大口径反射镜背部支撑结构的响应面优化方法
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摘要
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.
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.
引文
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[3]李桂华,王辉,熊召,等.高功率激光系统中大型光机组件的装配精度研究[J].机械工程学报,2015,51(11):116-122.[Li Gui-hua,Wang Hui,Xiong Zhao,et al.Assembly accuracy study of large optical units in high power laser system[J].Journal of Mechanical Engineering,2015,51(11):116-122]
[4]陈晓娟,傅学农,吴文凯,等.基于Pro/M的大口径反射镜的变形分析及其支撑优化[J].机械设计,2008,25(2):68-70.[Chen Xiao-juan,Fu Xue-nong,Wu Wen-kai,et al.Deformation analysis on large caliber reflector and its support optimization based on Pro/M[J].Journal of Machine Design,2008,25(2):68-70.]
[5]陈晓娟,王美聪,吴文凯,等.大口径反射镜波前畸变控制技术[J].强激光与粒子束,2011,23(12):3325-3328.[Chen Xiao-juan,Wang Mei-cong,Wu Wen-kai,et al.Wavefront distortion control for large aperture mirror[J].High Power Laser and Particle Beams,2011,23(12):3325-3328.]
[6]沈展鹏,陈晓娟,陈学前,等.大口径反射镜结构的两种参数优化方法[J].强激光与粒子束,2018,30(6):062001.[Shen Zhan-peng;Chen Xiao-juan;Chen Xue-qian,et al.Two parameter optimization methods for large aperture mirror[J].2018,30(6):062001.]
[7]Schittkowski K.NLPQL:A fortran subroutine solving constrained nonlinear programming problems[J].Annals of Operations Research,1986,5(1-4):485-500.
[8]Fletcher R,Leyffer S.Nonlinear programming without a penalty function[J].Mathematical Programming,2002,91(2):239-269.
[9]马永杰,云文霞.遗传算法研究进展[J].计算机应用研究,2012,29(4):1201-1206.[Ma Yong-jie,Yun Wen-xia.Research progress of genetic algorithm[J].Application Research of Computers,2012,29(4):1201-1206.]
[10]Mark A,Patrick W.Design of experiments:statistical principles of research design and analysis[J].Technimetrics,2001,43(2):236-237.
[11]Helton J C,Davis F J.Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems[J].Reliability Engineering&System Safety,2003,81(1):23-69.
[12]Helton J C,Johnson J D,Sallaberry C J,et al.Survey of sampling-based methods for uncertainty and sensitivity analysis[J].Reliability Engineering&System Safety,2006,91(10-11):1175-1209.
[13]Edwards J R.Alternatives to difference scores:Polynomial regression analysis and response surface methodology[J].Perspectives on Organizational Fit,2002:350-400.
[14]Kleijnen J P C.Kriging metamodeling in simulation:Areview[J].European Journal of Operational Research,2009,192(3):707-716.