基于改进灰狼算法优化SVR的航天侦察装备效能评估

doi:10.12305/j.issn.1001-506X.2021.10.25

Abstract

Abstract:

Quantitative evaluation of operational effectiveness is an important part of reconnaissance satellite system (RSS) construction and has important practical significance for its development and combat application. In view of the problems such as small number of evaluation sample data and nonlinear change of performance under the influence of multiple index factors, a support vector regression (SVR) evaluation method based on improved grey wolf optimizer (IGWO) is proposed. Opposition-based learning strategy and cosine nonlinear convergence factor are introduced to improve the convergence performance and global optimization capability of GWO. IGWO algorithm is applied to the optimization of effectiveness evaluation parameters based on SVR. Based on the characteristics of RSS, the evaluation index system and effectiveness evaluation model are constructed. Finally, the validity of the model and the rationality of the method are verified by simulation evaluation of RSS under a certain operational scenario.

Key words: support vector regression machine, operational effectiveness evaluation, space reconnaissance, parameter optimization, grey wolf optimizer

CLC Number:

TJ86

Chi HAN, Wei XIONG. Operational effectiveness evaluation of space reconnaissance equipment based on SVR optimized by improved grey wolf optimizer[J]. Systems Engineering and Electronics, 2021, 43(10): 2902-2910.

Figures/Tables 14

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References 33

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算法	描述
PSO	标准粒子群算法
GWO	GWO算法
IGWO_1	第2.2.1节策略IGWO算法
IGWO_2	第2.2.2节策略IGWO算法
IGWO	混合IGWO算法

参数	N	max	上限	下限
值	30	500	1e06	1e-03

测试函数	维度	范围	Min
${f_1} = \sum\nolimits_{i = 1}^n {x_i^2} $	30	[－100, 100]	0
${f_2} = \sum\nolimits_{i = 1}^n {\left\| {{x_i}} \right\|} + \prod\nolimits_{i = 1}^n {\left\| {{x_i}} \right\|} $	30	[－10, 10]	0
${f_3} = \sum\nolimits_{i = 1}^n {\left( {\sum\nolimits_{j = 1}^i {x_j^2} } \right)} $	30	[－100, 100]	0
${f_4} = \sum\nolimits_{i = 1}^n {\left[ {x_i^2 - 10\cos \left( {2\pi {x_i}} \right) + 10} \right]} $	30	[－5.12, 5.12]	0
${f_5} = - 20\exp \left[ { - \frac{1}{5}\sqrt {\left( {\sum\nolimits_{i = 1}^n {x_i^2} } \right)/n} } \right] - \exp \left[ {\left( {\sum\nolimits_{i = 1}^n {\cos \left( {2\pi {x_i}} \right)} } \right)/n} \right] + 20 + e$	30	[－32, 32]	0
${f_6} = \frac{1}{{4000}}\sum\limits_{i = 1}^n {x_i^2} - \prod\limits_{i = 1}^n {\cos \left( {\frac{{{x_i}}}{{\sqrt i }}} \right)} + 1$	30	[－600, 600]	0
${f_7} = 4x_1^2 - 2.1x_1^4 + x_1^6/3 + {x_1}{x_2} - 4x_2^2 + 4x_2^4$	2	[－5, 5]	-1.031 6
${f_8} = {\left( {{x_2} - \frac{{5.1}}{{4{\pi ^2}}}x_1^2 + \frac{5}{\pi }{x_1} - 6} \right)^2} + 10\left( {1 - \frac{1}{{8\pi }}} \right)\cos \;{x_1} + 10$	2	[－5, 5]	0.397 9
${f_9} = \left[ {1 + {{\left( {{x_1} + {x_2} + 1} \right)}^2} \cdot \left( {19 - 14{x_1} + 3x_1^2 - 14{x_2} + 6{x_1}{x_2} + 3x_2^2} \right)} \right] \cdot \left[ {30 + {{\left( {2{x_1} - 3{x_2}} \right)}^2} \cdot \left( {18 - 32{x_1} + 12x_1^2 + 48{x_2} - 36{x_1}{x_2} + 27x_2^2} \right)} \right]$	2	[－2, 2]	3

函数	PSO		GWO		IGWO_1		IGWO_2		IGWO
函数	Average	St.dev	Average	St.dev	Average	St.dev	Average	St.dev	Average	St.dev
f₁	3.67e-09	5.33e-09	3.79e-59	6.78e-59	1.02e-70	1.51e-70	8.47e-82	2.61e-81	7.72e-83	1.35e-82
f₂	1.59e-04	1.83e-04	8.74e-35	5.76e-35	2.98e-41	3.66e-41	3.96e-48	3.51e-48	2.07e-48	2.43e-48
f₃	14.304 2	4.827 6	4.21e-16	9.99e-16	1.04e-18	2.27e-18	4.31e-20	8.80e-20	9.45e-22	1.92e-21
f₄	49.748 9	10.103 0	0.442 0	1.397 7	5.68e-15	1.80e-14	0	0	0	0
f₅	1.45e-04	3.19e-04	1.76e-14	3.37e-15	1.23e-14	3.67e-15	7.64e-15	1.12e-15	7.99e-15	0
f₆	0.008 6	0.008 8	0.003 7	0.009 0	0.001 7	0.003 6	0.001 5	0.004 6	0	0
f₇	-1.031 6	4.24e-08	-1.031 6	7.32e-08	-1.031 6	1.30e-08	-1.031 6	0	-1.031 6	7.43e-09
f₈	0.397 9	7.72e-06	0.397 9	8.64e-06	0.397 9	2.08e-06	0.397 9	5.71e-07	0.397 9	0
f₉	3.000 0	5.41e-06	3.000 0	1.82e-06	3.000 0	1.52e-05	3.000 0	4.79e-06	3.000 0	1.26e-15

编号	半长轴/km	偏心率	轨道倾角/(°)	近地点辐角/(°)	升交点赤经/(°)	真近点角/(°)
LEO1-1/2/3	500	0	45.000 0	0	0	0/120/240
LEO2-4/5/6	500	0	45.109 2	0	89.889 8	30.16/150.16/270.16
LEO3-7/8/9	500	0	44.999 1	0	179.780 0	60.31/180.31/300.31
LEO4-10/11/12	500	0	44.889 7	0	269.891 0	90.16/210.16/330.16

Operational effectiveness evaluation of space reconnaissance equipment based on SVR optimized by improved grey wolf optimizer

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编号	x₁	x₂	x₃	x₄	x₅	x₆	效能
1	0.617 8	0.380 3	0.653 3	0.949 0	0.358 8	0.998 7	2.085 7
2	0.186 3	0.909 8	0.174 7	0.904 1	0.119 3	0.164 5	1.412 6
3	0.077 8	0.866 7	0.101 8	0.728 4	0.065 8	0.252 6	1.358 6
4	0.072 5	0.892 2	0.089 8	0.563 4	0.049 1	0.439 4	1.526 4
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
320	0.723 1	0.637 8	0.709 9	0.421 1	0.441 2	0.164 4	1.564 4

模型	RMSE	MAE	R²
默认参数SVR	0.033 726	0.023 826	0.869 13
IGWO-SVR	0.000 942	0.006 431	0.997 16
BPNN	0.036 635	0.038 615	0.861 33
GWO-SVR	0.019 211	0.022 481	0.928 99

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