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为了提高主反射镜轴向支撑点位置优化的效率和准确性,选择反向传播神经网络作为轴向支撑位置优化问题的代理模型。按照均匀分布在设计区间上取不同的口径、中心孔组合作为样本点,用参数化有限元模型计算对应的样本数据。用样本数据对神经网络模型进行训练和精度分析,确定了近似性能最佳的反向传播神经网络模型的结构和参数,建立了口径、中心孔和支撑位置与镜面最大变形量之间的映射关系。随机测试表明,建立的反向传播网络模型能在平均绝对偏差8E-5的精度水平下近似于有限元模型的结果。以两个轴向支撑位置的优化为例,与现有近似公式和基于有限元的优化方法相比,基于反向传播神经网络代理模型的优化方法能快速、准确地确定最佳支撑位置,并能给出镜面变形量的预测值。综合以上过程,设计制作了基于Matlab的轴向支撑优化工具箱。
In order to improve the efficiency and accuracy of the optimization of the position of the axial support points of the main reflector, the backpropagation neural network is selected as the surrogate model of the axial support position optimization problem. According to uniform distribution in the design interval to take different caliber, center hole combination as a sample point, the parametric finite element model to calculate the corresponding sample data. The neural network model was trained and analyzed by using the sample data. The structure and parameters of the backpropagation neural network model with the best approximation performance were determined. The mapping relationship between the caliber, the center hole and the support position and the maximum deformation of the mirror surface was established . Stochastic tests show that the established back propagation network model approximates the results of the finite element model at a level of accuracy of the mean absolute deviation 8E-5. Taking the optimization of two axial support positions as an example, the optimization method based on backpropagation neural network proxy model can quickly and accurately determine the optimal support position compared with the existing approximate formulas and the finite element based optimization methods Can give a prediction of the amount of specular deformation. Based on the above process, the axial support optimization toolbox based on Matlab is designed and manufactured.