Research on the adjustment of reflective surface of “FAST” based on geometric transformation and genetic algorithm

Aiming at the adjustment problem of the active reflecting surface of radio telescope (FAST), this paper adopts the method of combining geometric coordinate transformation and genetic algorithm. Firstly, in the case of the base position, the coordinates of the vertex of the ideal paraboloid under the base position are determined as $(0,0,-300.4)$ by constructing the transformation model of the ideal paraboloid in terms of polar coordinates and right angle coordinates. Then, for the case that the observed celestial body is in the general position ($\alpha=$ $36.795^{\circ}, \beta=78.169^{\circ}$), the spatial coordinate transformation formula is used to extend the model to the observation scene of multiple angles, and combined with the geometrical motion characteristics of the main cable node and the actuator, the amount of regulation of the main cable node is finally optimized by the genetic algorithm to ultimately achieve the adjustment of the active reflecting surface to make it fit more closely to the ideal paraboloid. The shape of the active reflective surface is finally adjusted by optimizing the adjustment amount of the main cable node through the genetic algorithm, so that the shape of the active reflective surface can be adjusted to fit the ideal paraboloid.