卫星监测任务仿真的序贯试验设计方法研究

doi:10.16182/j.issn1004731x.joss.23-0602

摘要/Abstract

摘要：

针对卫星监测任务仿真试验在复杂试验空间中无法兼顾样本点数量和模型精度的问题，提出一种基于点密度和局部非线性度的卫星仿真试验混合序贯试验设计方法。使用Voronoi划分描述离散点分布密度，借助泰勒展开式及样本点邻域梯度信息衡量非线性度，将两者组合计算综合指标，对样本点进行排序，进而添加新的样本点，直到满足停止准则。仿真结果表明：相比均匀设计和拉丁超立方设计，序贯试验设计方法在函数算例上可以在较少样本点的情况下达到停止准则。在仿真系统数据上，误差指标RMSE分别提高 $44.88 %$ 和 $38.77 %$ ，MAPE分别提高 $47.07 %$ 和 $37.4 %$ 。序贯试验设计方法相较于传统试验设计在样本点采集上可以有效降低采样数量，提升模型精度。

关键词: 卫星仿真试验, 试验设计, 序贯试验设计, 混合加点准则, 响应建模

Abstract:

Aiming at the problem that satellite monitoring mission simulation tests cannot take into account the number of sample points and model accuracy in the complex test space, a hybrid sequential test design method for satellite simulation tests based on sample density and local nonlinearity is proposed. Voronoi division is used to describe the density of discrete point distribution, and the nonlinearity is measured with the help of Taylor expansion and sample point neighborhood gradient information. The two are combined to calculate the hybrid metrics, and the sample points are ranked and new ones are added until the stopping criterion is satisfied. The simulation results show that the sequential experimental design method can meet the stopping criterion with fewer sample points on the function examples compared to the uniform and Latin hypercube designs. Using the simulated system data, the error metric RMSE results improved by 44.88% and 38.77%, the error metric MAPE results improved by 47.07% and 37.4%, respectively. Compared with the traditional experimental design, the sequential experimental design method can effectively reduce the number of sample points and improve the model accuracy.

Key words: satellite simulation experiment, experimental design, sequential experimental design, hybrid sampling points, response modeling

中图分类号:

T391.9

王彦琳,程志君,王子辰等 . 卫星监测任务仿真的序贯试验设计方法研究[J]. 系统仿真学报, 2024, 36(10): 2257-2264.

Wang Yanlin,Cheng Zhijun,Wang Zichen,et al . Research on Sequential Design Methods for Satellite Combat Simulation Tests[J]. Journal of System Simulation, 2024, 36(10): 2257-2264.

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测试函数名称	维度	测试区间
BOHACHEVSKY	2	[-100, 100]
MATYAS	2	[-10, 10]
PEAKS^[14]	2	[-5, 5]
SIX-HUMP CAMEL^[10]	2	[-2, 2]
ROSENBROCK^[15]	5	[5, 10]
BRATLEY ET AL. (1992)	6	[0, 1]

函数名称	LOLA-Voronoi	均匀设计	拉丁超立方设计
BOHACHE-VSKY	0.001 7	0.000 5	0.000 9
MATYAS	0.000 1	0.000 3	0.000 1
PEAKS	0.043 0	0.915 6	0.835 5
SIX-HUMP CAMEL	0.032 8	0.046 2	0.017 8

设计方法	样本数
设计方法	162	172	182	192
LOLA-Voronoi	0.018 5	0.009 2	0.004 1	0.004 8
均匀设计	0.013 9	0.015 0	0.006 8	0.006 5
拉丁超立方设计	0.008 3	0.010 1	0.006 0	0.006 2

设计方法	样本数
设计方法	172	182	192	202
LOLA-Voronoi	0.165 6	0.081 5	0.028 4	0.014 8
均匀设计	0.137 3	0.082 5	0.046 0	0.015 2
拉丁超立方设计	0.050 3	0.070 3	0.039 7	0.043 1

设计方法	样本数
设计方法	142	152	162	172
LOLA-Voronoi	0.011 0	0.009 9	0.009 5	0.008 5
均匀设计	0.011 2	0.010 3	0.011 3	0.008 8
拉丁超立方设计	0.010 7	0.011 4	0.009 6	0.008 9