基于最速下降法的可展开索网天线型面调整方法

考虑到索网结构的几何非线性和节点位移的高度耦合，为提高索网天线的型面调整效率，需设计合理的型面调整优化方法。文章根据双层索网结构的拓扑关系，将平衡矩阵和柔度矩阵分块化表示，通过偏导方法推导了任意平衡状态下型面误差对于张力阵拉力的梯度公式，利用型面误差梯度的无穷范数确定对型面误差影响最显著的张力阵单元。结合最速下降优化算法，采用型面误差负梯度方向作为优化路径。通过调节张力阵拉力，降低由于索网长度误差引起的型面误差。建立环形桁架天线的双层索网模型，进行型面调整数值试验，结果表明调整后的型面误差已趋近为零。

Surface adjustment method of deployable cable antenna based on steepest descent algorithm

Considering the geometric nonlinearity of cable structures and the high-degree coupling of nodal displacements, a reasonable optimization method is essential in order to improve the surface adjustment efficiency of cable antenna. The equilibrium matrix and flexibility matrix of double-layer cable-net structures were partitioned based on the topology. The gradient formula of surface error to the tensile forces of tension ties was derived in derivative form. The infinite norm of surface error gradient was used to determine the element of tension ties which has the most significant effect on the surface error. Based on the steepest descent algorithm, the negative gradient direction of surface error was chosen as the optimizing path. The surface error due to the length tolerances of cable elements is decreased by adjusting the tensile forces of tension ties. The double-layer cable-net model of AstroMesh antenna was established and some numerical surface adjustment experiments were carried out. Results indicate that the surface error after adjusting approaches zero.