Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (6): 16261644.doi: 10.23919/JSEE.2023.000020
• SYSTEMS ENGINEERING • Previous Articles
Chi HAN^{1}^{,}*(), Wei XIONG^{1}^{,}^{2}(), Minghui XIONG^{1}(), Zhen LIU^{1}()
Received:
20210322
Online:
20231218
Published:
20231229
Contact:
Chi HAN
Email:15850466132@163.com;13331094335@163.com;xtkxxmh@163.com;2981282863@qq.com
About author:
Supported by:
Chi HAN, Wei XIONG, Minghui XIONG, Zhen LIU. Support vector regressionbased operational effectiveness evaluation approach to reconnaissance satellite system[J]. Journal of Systems Engineering and Electronics, 2023, 34(6): 16261644.
Table 1
Comparison algorithm and description"
Algorithm  Description 
PSO  Standard particle swarm algorithm 
GWO  Standard gray wolf algorithm 
MFO  Mothflame optimization algorithm [ 
ALO  Ant lion optimizer [ 
SCA  Sine cosine algorithm [ 
WOA  Whale optimization algorithm [ 
MVO  Multiverse optimizer [ 
IGWO  Hybrid improved gray wolf algorithm 
Table 2
Benchmark function"
Function  Definition  Dimension  Range  Optimum 
f_{1}  30  [−100,100]  0  
f_{2}  30  [−10,10]  0  
f_{3}  30  [−100,100]  0  
f_{4}  30  [−100,100]  0  
f_{5}  30  [−30,30]  0  
f_{6}  30  [−100,100]  0  
f_{7}  30  [−1.28,1.28]  0  
f_{8}  30  [−500,500]  −418.9829×5  
f_{9}  30  [−5.12,5.12]  0  
f_{10}  30  [−32,32]  0  
f_{11}  30  [−600,600]  0  
f_{12}  2  [−5,5]  −1.0316  
f_{13}  2  [−5,5]  0.398  
f_{14}  2  [−2,2]  3 
Table 3
Comparison of experimental result"
Function  Item  PSO  MVO  MFO  ALO  SCA  WOA  GWO  IGWO 
f_{1}  Average  1.01e04  1.73e33  6.37e28  8.94e28  3.96e39  2.54e46  1.32e39  1.11e73 
Std.  1.54e04  2.09e33  9.30e28  9.38e28  4.74e39  4.64e46  8.71e40  2.81e73  
Time  0.0043  0.0083  0.0209  0.0195  0.0183  0.0184  0.0117  0.0158  
f_{2}  Average  1.99e02  4.93e20  1.40e16  1.04e16  1.48e23  4.14e28  1.42e23  9.23e52 
Std.  1.65e02  2.53e20  9.89e17  6.48e17  9.76e24  2.45e28  1.25e23  1.54e51  
Time  0.0056  0.0067  0.0131  0.0127  0.0106  0.0105  0.0065  0.0072  
f_{3}  Average  67.3020  5.14e06  4.88e06  7.04e06  2.20e08  5.25e07  1.29e08  7.67e11 
Std.  35.1326  1.48e05  5.13e06  1.42e05  5.98e08  3.56e07  2.94e08  1.12e10  
Time  0.0347  0.0393  0.0428  0.0406  0.0395  0.0397  0.0416  0.0297  
f_{4}  Average  1.0974  3.01e08  5.57e07  8.44e07  1.85e10  7.26e07  3.07e10  6.11e12 
Std.  0.2795  3.39e08  4.32e07  8.08e07  1.64e10  3.97e07  3.65e10  7.81e12  
Time  0.0044  0.0062  0.0119  0.0094  0.0095  0.0171  0.0056  0.0094  
f_{5}  Average  1.45e06  1.76e14  7.65e08  4.46e05  6.74e14  7.64e15  7.99e15  0 
Std.  3.19e04  3.37e15  8.56e07  2.24e05  8.47e15  1.12e15  0  0  
Time  0.0043  0.0094  0.0154  0.0141  0.0157  0.0094  0.0117  0.0115  
f_{6}  Average  3.47e01  6.56e04  7.14e01  1.1476  4.99e01  6.74e01  7.23e01  1.52e04 
Std.  2.39e01  3.82e04  4.26e01  2.52e01  4.56e01  1.68e01  2.52e01  1.56e04  
Time  0.0098  1.1535  0.0118  0.0121  0.0095  0.0094  0.0094  0.0056  
f_{7}  Average  1.76e01  1.34e03  2.14e03  1.79e03  1.29e03  1.02e03  9.65e04  2.25e04 
Std.  4.95e02  6.84e04  1.02e03  8.44e04  7.00e04  4.84e04  8.85e04  2.10e04  
Time  0.0103  0.0157  0.0184  0.0156  0.0157  0.0163  0.018  0.0119  
f_{8}  Average  0.3979  0.3979  0.3979  0.3979  0.3979  0.3979  0.3979  0.3979 
Std.  3.58e02  4.28e05  7.79e06  8.65e06  2.08e06  5.71e06  0  0  
Time  0.0275  0.0247  0.0247  0.0234  0.0332  0.0230  0.0276  0.0277  
f_{9}  Average  52.4065  1.0366  2.0143  1.6277  5.68e15  1.7677  0  0 
Std.  9.2906  2.0276  3.5410  2.4442  1.80e14  3.7301  0  0  
Time  0.0065  0.0119  0.0146  0.0123  0.0122  0.0121  0.0136  0.0062  
f_{10}  Average  1.03e01  3.61e14  1.07e13  1.06e13  1.26e14  1.51e14  1.40e14  3.73e15 
Std.  2.91e01  3.53e15  2.16e14  1.94e14  2.92e15  1.67e15  4.12e15  2.80e15  
Time  0.0077  0.0107  0.0139  0.0119  0.0108  0.0108  0.0136  0.0071  
f_{11}  Average  6.18e03  6.94e03  2.99e03  1.09e03  0  2.65e03  2.32e03  0 
Std.  7.37e03  1.29e02  9.45e03  3.47e03  0  5.73e03  7.35e03  0  
Time  0.007  0.0118  0.0143  0.0124  0.0117  0.012  0.0145  0.0083  
f_{12}  Average  −1.0316  −1.0316  −1.0316  −1.0316  −1.0316  −1.0316  −1.0316  −1.0316 
Std.  0  8.74e08  6.28e07  3.47e08  1.35e07  1.16e04  5.47e09  0  
Time  0.0283  0.0273  0.0244  0.0289  0.0284  0.0287  0.0232  0.0083  
f_{13}  Average  0.3979  0.3979  0.3979  0.3979  0.3979  0.3979  0.3979  0.3979 
Std.  6.67e04  4.93e07  7.67e06  1.75e04  5.24e05  0  5.24e05  0  
Time  0.0085  0.0066  0.0069  0.0069  0.0068  0.0069  0.0069  0.0069  
f_{14}  Average  3.0000  3.0000  3.0000  3.0000  3.0000  3.0000  3.0000  3.0000 
Std.  2.81e05  1.97e05  2.91e05  4.71e05  1.57e05  7.44e06  3.72e05  4.90e16  
Time  0.0084  0.0065  0.0065  0.0066  0.0065  0.0065  0.0065  0.0065 
Table 5
Initial parameter setting of IGWOSVR and other methods"
Method  Parameter item  Value 
SVR  SVR parameters  (2,1,0.01) 
IGWOSVR  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  
GWOSVR  Number of search agents  30 
Maximum iterations  500  
Minimum of SVR parameters  (1e−4,1e−4,0)  
Maximum of SVR parameters  (100,100,1) 
Table 6
Prediction accuracy results for all data of each method"
Dataset  SVR  IGWOSVR  BPNN  GWOSVR  
Average  Std.  Average  Std.  Average  Std.  Average  Std.  
a  1.70e01  6.19e02  4.62e02  3.50e03  3.05e01  6.05e02  1.10e01  7.19e02  
b  5.48e02  1.61e02  1.18e03  5.80e04  4.27e02  5.00e03  1.90e02  9.10e03  
c  8.62e02  2.71e02  7.60e03  1.20e05  1.26e02  1.00e03  1.06e02  3.70e03  
d  8.70e03  8.30e03  6.10e05  5.08e04  1.78e02  2.60e03  6.80e03  8.19e04  
e  1.26e02  2.20e03  2.80e03  2.98e05  1.90e02  5.80e03  1.28e02  1.90e03  
f  3.06e02  2.39e02  7.50e04  2.30e03  7.08e02  1.75e01  1.63e02  1.13e02  
g  3.54e01  1.65e01  1.58e01  2.78e02  7.99e01  2.72e01  4.26e01  6.73e02  
h  2.42e02  9.70e03  1.19e02  2.60e04  3.31e02  9.00e03  4.64e02  3.41e02 
Table 8
P values of IGWOSVR against other methods using Wilcoxon’s statistical test (bolded if P>α=5%)"
Dataset  IGWOSVR vs SVR  IGWOSVR vs GWOSVR  IGWOSVR vs BPNN 
a  6.16e05  1.40e02  5.93e04 
b  2.43e05  2.54e02  6.73e03 
c  1.68e05  3.93e01  1.19e01 
d  6.42e05  3.68e01  1.00e03 
e  6.42e05  7.82e04  8.52e04 
f  1.59e05  5.25e02  1.73e01 
g  4.57e05  5.67e05  2.64e03 
h  6.28e05  2.46e04  2.46e04 
Table 9
Orbital parameters of satellite constellations degree (°)"
Number  Semimajor axis  Eccentricity  Inclination  Argument of perigee  RAAN  True anomaly 
LEO11/2/3  500  0  45.0000  0  0  0/120/240 
LEO24/5/6  500  0  45.1092  0  89.8898  30.16/150.16/270.16 
LEO37/8/9  500  0  44.9991  0  179.7800  60.31/180.31/300.31 
LEO410/11/12  500  0  44.8897  0  269.8910  90.16/210.16/330.16 
Table 10
Structure of sample data"
Number  x_{1}  x_{2}  x_{3}  x_{4}  x_{5}  x_{6}  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 
320  0.7231  0.6378  0.7099  0.4211  0.4412  0.1644  1.5644 
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