LAMOST有限元模型的径向基网络修正法

Model updating of LAMOST using RBF neural networks

天文学的发展要求望远镜的口径越来越大,对其建立有限元模型进行动力学分析已成为必要步骤.为了保证理论分析结果符合实际,必须对有限元模型进行修正.针对大望远镜模型修正的难点,提出一种基于径向基神经网络的含有隐藏变量的改进迭代法.首先建立了LAMOST空间桁架和平衡系统的有限元模型.其次从实际出发,讨论了神经网络输入输出的选择方法.用有限的数据信息修正误差大的参数,而小误差参数作为神经网络的隐藏变量,可看作噪声而不予修正.采用均匀设计法获得神经网络的训练样本集,减小了计算量.然后在网络迭代求解过程中,每次在输出参数的附近增加均匀分布的若干个样本,而不是输出参数的单独一个样本,可防止网络性能突然变差,改善泛化特性.最后,悬臂梁和望远镜桁架仿真结果表明,含有隐藏变量的神经网络仍然能够收敛.用实测数据修正了LAMOST的平衡系统,表明了该方法的可行性和有效性.

The development of astronomy needs large telescopes. An accurate Finite Element Model （FEM） of the telescope which represents its real structure is required in dynamics simulation for better reliability. Therefore, we conduct a practical FEM updating method, an iterative algorithm based on Radial Basis Function （RBF） neural networks with bidden variables for Large Sky Area Multi-Object Spectroscopic Telescope （LAMOST）. Firstly, build the FEM of LAMOST space truss and balance system. Secondly, discuss the practical selection approaches for the input and output of RBF networks. Only modify big error parameters because of the limited test data. Small error parameters can be gained accurately enough before modeling. The small errors can be seen as noise and are not updated as the hidden variable of neural networks. Uniform design is adopted to get a smaller training sample set, which can reduce computation complexity. Thirdly, after an iterative process, add several uniform points around the last network output, instead of adding only one output point of the network. This improvement can enhance the generalization capability. Finally, a cantilever beam and LAMOST truss simulation results show that the method has good convergence. The balance system of LAMOST is updated using modal test data, which shows that the proposed method is feasible and effective in practice.