Support vector regression-based operational effectiveness evaluation approach to reconnaissance satellite system

doi:10.23919/JSEE.2023.000020

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (6): 1626-1644.doi: 10.23919/JSEE.2023.000020

• SYSTEMS ENGINEERING • Previous Articles

Support vector regression-based operational effectiveness evaluation approach to reconnaissance satellite system

Chi HAN¹^,*(), Wei XIONG¹^,²(), Minghui XIONG¹(), Zhen LIU¹()

¹ College of Aerospace Information, Space Engineering University, Beijing 101400, China
² Science and Technology on Complex Electronic System Simulation Laboratory, Space Engineering University, Beijing 101400, China

Received:2021-03-22 Online:2023-12-18 Published:2023-12-29
Contact: Chi HAN E-mail:15850466132@163.com;13331094335@163.com;xtkxxmh@163.com;2981282863@qq.com
About author:
HAN Chi was born in 1997. He received his B.S. degree from the Science and Technology on Complex Electronic System Simulation Laboratory, Space Engineering University in 2019, where he is currently pursuing his M.S. degree. His research interests include effectiveness evaluation of weapon system of ststems (WSoS), spatial information system analysis and satellite constellation design. E-mail: 15850466132@163.com

XIONG Wei was born in 1971. He received his Ph.D. degree from Beihang University in 2005. He is currently a professor with the Science and Technology on Complex Electronic System Simulation Laboratory, Space Engineering University. His research interests include the complex networks and systems engineering and theory. E-mail: 13331094335@163.com

XIONG Minghui was born in 1995. He received his M.S. degree from Space Engineering University, in 2019, where he is pursuing his Ph.D. degree. His current research interests include preference modeling, evolutionary many-objective optimization, and satellite constellation design. E-mail: xtkxxmh@163.com

LIU Zhen was born in 1995. He received his B.S. degree from the Space Engineering University in 2018, where he is pursuing his M.S. degree. His research interests include system modeling, system evaluation and deep reinforcement learning. E-mail: 2981282863@qq.com
Supported by:
This work was supported by the National Defense Science and Technology Key Laboratory Fund of China (XM2020XT1023).

Abstract

Abstract:

As one of the most important part of weapon system of systems (WSoS), quantitative evaluation of reconnaissance satellite system (RSS) is indispensable during its construction and application. Aiming at the problem of nonlinear effectiveness evaluation under small sample conditions, we propose an evaluation method based on support vector regression (SVR) to effectively address the defects of traditional methods. Considering the performance of SVR is influenced by the penalty factor, kernel type, and other parameters deeply, the improved grey wolf optimizer (IGWO) is employed for parameter optimization. In the proposed IGWO algorithm, the opposition-based learning strategy is adopted to increase the probability of avoiding the local optima, the mutation operator is used to escape from premature convergence and differential convergence factors are applied to increase the rate of convergence. Numerical experiments of 14 test functions validate the applicability of IGWO algorithm dealing with global optimization. The index system and evaluation method are constructed based on the characteristics of RSS. To validate the proposed IGWO-SVR evaluation method, eight benchmark data sets and combat simulation are employed to estimate the evaluation accuracy, convergence performance and computational complexity. According to the experimental results, the proposed method outperforms several prediction based evaluation methods, verifies the superiority and effectiveness in RSS operational effectiveness evaluation.

Key words: reconnaissance satellite system (RSS), support vector regression (SVR), gray wolf optimizer, opposition-based learning, parameter optimization, effectiveness evaluation

Chi HAN, Wei XIONG, Minghui XIONG, Zhen LIU. Support vector regression-based operational effectiveness evaluation approach to reconnaissance satellite system[J]. Journal of Systems Engineering and Electronics, 2023, 34(6): 1626-1644.

Figures/Tables 23

Fig 1

Fig 2

Fig 3

Fig 4

Table 1

Table 2

Benchmark function"

Function	Definition	Dimension	Range	Optimum
f₁	${f_1}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {x_i^2} $	30	[−100,100]	0
f₂	$ {f_2}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {\left\| {{x_i}} \right\| + \prod\limits_{i = 1}^n {\left\| {{x_i}} \right\|} } $	30	[−10,10]	0
f₃	${f_3}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n { { {\left( {\sum\limits_{j = 1}^i { {x_j} } } \right)}^2} }$	30	[−100,100]	0
f₄	${f_4}\left( x \right) = \max \left\{ {\left\| { {x_i} } \right\|} \right\};1 \leqslant i \leqslant n$	30	[−100,100]	0
f₅	$ {f_5}\left( x \right) = \displaystyle\sum\limits_{i = 1}^{n - 1} {\left[ {100{{\left( {{x_{i + 1}} - x_i^2} \right)}^2} + {{\left( {{x_i} - 1} \right)}^2}} \right]} $	30	[−30,30]	0
f₆	${f_6}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {{{\left( {{x_i} + 0.5} \right)}^2}} $	30	[−100,100]	0
f₇	${f_7}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {ix_i^4 + {\rm{rand}};{\rm{rand}} \in \left[ {0,1} \right]}$	30	[−1.28,1.28]	0
f₈	${f_8}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n { - {x_i}\sin \left( {\sqrt {\left\| {{x_i}} \right\|} } \right)} $	30	[−500,500]	−418.9829×5
f₉	${f_9}\left( x \right) = \displaystyle\sum\limits_{i = 1}^n {\left[ {x_i^2 - 10\cos \left( {2\text{π} {x_i} } \right) + 10} \right]}$	30	[−5.12,5.12]	0
f₁₀	$\begin{aligned}&f_{10}(x)=-20 \exp \left(-0.2 \sqrt{\left(\sum_{i=1}^n x_i^2\right) / n}\right)- \\&\quad \exp \left(\sum_{i=1}^n \cos \left(2 {\text{π} } x_i\right) / n\right)+20+e\end{aligned}$	30	[−32,32]	0
f₁₁	$f_{11}(x)=2.5 \times 10^{-4} \displaystyle\sum_{i=1}^n x_i^2-\displaystyle\prod_{i=1}^n \cos \left(\dfrac{x_i}{\sqrt{i} }\right)+1$	30	[−600,600]	0
f₁₂	$f_{12}(x)=4 x_1^2-2. 1 x_1^4+\dfrac{1}{3} x_1^6+x_1 x_2-4 x_2^2+4 x_2^4$	2	[−5,5]	−1.0316
f₁₃	$f_{13}(x)=\left(x_2-\dfrac{5.1}{4 {\text{π}}^2} x_1^2+\dfrac{5}{{\text{π}}} x_1-6\right)^2+10\left(1-\dfrac{1}{8 {\text{π}}}\right) \cos x_1+10$	2	[−5,5]	0.398
f₁₄	$\begin{gathered} f_{14}(x)= {\left[1+\left(x_1+x_2+1\right)^2\left(19-14 x_1+3 x_1^2-14 x_2+6 x_1 x_2+3 x_2^2\right)\right] }\times \\ \left[30+\left(2 x_1-3 x_2\right)^2\left(18-32 x_1+12 x_1^2+48 x_2-36 x_1 x_2+27 x_2^2\right)\right]\end{gathered}$	2	[−2,2]	3

Table 2

Table 3

Comparison of experimental result"

Function	Item	PSO	MVO	MFO	ALO	SCA	WOA	GWO	IGWO
f₁	Average	1.01e-04	1.73e-33	6.37e-28	8.94e-28	3.96e-39	2.54e-46	1.32e-39	1.11e-73
	Std.	1.54e-04	2.09e-33	9.30e-28	9.38e-28	4.74e-39	4.64e-46	8.71e-40	2.81e-73
	Time	0.0043	0.0083	0.0209	0.0195	0.0183	0.0184	0.0117	0.0158
f₂	Average	1.99e-02	4.93e-20	1.40e-16	1.04e-16	1.48e-23	4.14e-28	1.42e-23	9.23e-52
	Std.	1.65e-02	2.53e-20	9.89e-17	6.48e-17	9.76e-24	2.45e-28	1.25e-23	1.54e-51
	Time	0.0056	0.0067	0.0131	0.0127	0.0106	0.0105	0.0065	0.0072
f₃	Average	67.3020	5.14e-06	4.88e-06	7.04e-06	2.20e-08	5.25e-07	1.29e-08	7.67e-11
	Std.	35.1326	1.48e-05	5.13e-06	1.42e-05	5.98e-08	3.56e-07	2.94e-08	1.12e-10
	Time	0.0347	0.0393	0.0428	0.0406	0.0395	0.0397	0.0416	0.0297
f₄	Average	1.0974	3.01e-08	5.57e-07	8.44e-07	1.85e-10	7.26e-07	3.07e-10	6.11e-12
	Std.	0.2795	3.39e-08	4.32e-07	8.08e-07	1.64e-10	3.97e-07	3.65e-10	7.81e-12
	Time	0.0044	0.0062	0.0119	0.0094	0.0095	0.0171	0.0056	0.0094
f₅	Average	1.45e-06	1.76e-14	7.65e-08	4.46e-05	6.74e-14	7.64e-15	7.99e-15	0
	Std.	3.19e-04	3.37e-15	8.56e-07	2.24e-05	8.47e-15	1.12e-15	0	0
	Time	0.0043	0.0094	0.0154	0.0141	0.0157	0.0094	0.0117	0.0115
f₆	Average	3.47e-01	6.56e-04	7.14e-01	1.1476	4.99e-01	6.74e-01	7.23e-01	1.52e-04
	Std.	2.39e-01	3.82e-04	4.26e-01	2.52e-01	4.56e-01	1.68e-01	2.52e-01	1.56e-04
	Time	0.0098	1.1535	0.0118	0.0121	0.0095	0.0094	0.0094	0.0056
f₇	Average	1.76e-01	1.34e-03	2.14e-03	1.79e-03	1.29e-03	1.02e-03	9.65e-04	2.25e-04
	Std.	4.95e-02	6.84e-04	1.02e-03	8.44e-04	7.00e-04	4.84e-04	8.85e-04	2.10e-04
	Time	0.0103	0.0157	0.0184	0.0156	0.0157	0.0163	0.018	0.0119
f₈	Average	0.3979	0.3979	0.3979	0.3979	0.3979	0.3979	0.3979	0.3979
	Std.	3.58e-02	4.28e-05	7.79e-06	8.65e-06	2.08e-06	5.71e-06	0	0
	Time	0.0275	0.0247	0.0247	0.0234	0.0332	0.0230	0.0276	0.0277
f₉	Average	52.4065	1.0366	2.0143	1.6277	5.68e-15	1.7677	0	0
	Std.	9.2906	2.0276	3.5410	2.4442	1.80e-14	3.7301	0	0
	Time	0.0065	0.0119	0.0146	0.0123	0.0122	0.0121	0.0136	0.0062
f₁₀	Average	1.03e-01	3.61e-14	1.07e-13	1.06e-13	1.26e-14	1.51e-14	1.40e-14	3.73e-15
	Std.	2.91e-01	3.53e-15	2.16e-14	1.94e-14	2.92e-15	1.67e-15	4.12e-15	2.80e-15
	Time	0.0077	0.0107	0.0139	0.0119	0.0108	0.0108	0.0136	0.0071
f₁₁	Average	6.18e-03	6.94e-03	2.99e-03	1.09e-03	0	2.65e-03	2.32e-03	0
	Std.	7.37e-03	1.29e-02	9.45e-03	3.47e-03	0	5.73e-03	7.35e-03	0
	Time	0.007	0.0118	0.0143	0.0124	0.0117	0.012	0.0145	0.0083
f₁₂	Average	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316	−1.0316
	Std.	0	8.74e-08	6.28e-07	3.47e-08	1.35e-07	1.16e-04	5.47e-09	0
	Time	0.0283	0.0273	0.0244	0.0289	0.0284	0.0287	0.0232	0.0083
f₁₃	Average	0.3979	0.3979	0.3979	0.3979	0.3979	0.3979	0.3979	0.3979
	Std.	6.67e-04	4.93e-07	7.67e-06	1.75e-04	5.24e-05	0	5.24e-05	0
	Time	0.0085	0.0066	0.0069	0.0069	0.0068	0.0069	0.0069	0.0069
f₁₄	Average	3.0000	3.0000	3.0000	3.0000	3.0000	3.0000	3.0000	3.0000
	Std.	2.81e-05	1.97e-05	2.91e-05	4.71e-05	1.57e-05	7.44e-06	3.72e-05	4.90e-16
	Time	0.0084	0.0065	0.0065	0.0066	0.0065	0.0065	0.0065	0.0065

Table 3

Fig 5

Fig 6

Fig 7

Fig 8

Fig 9

Table 4

Table 5

Table 6

Fig 10

Table 7

Table 8

Table 9

Table 10

Fig 11

Fig 12

Table 11

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Algorithm	Description
PSO	Standard particle swarm algorithm
GWO	Standard gray wolf algorithm
MFO	Moth-flame optimization algorithm [41]
ALO	Ant lion optimizer [42]
SCA	Sine cosine algorithm [43]
WOA	Whale optimization algorithm [44]
MVO	Multi-verse optimizer [45]
IGWO	Hybrid improved gray wolf algorithm

Data	Dataset	Instance	Attribute	Characteristic
a	Tertiary structure	45730	9	Real
b	PM2.5	43824	13	Integer, real
c	Stability	10000	14	Real
d	Air quality	9358	15	Real
e	Student	649	33	Integer
f	Wine	4898	12	Real
g	German	1000	21	Integer, real
h	News popularity	39797	61	Integer, real

Method	Parameter item	Value
SVR	SVR parameters	(2,1,0.01)
IGWO-SVR	Number of search agents	30
	Maximum iterations	500
	Minimum of SVR parameters	(1e−4,1e−4,0)
	Maximum of SVR parameters	(100,100,1)
BPNN	Number of neurons in input layer	6
	Number of neurons in output layer	1
	Number of neurons in hidden layer	10
	Learning efficiency	0.1
	Error limitation	0.001
GWO-SVR	Number of search agents	30
	Maximum iterations	500
	Minimum of SVR parameters	(1e−4,1e−4,0)
	Maximum of SVR parameters	(100,100,1)

Dataset	SVR		IGWO-SVR		BPNN		GWO-SVR
Dataset	Average	Std.	Average	Std.	Average	Std.	Average	Std.
a	1.70e-01	6.19e-02	4.62e-02	3.50e-03	3.05e-01	6.05e-02	1.10e-01	7.19e-02
b	5.48e-02	1.61e-02	1.18e-03	5.80e-04	4.27e-02	5.00e-03	1.90e-02	9.10e-03
c	8.62e-02	2.71e-02	7.60e-03	1.20e-05	1.26e-02	1.00e-03	1.06e-02	3.70e-03
d	8.70e-03	8.30e-03	6.10e-05	5.08e-04	1.78e-02	2.60e-03	6.80e-03	8.19e-04
e	1.26e-02	2.20e-03	2.80e-03	2.98e-05	1.90e-02	5.80e-03	1.28e-02	1.90e-03
f	3.06e-02	2.39e-02	7.50e-04	2.30e-03	7.08e-02	1.75e-01	1.63e-02	1.13e-02
g	3.54e-01	1.65e-01	1.58e-01	2.78e-02	7.99e-01	2.72e-01	4.26e-01	6.73e-02
h	2.42e-02	9.70e-03	1.19e-02	2.60e-04	3.31e-02	9.00e-03	4.64e-02	3.41e-02

Dataset	SVR	IGWO-SVR	BPNN	GWO-SVR
a	16.24	17.76	33.01	31.37
b	15.35	9.93	21.26	22.83
c	10.42	14.76	15.53	22.79
d	35.33	19.63	28.50	17.43
e	4.83	3.58	6.37	9.50
f	1.31	1.02	7.27	4.28
g	15.94	18.24	16.45	24.83
h	15.88	12.61	23.95	13.89

Support vector regression-based operational effectiveness evaluation approach to reconnaissance satellite system

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Dataset	IGWO-SVR vs SVR	IGWO-SVR vs GWO-SVR	IGWO-SVR vs BPNN
a	6.16e-05	1.40e-02	5.93e-04
b	2.43e-05	2.54e-02	6.73e-03
c	1.68e-05	3.93e-01	1.19e-01
d	6.42e-05	3.68e-01	1.00e-03
e	6.42e-05	7.82e-04	8.52e-04
f	1.59e-05	5.25e-02	1.73e-01
g	4.57e-05	5.67e-05	2.64e-03
h	6.28e-05	2.46e-04	2.46e-04

Number	Semimajor axis	Eccentricity	Inclination	Argument of perigee	RAAN	True anomaly
LEO1-1/2/3	500	0	45.0000	0	0	0/120/240
LEO2-4/5/6	500	0	45.1092	0	89.8898	30.16/150.16/270.16
LEO3-7/8/9	500	0	44.9991	0	179.7800	60.31/180.31/300.31
LEO4-10/11/12	500	0	44.8897	0	269.8910	90.16/210.16/330.16

Number	x₁	x₂	x₃	x₄	x₅	x₆	Effectiveness
1	0.6178	0.3803	0.6533	0.9490	0.3588	0.9987	2.0857
2	0.1863	0.9098	0.1747	0.9041	0.1193	0.1645	1.4126
3	0.0778	0.8667	0.1018	0.7284	0.0658	0.2526	1.3586
4	0.0725	0.8922	0.0898	0.5634	0.0491	0.4394	1.5264
$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $	$\vdots $
320	0.7231	0.6378	0.7099	0.4211	0.4412	0.1644	1.5644

Model	RMSE	MAE	R-square	Time/s
SVR	0.035736	0.023742	0.85732	1.942
IGWO-SVR	0.000935	0.006358	0.99735	2.484
BPNN	0.035732	0.039750	0.87158	3.389
GWO-SVR	0.019308	0.024802	0.92869	2.015

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