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摘要:
为了高效地分析空间飞越过程中航天器的初始位置对发射窗口的影响，研究了空间飞越任务流程，提出了不同初始条件下发射窗口的数值计算方法。在此基础上，为提高计算效率，研究了代理模型技术，包括样本点选取方法、代理模型构造方法和精度校验方法。对比分析了径向基函数（RBF）模型和Kriging模型，结果证明前者精度更高。使用RBF模型对不同初始条件下的发射窗口进行计算，耗时仅为使用真实模型时的0.29%，且精度校验满足要求，表明代理模型可以快速有效地分析初始条件对发射窗口的影响，为空间飞越轨道规划与设计提供理论依据和参考。
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关键词:
- 空间飞越 /
- 发射窗口 /
- 代理模型 /
- 试验设计 /
- 径向基函数(RBF)
Abstract:In order to analyze the influence of initial positions on the launch window in space fly-by problem efficiently, the process of space fly-by was studied firstly in this paper. Then, a numerical method to calculate the launch window under different initial conditions was proposed. For improving calculation efficiency, surrogate model technology was studied, including sample points selection methods, surrogate models construction methods, and accuracy assessment methods. On the basis, two models, radial basis function (RBF) model and Kriging model, were compared. The results show that RBF model is more accurate for the problem in this paper. So it was applied to calculate launch windows under different conditions, which costs only 0.29% of the time that the true model costs, and the accuracy meets requirement. The results prove that using surrogate models can efficiently analyze the influence of initial conditions on the launch window, which will provide valuable theoretical foundation and reference for the orbital planning and design of space fly-by missions.
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Key words:
- space fly-by /
- launch window /
- surrogate model /
- design of tests /
- radial basis function (RBF)
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图 5 真实模型和RBF模型的发射窗口长度等值线图
Figure 5. Contour map of launch window length of true model and RBF model
表 1 t0时刻轨道根数
Table 1. Orbit elements at moment t0
航天器 a/km e i/(°) Ω/(°) ω/(°) 飞越航天器 6 978 0.06 97.1 180 0 目标航天器 7 878 0.15 102.0 180 90 
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表 2 两种代理模型精度对比
Table 2. Accuracy comparison of two surrogate models
模型 R2 RMSE RBF模型 0.993 0.018 Kriging模型 0.952 0.049
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表 3 代理模型和真实模型计算时间对比
Table 3. Comparison of calculation time between surrogate model and true model
s 模型
代理模型
构建时间发射窗口
计算时间总计算
时间真实模型 57 688 57 688 RBF模型 3 473 168 3 641
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