基于混合优化方法的大口径主镜设计  

Design of Large-Aperture Primary Mirror Based on Hybrid Optimization Method

作　　者：孙奇 宫雪非[1,2] Qi Sun;Xuefei Gong(National Astronomical Observatories/Nanjing Institute of Astronomical Optics&Technology,Chinese Academy of Sciences,Nanjing,Jiangsu 210042,China;CAS Key Laboratory of Astronomical Optics&Technology,Nanjing Institute of Astronomical Optics&Technology,Nanjing,Jiangsu 210042,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院国家天文台南京天文光学技术研究所,江苏南京210042 [2]中国科学院天文光学技术重点实验室(南京天文光学技术研究所),江苏南京210042 [3]中国科学院大学,北京100049

出　　处：《光学学报》2020年第22期108-115,共8页Acta Optica Sinica

基　　金：国家自然科学基金(11873014)。

摘　　要：混合使用响应面近似模型和直接优化方法对主镜进行轻量化和支撑点布局集成设计,并以2.5 m地基光学望远镜的超低膨胀主镜为例,对该方法的参数敏感性分析、基于Kriging响应面多目标遗传算法的全局优化、基于混合整数序列二次规划梯度算法的局部优化过程进行研究,并采用折衷规划理论制定评价函数。集成优化结果表明,与相同尺寸的实心镜相比,主镜采用背部局部开放式六边形孔夹芯三明治结构时,轻量化率为72.13%。主镜轴向采用54点whiffletree被动支撑,在光轴竖直及重力载荷下镜面变形的均方根值为6.08 nm,各项指标均满足设计要求。In this paper,a hybrid use of response surface approximation methodology and direct optimization method is utilized to design the lightweight and support point layout of the primary mirror.Taking the ultra-low expansion primary mirror of a 2.5 m ground-based optical telescope as an example,the parameter sensitivity analysis of this method,the global optimization of multi-objective genetic algorithm based on Kriging response surface,the local optimization process based on the gradient algorithm of the mixed-integer sequential quadratic programming are studied,and the evaluation function is formulated using the compromise programming theory.The results of integrated optimization show that,compared with the solid mirror of the same size,the lightweight rate is 72.13%when the primary mirror adopts a partially open hexagonal hole sandwich structure on the back.The primary mirror adopts 54-point whiffletree passive support in the axial direction.The root mean square of the mirror surface deformation under the vertical optical axis and gravity load is 6.08 nm,and all indexes meet the design requirements.

关 键 词：地基光学望远镜 轻量化设计 主镜支撑 集成优化设计 混合优化方法 

分 类 号：TH751[机械工程—仪器科学与技术]