SHAPE ACCURACY ADJUSTMENT OF CABLE-MESH REFLECTOR USING LEAST SQUARES METHOD

An iteration approach, based on least squares optimization, for shape accuracy adjustment of the active cable-mesh reflector in large radio telescope is presented according to the demands of the reflector deformation. The optimization model regarding nodal force increment as design variable is established to minimize the sum of residual squares of node position relative to the design paraboloid. The displacement field to deform the reflector can be obtained by linearizing the residual function. Static analytical model is established with cable element deduced on the expression of elastic catenary of a cable, so the nodal force increment corresponding to a certain displacement field can be solved. The numerical example shows that the method proposed possesses a rapid convergence rate.