论文标题
基于计算机模拟的快速活跃反射器调整算法的研究
Research on FAST Active Reflector Adjustment Algorithm Based on Computer Simulation
论文作者
论文摘要
根据2021高等教育俱乐部杯国家大学生数学竞赛的背景，根据中国天空之眼（FAST）射电望远镜的相关数据，主要有线节点和执行器通过数学建模和计算机模拟方法进行调整和控制，以实现主动反射器。形状的调整使其能够更好地接收外部天体的信号并提高反射器的利用率，从而达到较高的进料舱接收率。在本文中，提出了基于空间坐标轴的旋转矩阵的点映射算法，即提出映射矩阵，通过数学推导获得映射矩阵，并基于原始球形表面和原始的副核苷的线性插值算法获得了线性插值算法。当插值比调整为89％以满足现实限制下的最佳解决方案时。然后，提出了基于空间线性不变性的三维空间信号反射模型。每个反射面板都用作评估指数。对于每个反射表面，定义了馈线上信号可访问性的0-1变量。信号被映射到馈线所在的平面，从而降低了许多计算困难。最后，发现可以接收反射信号账户的饲料舱面板为19.3％。与原始的球形反射模型相比，本文建立的工作抛物面模型的信号比增加了224％。
Based on the background of the 2021 Higher Education Club Cup National College Students Mathematical Contest in Modeling A, according to the relevant data of the China Sky Eye (FAST) radio telescope, the main cable nodes and actuators are adjusted and controlled by mathematical modeling and computer simulation methods to realize the active reflector. The adjustment of the shape enables it to better receive the signal of the external celestial body and improve the utilization rate of the reflector, so as to achieve a higher receiving ratio of the feed cabin. In this paper, a point set mapping algorithm based on the rotation matrix of the spatial coordinate axis is proposed, that is, the mapping matrix is obtained by mathematical derivation, and the linear interpolation algorithm based on the original spherical surface and the ideal paraboloid to solve the working paraboloid is obtained. When the interpolation ratio is adjusted to 89% to satisfy the optimal solution under realistic constraints. Then, a three-dimensional spatial signal reflection model based on spatial linear invariance is proposed. Each reflective panel is used as an evaluation index. For each reflective surface, the 0-1 variable of signal accessibility on the feeder is defined. The signal is mapped to the plane where the feeder is located, which reduces a lot of computational difficulty. Finally, it is found that the panel of the feed cabin that can receive the reflected signal accounts for 19.3%. Compared with the original spherical reflection model, the working paraboloid model established in this paper has a The signal ratio has increased by 224%.
