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

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

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。

The development of anti-stealth technology poses a strong challenge to the stealth performance of miltary 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 re-peatedly fil 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 sen-sitivity 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 dif-ferentiation 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 ef-ficiency of gradient calculation,and provides support to the optimal design of stealth military aircraft.