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一种顾及方向遮蔽性的高效空间插值方法

周长聪 刘洪威 何宝明 王维 谭春龙

周长聪,刘洪威,何宝明,等. 一种顾及方向遮蔽性的高效空间插值方法[J]. 北京航空航天大学学报,2023,49(6):1278-1286 doi: 10.13700/j.bh.1001-5965.2021.0443
引用本文: 周长聪,刘洪威,何宝明,等. 一种顾及方向遮蔽性的高效空间插值方法[J]. 北京航空航天大学学报,2023,49(6):1278-1286 doi: 10.13700/j.bh.1001-5965.2021.0443
ZHOU C C,LIU H W,HE B M,et al. An efficient spatial interpolation method involving position shading[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(6):1278-1286 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0443
Citation: ZHOU C C,LIU H W,HE B M,et al. An efficient spatial interpolation method involving position shading[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(6):1278-1286 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0443

一种顾及方向遮蔽性的高效空间插值方法

doi: 10.13700/j.bh.1001-5965.2021.0443
基金项目: 国家自然科学基金(51975476);陕西省自然科学基础研究计划(2020JM-135);航空科学基金(20200029053001)
详细信息
    作者简介:

    周长聪等:一种顾及方向遮蔽性的高效空间插值方法

    通讯作者:

    E-mail:changcongzhou@nwpu.edu.cn

  • 中图分类号: V211.3

An efficient spatial interpolation method involving position shading

Funds: National Natural Science Foundation of China (51975476); Natural Science Basic Research Program of Shaanxi (2020JM-135); Aeronautical Science Foundation of China (20200029053001)
More Information
  • 摘要:

    反距离权重插值方法在航空航天中有着广泛的应用,但其存在仅考虑距离关系而忽视方位关系的缺点,顾及方向遮蔽性的调和反距离权重插值方法弥补了这种不足,提高了插值精度,但仅适用于平面插值。借鉴该方法的基本假设,根据归一化后样本点的不同空间分布,以平面均匀角和球面均匀角为基准,制定统一的均匀性量化标准,提出一种更具普适性的三维空间插值方法。在搜索插值点的临近样本点时,提出一种最近邻搜索算法,极大提高了插值计算效率。通过测试函数计算发现,与反距离权重插值方法相比,所提插值方法误差显著降低。将所提插值方法应用于某型民用飞机短舱的气动载荷插值,结果表明,所提插值方法兼具高效和高精度的优点。

     

  • 图 1  Lij对遮蔽性的反映

    Figure 1.  Reflection of Lij on position shading

    图 2  样本点处理方式

    Figure 2.  Sample point processing method

    图 3  不同空间形状

    Figure 3.  Different space shapes

    图 4  球面均匀角获取流程

    Figure 4.  Spherical uniform angle acquisition process

    图 5  球面电荷受力分析

    Figure 5.  Force analysis of spherical charge

    图 6  计算耗时对比

    Figure 6.  Comparison of calculation time

    图 7  AIDW-DP程序设计流程

    Figure 7.  Programming flow of AIDW-DP

    图 8  插值平均误差随搜索点数的变化

    Figure 8.  Variation of interpolation average error with number of search points

    图 9  插值平均误差随权指数的变化

    Figure 9.  Variation of interpolation average error with weight index

    图 10  短舱有限元分析模型

    Figure 10.  Finite element analysis model of nacelle

    图 11  二次插值过程

    Figure 11.  Process of twice interpolation

    图 12  气动结点载荷和插值后有限元结点载荷

    Figure 12.  Aerodynamic nodal load and interpolated finite element nodal load

    图 13  气动载荷插值的误差

    Figure 13.  Error of aerodynamic load interpolation

    表  1  测试函数

    Table  1.   Test functions

    函数编号函数表达式
    1${x^2} + {y^2} + {{\textit{z}}^2}$
    2${x^3} + {y^3} + {{\textit{z}}^3} + x{y^2} + x{{\textit{z}}^2} + y{{\textit{z}}^2} + xy{\textit{z}}$
    3$3{\left( {1 - x} \right)^2}{ {\text{e} }^{ - {x^2} - { {\left( {y + 1} \right)}^2} } } - 10\left( {x - {x^3} - {y^5} } \right){ {\text{e} }^{ - {x^2} } } - { {\text{e} }^{ - { {\left( {x + 1} \right)}^2} - {y^{2} } } /3} + { {\text{e} }^{\textit{z}}}$
    下载: 导出CSV

    表  2  不同插值方法的计算耗时对比

    Table  2.   Comparison of computation time of different interpolation methods s

    样本点数IDWLu’s AIDWAIDW-DP
    20×20×202.732.710.11
    40×40×4021.9421.900.13
    60×60×6074.3874.480.14
    下载: 导出CSV

    表  3  插值误差统计

    Table  3.   Statistics of interpolation error

    插值方法误差均值/${10^{ - 5}}$中误差/${10^{ - 4}}$最大误差/${10^{ - 3}}$
    IDW8.772.728.74
    AIDW-DP6.402.388.41
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-08-05
  • 录用日期:  2021-10-07
  • 网络出版日期:  2021-11-01
  • 整期出版日期:  2023-06-30

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