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.