4.52 5.14 5.07 4.52 5.14 5.06
    下载: 导出CSV

    表  8  Z向变形模态叠加原理计算结果

    Table  8.   Z-direction deformation calculated by modal superposition principle

    工作速度/(m·s-1) 工作高度/km ANSYS Workbench
    Z向变形量/mm
    模态叠加原理
    Z向变形量/mm
    测点7 测点12 测点15 测点7 测点12 测点15
    250 1.5 73.36 176.36 250.83 73.24 176.03 250.31
    200 1.5 46.80 112.48 159.97 46.70 112.23 159.54
    2.0 44.44 106.81 151.91 44.35 106.58 151.52
    6.5 27.31 65.67 93.41 27.28 65.60 93.31
    7.0 25.81 62.08 88.31 25.80 62.02 88.24
    7.5 24.38 58.64 83.43 24.37 58.60 83.37
    8.0 23.01 55.35 78.75 23.01 55.32 78.72
    185 2.5 36.04 86.66 123.28 36.00 86.56 123.13
    235 2.5 58.36 140.34 199.63 58.31 140.18 199.40
    285 2.5 86.05 206.92 294.36 85.97 206.70 294.02
    下载: 导出CSV

    表  9  本文模型与模态叠加原理计算误差值对比

    Table  9.   Comparison of error values calculated by proposed model and modal superposition principle

    工作速度/(m·s-1) 工作高度/km Y Z
    ANSYS仿真位移/mm 模态叠加原理误差/mm 本文模型误差/mm ANSYS仿真位移/mm 模态叠加原理误差/mm 本文模型误差/mm
    250 1.5 4.30 0.004 0.011 250.83 0.520 0.303
    200 1.5 2.74 0.004 0.013 159.97 0.426 0.182
    2.0 2.60 0.004 0.011 151.91 0.388 0.169
    6.5 1.61 0.002 0.002 93.41 0.101 0.084
    7.0 1.52 0.002 0.004 88.31 0.078 0.146
    7.5 1.44 0.002 0.007 83.43 0.054 0.251
    8.0 1.36 0.002 0.010 78.75 0.031 0.415
    185 2.5 2.12 0.002 0.002 123.28 0.155 0.091
    235 2.5 3.44 0.003 0.003 199.63 0.232 0.148
    285 2.5 5.07 0.004 0.003 294.36 0.341 0.109
    下载: 导出CSV

    表  10  全站仪测量值

    Table  10.   Total station measurement values

    加载/N Y向位移/mm Z向位移/mm
    测点1 测点2 测点1 测点2
    4.9 -0.18 -0.18 -2.97 -4.50
    9.8 -0.34 -0.42 -5.70 -8.70
    14.7 -0.56 -0.57 -8.51 -13.01
    19.6 -0.79 -0.84 -11.45 -17.49
    24.5 -0.96 -1.06 -14.17 -21.66
    29.4 -1.14 -1.32 -16.95 -25.93
    34.3 -1.36 -1.55 -19.66 -29.98
    39.2 -1.57 -1.81 -22.45 -34.24
    44.1 -1.77 -2.04 -25.13 -38.30
    49 -2.06 -2.28 -27.88 -42.32
    下载: 导出CSV

    表  11  预测值与全站仪测量值对比

    Table  11.   Comparison of predicted and total station measurement values

    测点 加载/N Y向位移/mm Z向位移/mm
    全站仪测量值 本文方法预测值 绝对误差 全站仪测量值 本文方法预测值 绝对误差
    测点1 39.2 -1.57 -1.51 0.06 -22.45 -22.52 0.07
    44.1 -1.77 -1.78 0.01 -25.13 -25.08 0.05
    49 -2.06 -2.06 0 -27.88 -27.57 0.31
    测点2 39.2 -1.81 -1.84 0.03 -34.24 -34.41 0.17
    44.1 -2.04 -2.09 0.05 -38.3 -38.39 0.09
    49 -2.28 -2.34 0.06 -42.32 -42.31 0.01
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-04-22
  • 录用日期:  2019-07-19
  • 刊出日期:  2020-01-20

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