大口径反射镜背部支撑结构的响应面优化方法

Response Surface Optimization Method for Mirror Distortion of Large Aperture Mirror

惯性约束聚变(ICF)装置中大口径反射镜在自重作用下的畸变常常导致其面形精度降低,从而降低整个激光装置的打靶精度。为了满足反射镜面形精度要求,以反射镜通光表面面形峰谷值(PV值)为优化目标,以支撑点位置为设计变量,对两种反射镜背部支撑方式进行优化研究。通过对试验设计方法、常用响应面类型和优化算法的分析,综合考虑优化效率与精度,最终选取Kriging响应面结合遗传算法开展优化工作。为提高优化效率,提出了两步优化策略。首先建立基于全设计范围的粗精度响应面模型,得到表示设计变量与目标量关系的曲面与初步优化结果。然后基于初步优化结果,缩小设计范围建立高精度响应面模型,进一步优化支撑点位置以得到最佳支撑形式。结果表明响应面优化的最优解与该点处的有限元计算结果非常接近,与在有限元模型上直接优化结果的误差在可接受范围内,但计算效率得到了很大提升。

The distortion of large aperture mirror by its weight in inertial confinement fusion (ICF) often leads to the reduction of its surface shape accuracy, thereby reducing the accuracy of the whole laser device. In order to meet the requirement of surface shape accuracy, the optimization study is conducted on the back-support of two kinds of mirrors with peak-valley(PV) value of aperture surface as the optimization objective and the position of supporting points as the design variables. Through the analysis of design of experiment methods, common response surface models and optimization algorithms, with the optimization efficiency and accuracy considered comprehensively,Kriging response surface is finally selected to carry out optimization research with genetic algorithm. A two-step optimization strategy is proposed to improve the optimization efficiency. Firstly, the rough response surface model is established based on the design space, preliminary optimization results and the surface indicating the relationship between design variables and objective are obtained. Then, based on the preliminary optimization results, the design space is narrowed, the high-precision response surface model is established to optimize the position of the support points to obtain the best form of support. The results of response surface optimization are very close to those of direct optimization and they all meet the design requirements, but calculation efficiency of response surface optimization is greatly improved.