Two parameter optimization methods for large aperture mirror
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摘要: 大口径反射镜在自重作用下发生变形，变形过大会引起镜片通光表面的峰谷值较大，难以满足光机装置打靶精度的要求。建立了典型反射镜结构的有限元仿真模型，以计算镜片表面峰谷值；优化了安装柱的位置、尺寸及镜片厚度等参数，使镜片通光表面形变峰谷值最小。分别采用了基于有限元模型的直接优化和基于代理模型的优化，均获得了结构最优参数，使形变峰谷值比初始值降低了74%。相比而言，基于代理模型的优化还可提供目标量随设计变量的变化情况以及变量灵敏度分析，更有利于设计决策。当设计变量个数多、范围宽时，可先根据先验知识或低精度代理模型缩小设计范围，然后建立紧缩范围的高精度代理模型并进行优化，可有效避免大量计算。根据“三圆柱”支撑结构的参数优化结果，建议采用“四圆柱”支撑设计，以获得更高的面形精度。Abstract: Much deformation of the large aperture mirror by deadweight leads to large PV (peak-to-valley) value of its aperture surface, and it is hard to ensure the point accuracy on laser beams of optical facility. Finite element model is built up to calculate the PV value of the mirror surface in this paper. Moreover, parameters including position and size of erection column as well as the mirror thickness are optimized in order to minimize the PV value of the aperture surface. Both the direct optimization based on finite element model and the optimization based on surrogate model are adopted herein, and the PV value is reduced by 74% of its initial value as a result. In contrast to direct optimization, optimization based on surrogate model conveniently provides the objective variation with design variables and sensitivity analysis as well, which brings much benefit for structure design. In case of numerous and wide-range design variables, it is suggested to firstly decrease the design range according to prior knowledge or low-fidelity surrogate model and then optimize the parameters based on high-fidelity surrogate model within the shrunk range in order to avoid large amount of calculation. Furthermore, a scheme of four-cylinder support is recommended to replace the three-cylinder support for smaller PV value according to the optimization result.
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Key words:
- peak-to-valley value /
- finite element model /
- optimization /
- surrogate model /
- sensitivity analysis
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图 1 反射镜安装及几何尺寸参数示意
Figure 1. Schematic diagram of assembling and geometry parameters of the mirror
图 2 设计变量取初始值时镜片的有限元网格及镜面变形
Figure 2. Mesh and deformation of the mirror with initial design variables
图 8 各设计变量对PV值的局部灵敏度和全局灵敏度
Figure 8. Local and global sensitivity of design variables to PV value
图 9 优化后反射镜通光表面的离面位移云图(半模型)
Figure 9. Off-plane displacement on the aperture surface of half-model after optimization
表 1 设计变量的范围和初值
Table 1. The range and initial value of the design variables
variables lower bound/mm upper bound/mm initial value/mm h1 60 240 150 h2 60 240 150 w 100 160 100 D 30 80 60 T 70 100 85 
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表 2 优化结果对比
Table 2. Comparison of the optimization results
method PV value/nm design variables/mm h1 h2 w D T initial value 254.8 150.0 150.0 100.0 60.0 85.0 direct optimization 66.3 240.0 68.3 116.2 80.0 100.0 optimization based on whole-range surrogate model 85.3 205.4 63.3 106.6 79.6 99.9 optimization based on shrunk-range surrogate model 67.1 239.7 69.3 117.7 78.7 99.9
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