流体力学与飞行力学

基于伴随方程和自动微分的雷达散射截面表面灵敏度计算

  • 周琳 ,
  • 陈宪 ,
  • 黄江涛 ,
  • 邓俊 ,
  • 高正红
展开
  • 1.中国空气动力研究与发展中心,绵阳 621000
    2.西北工业大学 航空学院,西安 710072
.E-mail: hjtcyf@163.com

收稿日期: 2023-02-01

  修回日期: 2023-02-09

  录用日期: 2023-02-15

  网络出版日期: 2023-03-31

Radar cross section surface sensitivity calculation based on adjoint approach and automatic differentiation

  • Lin ZHOU ,
  • Xian CHEN ,
  • Jiangtao HUANG ,
  • Jun DENG ,
  • Zhenghong GAO
Expand
  • 1.China Aerodynamics Research and Development Center,Mianyang 621000,China
    2.School of Aeronautics,Northwestern Polytechnical University,Xi’an 710072,China
E-mail: hjtcyf@163.com

Received date: 2023-02-01

  Revised date: 2023-02-09

  Accepted date: 2023-02-15

  Online published: 2023-03-31

摘要

反隐身技术的发展对军用飞行器的隐身性能提出更高要求,针对经典电磁场伴随方法无法获得表面灵敏度,难以为优化设计提供直观指导,且梯度求解时需反复填充阻抗矩阵,当设计变量、入射角度较多时梯度求解效率下降的问题,提出了基于伴随方程和自动微分的雷达散射截面表面灵敏度计算方法,并结合基函数特点提出了表面灵敏度的稀疏存储和稀疏矩阵-矢量相乘方法,避免了直接计算表面灵敏度时计算量、存储量无法承受的问题。提出的表面灵敏度计算方法可以通过一次阻抗矩阵偏导数求解得到所有网格点的表面灵敏度,避免反复填充阻抗矩阵的问题。当入射角度改变时,求解任意数量设计变量梯度的计算量约为8次矩阵-向量乘,显著提升基于伴随方程的梯度计算效率,为作战飞机气动隐身一体化优化设计提供有力技术支撑。

本文引用格式

周琳 , 陈宪 , 黄江涛 , 邓俊 , 高正红 . 基于伴随方程和自动微分的雷达散射截面表面灵敏度计算[J]. 航空学报, 2023 , 44(22) : 128508 -128508 . DOI: 10.7527/S1000-6893.2023.28508

Abstract

The development of anti-stealth technology poses a strong challenge to the stealth performance of military aircraft. The classical electromagnetic adjoint approach cannot obtain the surface sensitivity information, and therefore cannot provide intuitive guidance for the optimal design. Moreover, in the classical adjoint approach, the need to repeatedly fill the impedance matrix during gradient calculation leads to low efficiency, particularly with a large number of design variables and incident angles. This paper proposes an approach to calculating radar cross section surface sensitivity based on the adjoint and automatic differentiation method. A sparse matrix storage method considering the characters of the Rao-Wilton-Glisson basis function is adopted to reduce the memory requirements of the impedance matrix differentiation. The proposed method can obtain the surface sensitivity of all surface nodes with one matrix differentiation calculation. For different incident angles, the calculation of design variable gradients of any number will not exceed 16 matrix-vector products. The proposed surface sensitivity calculation approach can effectively improve the efficiency of gradient calculation, and provides support to the optimal design of stealth military aircraft.

参考文献

1 桑建华. 飞行器隐身技术[M]. 北京: 航空工业出版社, 2013.
  SANG J H. Low-observable technologies of aircraft[M]. Beijing: Aviation Industry Press, 2013 (in Chinese).
2 姬金祖, 黄沛霖, 马云鹏. 隐身原理[M]. 北京: 北京航空航天大学出版社, 2018.
  JI J Z, HUANG P L, MA Y P. Stealth principle[M]. Beijing: Beijing University of Aeronautics & Astronautics Press, 2018 (in Chinese).
3 ZHOU L, HUANG J T, GAO Z H. Radar cross section gradient calculation based on adjoint equation of method of moment[C]∥ZHANG X. Asia-Pacific International Symposium on Aerospace Technology. Singapore: Springer, 2019: 1427-1445.
4 ZHOU L, HUANG J T, GAO Z H, et al. Three-dimensional aerodynamic/stealth optimization based on adjoint sensitivity analysis for scattering problem[J]. AIAA Journal202058(6): 2702-2715.
5 周琳, 黄江涛, 高正红. 基于离散伴随方程的三维雷达散射截面几何灵敏度计算[J]. 航空学报202041(5): 623361.
  ZHOU L, HUANG J T, GAO Z H. Calculation of geometric sensitivity of three-dimensional radar cross section based on discrete adjoint equation[J]. Acta Aeronautica et Astronautica Sinica202041(5): 623361 (in Chinese).
6 LI M, CHEN J J, FENG X Y, et al. An efficient adjoint method for the aero-stealth shape optimization design[J]. Aerospace Science and Technology2021118: 107017.
7 黄江涛, 周琳, 陈宪, 等. 基于NS/CFIE伴随方法的飞行器气动隐身综合优化[J].航空学报202344(12): 127757.
  HUANG J T, ZHOU L, CHEN X, et al. Integrated aerodynamic and stealth optimization of aircraft based on NS/CFIE adjoint equations [J]. Acta Aeronautica et Astronautica Sinica202344(12): 127757 (in Chinese).
8 GEORGIEVA N K, GLAVIC S, BAKR M H, et al. Feasible adjoint sensitivity technique for EM design optimization[C]∥ 2002 IEEE MTT-S International Microwave Symposium Digest. Piscataway: IEEE Press, 2002: 971-974.
9 TOIVANEN J I, MAKINEN R A E, JARVENPAA S, et al. Electromagnetic sensitivity analysis and shape optimization using method of moments and automatic differentiation[J]. IEEE Transactions on Antennas and Propagation200957(1): 168-175.
10 KATAJA J, J?RVENP?? S, TOIVANEN J I, et al. Shape sensitivity analysis and gradient-based optimization of large structures using MLFMA[J]. IEEE Transactions on Antennas and Propagation201462(11): 5610-5618.
11 KATAJA J, TOIVANEN J I. On shape differentiation of discretized electric field integral equation[J]. Engineering Analysis With Boundary Elements201337(9): 1197-1203.
12 HARRINGTON R F. Field Computation by Moment Methods[M]. Piscataway: Wiley-IEEE Press, 1993.
13 SONG J M, CHEW W C. Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering[J]. Microwave and Optical Technology Letters199510(1): 14-19.
14 聂在平, 胡俊, 姚海英, 等. 用于复杂目标三维矢量散射分析的快速多极子方法[J]. 电子学报199927(6): 104-109.
  NIE Z P, HU J, YAO H Y, et al. Fast multipole method for three-dimensional vector scattering analysis of complex targets[J]. Acta Electronica Sinica199927(6): 104-109 (in Chinese).
15 BONDESON A, YANG Y, WEINERFELT P. Shape optimization for radar cross sections by a gradient method[J]. International Journal for Numerical Methods in Engineering200461(5): 687-715.
16 JAMESON A, KIM S. Reduction of the adjoint gradient formula for aerodynamic shape optimization problems[J]. AIAA Journal200341(11): 2114-2129.
17 BURDYSHAW C E, ANDERSON W K. A general and extensible unstructured mesh adjoint method[J]. Journal of Aerospace Computing, Information, and Communication20052(10): 401-413.
18 MURA G L, HINCHLIFFE B L, QIN N, et al. Efficient method to eliminate mesh sensitivity in adjoint-based optimization[J]. AIAA Journal201755(4): 1140-1151.
19 NIELSEN E J, PARK M A. Using an adjoint approach to eliminate mesh sensitivities in computational design[J]. AIAA Journal200644(5): 948-953.
20 RAO S, WILTON D, GLISSON A. Electromagnetic scattering by surfaces of arbitrary shape[J]. IEEE Transactions on Antennas and Propagation198230(3): 409-418.
21 麻军. 矩量法及其并行计算在粗糙面和目标电磁散射中的应用[D]. 西安: 西安电子科技大学, 2009.
  MA J. Application of moment method and its parallel calculation in electromagnetic scattering from rough surface and target[D]. Xi’an: Xidian University, 2009 (in Chinese).
22 张玉. 电磁场并行计算[M]. 西安: 西安电子科技大学出版社, 2006.
  ZHANG Y. Parallel computation in electromagnetics[M]. Xi’an: Xidian University Press, 2006 (in Chinese).
23 HASCOET L P V. TAPENADE 2.1: User’s guide[R]. Pairs: INRIA, 2004.
24 GIBSON W C. The method of moments in electromagnetics[M]. 3rd ed. Boca Raton : C & H/CRC Press, 2021.
25 WOO A C, WANG H T G, SCHUH M J, et al. EM programmer’s notebook-benchmark radar targets for the validation of computational electromagnetics programs[J]. IEEE Antennas and Propagation Magazine199335(1): 84-89.
文章导航

/