空战模式下航空集群射频隐身性能评估方法

doi:10.3969/j.issn.1001-506X.2020.12.18

摘要/Abstract

摘要：

为解决空战模式下航空集群射频(radio frequency, RF)隐身性能评估问题,提出一种基于正态波动犹豫模糊集(normal wiggly hesitant fuzzy set, NWHFS)的评估算法。首先，通过基于正态波动犹豫模糊信息的最优-最劣方法(best-worst method, BWM)构建权重确定模型,获得属性权重向量和一致性检验系数。其次，根据集群用频设备参数和具体空战场景提取RF隐身性能评估因子,并得到其计算公式。然后，组织专家根据评估因子结合主观经验构建评价矩阵,并利用属性权重向量聚合评价信息。最后，将NWHFS分数函数作为评估指标,对不同想定下的航空集群RF隐身性能定量评估。仿真算例和对比分析说明了所提方法的可行性和有效性。

关键词: 空战模式, 航空集群, 正态波动犹豫模糊集, 射频隐身, 最优-最劣方法

Abstract:

In order to solve the radio frequency (RF) stealth performance evaluation problem of aircraft swarm in air combat mode, an evaluation algorithm based on normal wiggly hesitant fuzzy set (NWHFS) is proposed. Firstly, a weight-determining model based on the best-worst method (BWM) with normal wiggly hesitant fuzzy information is constructed, the attribute weight vectors and consistency check coefficients are obtained. Secondly, based on the swarm's frequency equipment parameters and specific air combat scenarios, the RF stealth performance evaluation factors and their calculation formulas are obtained. And then, a evaluation matrix based on evaluation factor and its subjective experience is constructed and the attribute weight vector is used to aggregate the evaluation information. Finally, the NWHFS score function is used as evaluation index to quantitatively evaluate the RF stealth performance of aircraft swarm in different scenario. Simulation example and comparison analysis verify the feasibility and effectiveness of the proposed evaluation method.

Key words: air combat mode, aircraft swarm, normal wiggly hesitant fuzzy set (NWHFS), radio frequency stealth, best-worst method (BWM)

中图分类号:

V11
TJ85

杨诚修, 王谦喆, 祝捷, 李昂. 空战模式下航空集群射频隐身性能评估方法[J]. 系统工程与电子技术, 2020, 42(12): 2811-2818.

Chengxiu YANG, Qianzhe WANG, Jie ZHU, Ang LI. Evaluation method of radio frequency stealth performance of aircraft swarm in air combat mode[J]. Systems Engineering and Electronics, 2020, 42(12): 2811-2818.

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参考文献 31

1	HU L P , BAI P , LIANG X L , et al. Solution and optimization of aircraft swarm cooperating anti-stealth formation configuration[J]. IEEE Access, 2018, 6 (99): 71485- 71496.
2	WANG W Q . Moving-target tracking by cognitive RF stealth radar using frequency diverse array antenna[J]. IEEE Trans.on Geoscience and Remote Sensing, 2016, 54 (7): 3764- 3773. doi: 10.1109/TGRS.2016.2527057
3	WANG W Q. Adaptive RF stealth beamforming for frequency diverse array radar[C]//Proc.of the IEEE 23rd European Signal Processing Conference, 2015: 1158-1161.
4	FU Y J, LI Y, HUANG Q D, et al. Design and analysis of LFM/Barker RF stealth signal waveform[C]//Proc.of the 11th Conference on Industrial Electronics and Applications, 2016: 591-595.
5	CHANG W S , TAO H H , LIU Y B , et al. Design of synthetic aperture radar low-intercept radio frequency stealth[J]. Journal of Systems Engineering and Electronics, 2020, 31 (1): 64- 72.
6	SHI C G , WANG F , SELLATHURAI M , et al. Low probability of intercept-based optimal power allocation scheme for an integrated multistatic radar and communication system[J]. IEEE Systems Journal, 2020, 14 (1): 983- 994. doi: 10.1109/JSYST.2019.2931754
7	WANG F , SELLATHURAI M , LIU W G , et al. Security information factor based airborne radar RF stealth[J]. Journal of Systems Engineering and Electronics, 2015, 26 (2): 258- 266.
8	何召阳, 王谦喆, 宋博文, 等. 雷达信号波形域射频隐身性能评估方法[J]. 系统工程与电子技术, 2017, 39 (10): 2234- 2238.
	HE Z Y , WANG Q Z , SONG B W , et al. RF stealth performance evaluation method for radar signal waveform[J]. Systems Engineering and Electronics, 2017, 39 (10): 2234- 2238.
9	曾小东. 基于层次分析法的射频隐身性能评估[J]. 现代雷达, 2018, 40 (8): 16- 19.
	ZENG X D . RF stealth efficiency evaluation based on the analytic hierarchy process[J]. Modern Radar, 2018, 40 (8): 16- 19.
10	吴华, 史忠亚, 沈文迪, 等. 基于改进G-GIFSS算法的雷达LPI性能评估方法[J]. 系统工程与电子技术, 2017, 39 (6): 1256- 1260.
	WU H , SHI Z Y , SHEN W D , et al. Radar LPI performance assessment method based on extended G-GIFSS algorithm[J]. Systems Engineering and Electronics, 2017, 39 (6): 1256- 1260.
11	YANG C X, WANG Q Z, PENG W D, et al. Multi-domain evaluation method for RF stealth performance based on IFA-TOPSIS with hesitant fuzzy sets[C]//Proc.of the Optoelectronic Devices and Integration, 2019.
12	REN Z L , XU Z S , WANG H . Normal wiggly hesitant fuzzy sets and their application to environmental quality evaluation[J]. Knowledge-Based Systems, 2018, 159, 286- 297. doi: 10.1016/j.knosys.2018.06.024
13	TORRA V . Hesitant fuzzy sets[J]. International Journal of Intelligent Systems, 2010, 25 (6): 529- 539.
14	CHEN N , XU Z S , XIA M M . Interval-valued hesitant preference relations and their applications to group decision making[J]. Knowledge-Based Systems, 2013, 37, 528- 540. doi: 10.1016/j.knosys.2012.09.009
15	YU D . Triangular hesitant fuzzy set and its application to teaching quality evaluation[J]. Journal of Information & Computational Science, 2013, 10 (7): 1925- 1934.
16	NARAYANAMOORTHY S , RAMYA L , BALEANU D , et al. Application of normal wiggly dual hesitant fuzzy sets to site selection for hydrogen underground storage[J]. International Journal of Hydrogen Energy, 2019, 44 (54): 28874- 28892. doi: 10.1016/j.ijhydene.2019.09.103
17	LIU P D , XU H X , GENG Y S . Normal wiggly hesitant fuzzy linguistic power Hamy mean aggregation operators and their application to multi-attribute decision-making[J]. Computers & Industrial Engineering, 2020, 140, 106224.
18	LIU P D , XU H X , PEDRYCZ W . A normal wiggly hesitant fuzzy linguistic projection-based multiattributive border approximation area comparison method[J]. International Journal of Intelligent Systems, 2020, 35 (3): 432- 469. doi: 10.1002/int.22213
19	LIU Z , LI L , WANG X , et al. A novel multiple attribute decision making method based on (power Muirhead mean operator under normal wiggly hesitant fuzzy environment)[J]. Journal of Intelligent & Fuzzy Systems, 2019, 37 (5): 7003- 7023.
20	YANG C , WANG Q , PENG W , et al. A normal wiggly pythagorean hesitant fuzzy bidirectional projection method and its application in EV power battery recycling mode selection[J]. IEEE Access, 2020, 8, 62164- 62180. doi: 10.1109/ACCESS.2020.2984242
21	YANG C X , WANG Q Z , PENG W D , et al. A multi-criteria group decision-making approach based on improved BWM and MULTIMOORA with normal wiggly hesitant fuzzy information[J]. International Journal of Computational Intelligence Systems, 2020, 13 (1): 366- 381.
22	REZAEI J . Best-worst multi-criteria decision-making method[J]. Omega, 2015, 53, 49- 57. doi: 10.1016/j.omega.2014.11.009
23	ALI A , RASHID T . Hesitant fuzzy best-worst multi-criteria decision-making method and its applications[J]. International Journal of Intelligent Systems, 2019, 34 (8): 1953- 1967. doi: 10.1002/int.22131
24	MI X M , LIAO H C . An integrated approach to multiple criteria decision making based on the average solution and normalized weights of criteria deduced by the hesitant fuzzy best worst method[J]. Computers & Industrial Engineering, 2019, 133, 83- 94.
25	LIAO H C , MI X M , YU Q , et al. Hospital performance evaluation by a hesitant fuzzy linguistic best worst method with inconsistency repairing[J]. Journal of Cleaner Production, 2019, 232, 657- 671. doi: 10.1016/j.jclepro.2019.05.308
26	LIU A J , JI X H , LU H , et al. The selection of 3PRLs on self-service mobile recycling machine: interval-valued Pythagorean hesitant fuzzy best-worst multi-criteria group decision-making[J]. Journal of Cleaner Production, 2019, 230, 734- 750. doi: 10.1016/j.jclepro.2019.04.257
27	LI J , WANG J Q , HU J H . Multi-criteria decision-making method based on dominance degree and BWM with probabilistic hesitant fuzzy information[J]. International Journal of Machine Learning and Cybernetics, 2019, 10 (7): 1671- 1685. doi: 10.1007/s13042-018-0845-2
28	MOU Q , XU Z S , LIAO H C . A graph based group decision making approach with intuitionistic fuzzy preference relations[J]. Computers & Industrial Engineering, 2017, 110, 138- 150.
29	HE Z Y, WANG Q Z, SONG B W. Multi domain joint evaluation method for radio frequency stealth performance of airborne electron[C]//Proc.of the IEEE 3rd International Conference on Computer and Communications, 2017: 2732-2736.
30	SHI C G , ZHOU J J , WANG F . Adaptive resource management algorithm for target tracking in radar network based on low probability of intercept[J]. Multidimensional Systems and Signal Processing, 2018, 29 (4): 1203- 1226. doi: 10.1007/s11045-017-0494-8
31	何杰.飞机射频隐身性能评估指标研究与软件实现[D].南京:南京航空航天大学, 2015.
	HE J. Research on aircraft RF stealth performance evaluation indexes and simulation system implementation[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2015.

想定	捷变频次数/次	目标距离/km	等效波束俯仰角、方位角/(°)	集群最大开机时间/ms	辐射源数量/个	占空比
1	24	110	4.2、3.2	700	2	6.4/13
2	28	120	3.8、2.4	640	3	8.3/25
3	12	80	4.6、2.8	950	1	7/20
4	19	100	4.5、3.7	780	2	9/37

	C₁	C₂	C₃	C₄	C₅
最优 C₃	＜(0.7, 0.8), {(0.67, 0.70, 0.73), (0.77, 0.80, 0.83)}＞	＜(0.6, 0.7, 0.8), {(0.33, 0.41, 0.47), (0.54, 0.73, 0.86), (0.70, 0.82, 0.91)}＞	＜(0.5), {(0.5, 0.5, 0.5)}＞	＜(0.8, 0.9), {(0.77, 0.80, 0.83), (0.87, 0.9, 0.93)}＞	＜(0.5, 0.6), {(0.47, 0.50, 0.53), (0.57, 0.60, 0.63)}＞
最劣 C₄	＜(0.5, 0.7, 0.8), {(0.45, 0.51, 0.55), (0.58, 0.72, 0.82), (0.73, 0.81, 0.87}＞	＜(0.5, 0.8, 0.9), {(0.43, 0.51, 0.57), (0.64, 0.83, 0.96), (0.79, 0.92, 1)}＞	＜(0.8, 0.9), {(0.77, 0.80, 0.83), (0.87, 0.9, 0.93)}＞	＜(0.5), {(0.5, 0.5, 0.5)}＞	＜(0.6, 0.8, 0.9), {(0.55, 0.61, 0.57), (0.64, 0.83, 0.96), (0.80, 0.92, 1)}＞

α	最优评估因子C₃					最劣评估因子C₄
α	C₁	C₂	C₃	C₄	C₅	C₁	C₂	C₃	C₄	C₅
0.1	0.743	0.685	0.5	0.843	0.543	0.638	0.686	0.843	0.5	0.737
0.3	0.734	0.670	0.5	0.834	0.534	0.617	0.659	0.834	0.5	0.716
0.5	0.724	0.655	0.5	0.824	0.524	0.595	0.631	0.824	0.5	0.695
0.7	0.714	0.640	0.5	0.814	0.514	0.574	0.604	0.814	0.5	0.674
0.9	0.705	0.626	0.5	0.805	0.504	0.553	0.577	0.805	0.5	0.653

评估因子	A₁	A₂	A₃	A₄
C₁	0.972	0.931	0.919	0.907
C₂	0.998	0.999	0.997	0.998
C₃	0.974	0.996	0.909	0.938
C₄	0.900	0.908	0.864	0.889
C₅	0.621	0.631	0.295	0.385

评估因子	A₁	A₂	A₃	A₄
C₁	({0.97, 0.973}, {(0.969, 0.97, 0.971), (0.972, 0.973, 0.974)})	({0.928, 0.931, 0.938}, {(0.926, 0.928, 0.931), (0.927, 0.931, 0.935), (0.936, 0.938, 0.940)})	({0.917, 0.920}, {(0.916, 0.917, 0.918), (0.919, 0.920, 0.921)})	({0.902, 0.908}, {(0.90, 0.902, 0.904), (0.906, 0.908, 0.91)})
C₂	({0.997, 0.998}, {(0.9967, 0.997, 0.9973), (0.9977, 0.998, 0.9983)})	({0.998, 0.999}, {0.9977, 0.998, 0.9983}, (0.9987, 0.999, 0.9993)})	({0.996, 0.997}, {(0.9957, 0.996, 0.0.9963), (0.9967, 0.997, 0.9973)})	({0.997, 0.998}, {(0.9967, 0.997, 0.9973), (0.9977, 0.998, 0.9983)})
C₃	({0.972, 0.975}, {(0.971, 0.972, 0.973), (0.974, 0.975, 0.976)})	({0.994, 0.996}, {(0.993, 0.994, 0.995), (0.995, 0.996, 0.997)})	({0.898, 0.906, 0.911}, {(0.896, 0.898, 0.9), (0.904, 0.909, 0.914), (0.907, 0.911, 0.915)})	({0.936, 0.939}, {(0.935, 0.936, 0.937), (0.938, 0.939, 0.94)})
C₄	({0.9, 0.92}, {(0.894, 0.90, 0.906), (0.914, 0.92, 0.926)})	({0.899, 0.901, 0.904}, {(0.898, 0.899, 0.9), (0.899, 0.901, 0.903), (0.903, 0.904, 0.905)})	({0.864, 0.867}, {(0.863, 0.864, 0.865), (0.866, 0.867, 0.868)})	({0.887, 0.889}, {(0.886, 0.887, 0.888), (0.888, 0.889, 0.890)})
C₅	({0.619, 0.622, 0.624}, {(0.618, 0.619, 0.620), (0.620, 0.622, 0.624), (0.623, 0.624, 0.625)})	({0.631, 0.633}, {(0.630, 0.631, 0.632), (0.632, 0.633, 0.634)})	({0.294, 0.296}, {(0.293, 0.294, 0.295), (0.295, 0.296, 0.297)})	({0.384, 0.386}, {(0.383, 0.384, 0.385), (0.385, 0.386, 0.387)})