面向战斗力指数定量分析的局部逼近方法

郭恩泽; 刘国彬; 邹永杰; 刘正堂; 孙健; 张洪德

doi:10.11884/HPLPB202436.240163

面向战斗力指数定量分析的局部逼近方法

doi: 10.11884/HPLPB202436.240163

1.
中国人民解放军 63893部队，河南洛阳 471003
2.
中国人民解放军陆军工程大学通信士官学校，重庆 400035

基金项目: 重庆市自然科学基金项目(CSTB2022NSCQ-MSX1257)

详细信息

作者简介:
郭恩泽，g1903632257@163.com

通讯作者:
张洪德，hdzhang264@126.com。

中图分类号: TP183
计量
- 文章访问数: 28
- HTML全文浏览量: 28
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-14
- 修回日期: 2024-08-24
- 录用日期: 2024-07-08
- 网络出版日期: 2024-09-21

A novel local approximation approach for quantitative analysis of combat power index

1.
Unit 63893 of the PLA, Luoyang 471003, China
2.
Communication Sergeant School, Army Engineering University, Chongqing 400035, China

摘要

摘要: 战斗力指数的定量化研究是军队实现信息化建设必须解决的难题。针对战斗力指数研究存在定量研究较少、方法精度较低、鲁棒性不强等问题，以及战斗力指数函数本身为复杂规则主导、多变量数学模型、影响因素强耦合等难以拟合的限制，受模糊逻辑理论中对规则的数学分析方法启发，提出了一种基于局部逼近的战斗力指数函数拟合方法，并结合神经网络强大的自学习和自推导能力，构建了相应的基于径向基神经网络(RBF)的定量计算模型。仿真对比实验表明，该方法比利用全局逼近的方法误差率低约2%和6%，且表现出更强的鲁棒性。该计算方法具有较强的实用性，而且具备向其他军事领域迁移的可能性，具备良好的工程应用前景。
- 战斗力指数 /
- 定量分析 /
- 神经网络 /
- 局部逼近 /
- 模糊逻辑
Abstract: The quantitative study of combat effectiveness index is crucial for the informationization construction of the military. Aiming to limits of quantitative research, low method accuracy, and weak robustness in the study of combat effectiveness index, as well as the limitations of complex rule dominated, multivariate mathematical models, and strong coupling of influencing factors in the combat effectiveness index function itself, inspired by the mathematical analysis methods of rules in fuzzy logic theory, a local approximation based method for fitting combat effectiveness index function is proposed. Combined with the powerful self-learning and self-deduction capabilities of neural networks, a corresponding quantitative calculation model based on radial basis function (RBF) is constructed. Simulation comparative experiments show that the proposed method has an error rate of about 2% and 6% lower than the current best performing method using global approximation, and exhibits stronger robustness. Our method has strong practicality, which can be migrated to other military fields, and has good engineering application prospects.
- combat effectiveness index /
- quantitative analysis /
- neural network /
- local approximation /
- fuzzy logic

HTML全文

图 1 前馈神经网络结构图

Figure 1. Structure diagram of feedforward neural network

下载: 全尺寸图片幻灯片

图 2 战斗力指数计算模型

Figure 2. Calculation model for combat effectiveness index

下载: 全尺寸图片幻灯片

图 3 不同方法的性能对比

Figure 3. Performance comparison of different methods

下载: 全尺寸图片幻灯片

图 4 不同方法对各样本的误差率对比图

Figure 4. Comparison chart of error rates of different methods for each sample

下载: 全尺寸图片幻灯片

表 1 某系统指标与对应战斗力指数（训练样本）

Table 1. A certain system indicator and corresponding combat effectiveness index (training sets)

No.	$ X1 $	$ X2 $	$ X3 $	$ X4 $	$ X5 $	$ X6 $	$ X7 $	Index
1	0.008	0.3839	0.4643	0.2578	0.4651	1	1	0.1
2	0.3867	0.6727	0.4041	0.987	0.0361	1	0	0.6567
3	0.6247	0.0751	0.3834	0.9626	0.3681	0	1	0.4802
4	0.8994	0.6203	0.3388	0.8733	0.4711	0	1	0.5627
5	0.7807	0.602	0.5827	0.7677	0.3319	0	0	0.4575
6	0.5801	0.6814	0.4982	0.5691	0.6989	0	1	0.4807
7	0.6861	0.9761	0.5345	0.0551	0.3001	1	0	0.5307
8	0.9918	0.5446	0.1884	0.8012	0.2498	0	1	0.5325
9	0.1517	0.3264	0.9244	0.4749	0.7514	1	1	0.6498
10	0.006	0.3241	0.1342	0.0568	0.2861	1	1	0.1
11	0.3237	0.6433	0.7615	0.4408	0.4257	0	1	0.3989
12	0.1183	0.7009	0.8832	0.9238	0.7334	1	1	0.6995
13	0.3798	0.3365	0.1264	0.2612	0.3381	1	1	0.5844
14	0.5788	0.9003	0.5844	0.1539	0.1008	1	0	0.5619
15	0.4714	0.0867	0.4697	0.0271	0.5766	1	0	0.4416
16	0.8938	0.0379	0.7388	0.2354	0.4514	1	0	0.6032
17	0.1562	0.2596	0.2821	0.8051	0.6745	0	1	0.3453
18	0.395	0.945	0.0852	0.8615	0.8387	1	0	0.6977
19	0.3299	0.7363	0.8801	0.8847	0.7278	0	1	0.5007
20	0.0009	0.5256	0.4316	0.3064	0.7449	0	0	0.1
21	0.2083	0.896	0.2374	0.3735	0.8784	0	0	0.298
22	0.2117	0.7423	0.8269	0.1996	0.0336	1	0	0.5211
23	0.6431	0.4766	0.1992	0.8318	0.1808	0	0	0.3949
24	0.9829	0.961	0.4124	0.102	0.6919	1	0	0.604
25	0.2151	0.2478	0.8876	0.2154	0.8752	0	1	0.3405
26	0.3991	0.565	0.31	0.3312	0.2412	0	0	0.2705
27	0.8604	0.2769	0.6531	0.3415	0.0994	1	1	0.6933
28	0.4469	0.682	0.826	0.6095	0.7994	1	0	0.7053
29	0.7401	0.6015	0.51	0.3157	0.8019	0	1	0.4477
30	0.001	0.5982	0.7531	0.6396	0.8263	0	1	0.1
31	0.1449	0.3029	0.3186	0.0775	0.0949	1	0	0.408
32	0.5117	0.3233	0.8123	0.506	0.633	1	1	0.7331
33	0.8103	0.1576	0.8691	0.5492	0.8843	1	1	0.8037
34	0.2604	0.5971	0.2858	0.7397	0.2944	0	0	0.3059
35	0.1761	0.5774	0.0948	0.9358	0.2587	0	0	0.2748
36	0.3009	0.8167	0.4445	0.0062	0.5587	1	1	0.5218
37	0.3245	0.217	0.7227	0.1615	0.8302	0	0	0.2582
38	0.3474	0.1725	0.3881	0.9169	0.7404	0	0	0.3641
39	0.5416	0.6636	0.7911	0.0836	0.184	1	0	0.527
40	0.002	0.3116	0.6413	0.354	0.8512	0	1	0.1
41	0.6394	0.7194	0.0269	0.2757	0.6934	0	0	0.3169
42	0.5142	0.1377	0.0843	0.1952	0.0695	0	0	0.1917
43	0.3289	0.4986	0.5695	0.3578	0.9369	1	1	0.6825
44	0.7178	0.3608	0.9264	0.2859	0.5528	1	1	0.716
45	0.6938	0.1595	0.1447	0.0897	0.5322	0	0	0.2009
46	0.5764	0.3444	0.6178	0.1244	0.3252	1	1	0.5985
47	0.8081	0.0461	0.3649	0.4704	0.7324	0	0	0.3727
48	0.4148	0.3836	0.9863	0.5829	0.1511	1	0	0.6372
49	0.3204	0.2348	0.5684	0.3432	0.2111	1	1	0.6068
50	0.0005	0.3179	0.8168	0.5232	0.3022	0	0	0.1

下载: 导出CSV

表 2 某系统指标与对应战斗力指数（测试样本）

Table 2. A certain system indicator and corresponding combat effectiveness index (testing sets)

	$ X1 $	$ X2 $	$ X3 $	$ X4 $	$ X5 $	$ X6 $	$ X7 $	Index
1	0.0005	0.2067	0.1139	0.871	0.7812	0	1	0.1
2	0.188	0.1795	0.2392	0.7679	0.895	0	1	0.3629
3	0.2353	0.6651	0.2227	0.4676	0.1871	1	1	0.6112
4	0.2476	0.6042	0.6518	0.4204	0.8361	1	1	0.68
5	0.1531	0.0344	0.9427	0.9131	0.8684	1	0	0.6126
6	0.3836	0.9837	0.8784	0.3039	0.7341	1	0	0.6526
7	0.1803	0.2427	0.1258	0.4698	0.4155	1	0	0.5014
8	0.3009	0.9656	0.8944	0.4122	0.7063	1	1	0.7264
9	0.1653	0.7884	0.04	0.1822	0.641	0	1	0.282
10	0.002	0.036	0.3512	0.3792	0.7557	0	0	0.1
11	0.8181	0.0879	0.7492	0.0687	0.9076	0	0	0.2601
12	0.1821	0.7894	0.9551	0.8734	0.2748	1	0	0.6354
13	0.8478	0.0628	0.4018	0.0943	0.3653	1	0	0.501
14	0.2354	0.2679	0.7004	0.521	0.774	0	0	0.3096
15	0.2537	0.2642	0.5144	0.522	0.637	0	1	0.3634
16	0.8409	0.2052	0.5102	0.5375	0.0479	0	0	0.3665
17	0.2454	0.3239	0.093	0.4991	0.2922	1	0	0.5214
18	0.2087	0.0236	0.6018	0.5521	0.5491	0	1	0.3359
19	0.7743	0.213	0.0106	0.1927	0.9038	1	0	0.5665
20	0.004	0.2646	0.0695	0.8439	0.4707	0	1	0.1

下载: 导出CSV

参考文献(40)

[1]	李璟. 战斗力解析[M]. 北京: 国防大学出版社, 2013 Li Jing. Analysis of combat effectiveness[M]. Beijing: National Defense University Press, 2013
[2]	Rai R N, Bolia N. Optimal decision support for air power potential[J]. IEEE Transactions on Engineering Management, 2014, 61(2): 310-322. doi: 10.1109/TEM.2013.2293420
[3]	何帆, 李其祥, 黄东. 基于灰色层次模型的新型装备战斗力评估[J]. 火力与指挥控制, 2016, 41(11):129-133 doi: 10.3969/j.issn.1002-0640.2016.11.030 He Fan, Li Qixiang, Huang Dong. Evaluation of capability of new-type equipment based on grey-AHP[J]. Fire Control & Command Control, 2016, 41(11): 129-133 doi: 10.3969/j.issn.1002-0640.2016.11.030
[4]	Qi Zongfeng, Wang Guosheng. Effectiveness evaluation of electronic warfare command and control system based on grey AHP method[J]. Journal of Chemical and Pharmaceutical Research, 2014, 6(7): 535-542.
[5]	曹冠平, 王跃利, 张立韬. 关联规则挖掘在作战实验数据分析中的应用[J]. 指挥控制与仿真, 2019, 41(2):70-74 doi: 10.3969/j.issn.1673-3819.2019.02.014 Cao Guanping, Wang Yueli, Zhang Litao. Application of association rule mining in combat experiment data analysis[J]. Command Control & Simulation, 2019, 41(2): 70-74 doi: 10.3969/j.issn.1673-3819.2019.02.014
[6]	刘玮, 周华任, 黄春艳. 基于灰色-熵权法的合成旅装备战斗力评估[J]. 计算机仿真, 2023, 40(4):26-30 doi: 10.3969/j.issn.1006-9348.2023.04.006 Liu Wei, Zhou Huaren, Huang Chunyan. Combat effectiveness evaluation of synthetic brigade equipment based on combined grey entropy weight method[J]. Computer Simulation, 2023, 40(4): 26-30 doi: 10.3969/j.issn.1006-9348.2023.04.006
[7]	文博宇, 胡磊, 张岐龙, 等. Dynamic trajectory quality evaluation of ballistic missiles based on TOPSIS[J]. 舰船电子对抗, 2022, 45(1):45-49 Wen Boyu, Hu Lei, Zhang Qilong, et al. Radar emitter signal recognition based on extended residual network[J]. Shipboard Electronic Countermeasure, 2022, 45(1): 45-49
[8]	卜广志. 基于AOE模型的装备对作战体系的贡献率评估方法[J]. 火力与指挥控制, 2020, 45(12):18-22 doi: 10.3969/j.issn.1002-0640.2020.12.004 Bu Guangzhi. An assessment method of armament contribution to operational system based on AOE model[J]. Fire Control & Command Control, 2020, 45(12): 18-22 doi: 10.3969/j.issn.1002-0640.2020.12.004
[9]	薛辉, 王源, 张天鹏, 等. 随机组合约束下的联合火力打击弹药需求预测模型[J]. 兵工学报, 2019, 40(8):1716-1724 doi: 10.3969/j.issn.1000-1093.2019.08.022 Xue Hui, Wang Yuan, Zhang Tianpeng, et al. Demand forecasting model for joint fire strike ammunition under stochastic combination constraints[J]. Acta Armamentarii, 2019, 40(8): 1716-1724 doi: 10.3969/j.issn.1000-1093.2019.08.022
[10]	薛辉, 刘铁林, 张鹏. 基于损失交换比的武器装备回合战斗力指数评估[J]. 装甲兵工程学院学报, 2018, 32(2):7-12 doi: 10.3969/j.issn.1672-1497.2018.02.002 Xue Hui, Liu Tielin, Zhang Peng. Evaluation of round combat effectiveness index for weapon equipment based on loss exchange ratio[J]. Journal of Academy of Armored Force Engineering, 2018, 32(2): 7-12 doi: 10.3969/j.issn.1672-1497.2018.02.002
[11]	杨鹏, 倪小清. 登陆作战的多维战斗力指数—兰彻斯特方程[J]. 舰船电子工程, 2016, 36(5):27-30 doi: 10.3969/j.issn.1627-9730.2016.05.007 Yang Peng, Ni Xiaoqing. Lanchester equation based on multi-domain fighting index[J]. Ship Electronic Engineering, 2016, 36(5): 27-30 doi: 10.3969/j.issn.1627-9730.2016.05.007
[12]	董泽委, 胡起伟, 孙宝琛. 基于BP神经网络的集群装备战斗力指数评估[J]. 火力与指挥控制, 2011, 36(11):87-90 doi: 10.3969/j.issn.1002-0640.2011.11.023 Dong Zewei, Hu Qiwei, Sun Baochen. Equipment combat power index assessment based on BP neural network[J]. Fire Control & Command Control, 2011, 36(11): 87-90 doi: 10.3969/j.issn.1002-0640.2011.11.023
[13]	郭恩泽, 何斌斌, 武艺楠, 等. 面向战斗力指数计算的BP神经网络设计研究[J]. 舰船电子对抗, 2024, 48(3):456-462 Guo Enze, He Binbin, Wu Yinan, et al. Research on the design of BP Neural network for calculating combat effectiveness index[J]. Shipboard Electronic Countermeasure, 2024, 48(3): 456-462
[14]	Goh A T C. Back-propagation neural networks for modeling complex systems[J]. Artificial Intelligence in Engineering, 1995, 9(3): 143-151. doi: 10.1016/0954-1810(94)00011-S
[15]	Wang Hanyu, Dong Helei, Zhang Lei, et al. Prediction of dynamic temperature rise of thermocouple sensors based on genetic algorithm-back propagation neural network[J]. IEEE Sensors Journal, 2022, 22(24): 24121-24129. doi: 10.1109/JSEN.2022.3217826
[16]	Rumelhart D E, Hinton G E, Williams R J. Learning representations by back-propagating errors[J]. Nature, 1986, 323(6088): 533-536. doi: 10.1038/323533a0
[17]	Li He, Guo Shuxiang, Wang Hanze, et al. Subject-independent continuous estimation of sEMG-based joint angles using both multisource domain adaptation and BP neural network[J]. IEEE Transactions on Instrumentation and Measurement, 2023, 72: 4000910.
[18]	Hou J, Yao D, Wu F, et al. Online vehicle velocity prediction using an adaptive radial basis function neural network[J]. IEEE Transactions on Vehicular Technology, 2021, 70(4): 3113-3122. doi: 10.1109/TVT.2021.3063483
[19]	Gong Maoguo, Liu Jia, Qin A K, et al. Evolving deep neural networks via cooperative coevolution with backpropagation[J]. IEEE Transactions on Neural Networks and Learning Systems, 2021, 32(1): 420-434. doi: 10.1109/TNNLS.2020.2978857
[20]	Gao Xinyu, Mou Jun, Banerjee S, et al. Color-gray multi-image hybrid compression–encryption scheme based on BP neural network and knight tour[J]. IEEE Transactions on Cybernetics, 2023, 53(8): 5037-5047. doi: 10.1109/TCYB.2023.3267785
[21]	Pan Xiuqin, Zhou Wangsheng, Lu Yong, et al. Prediction of network traffic of smart cities based on DE-BP neural network[J]. IEEE Access, 2019, 7: 55807-55816. doi: 10.1109/ACCESS.2019.2913017
[22]	Lu Qidong, Yang Rui, Zhong Maiying, et al. An improved fault diagnosis method of rotating machinery using sensitive features and RLS-BP neural network[J]. IEEE Transactions on Instrumentation and Measurement, 2020, 69(4): 1585-1593. doi: 10.1109/TIM.2019.2913057
[23]	Zhao Liang, Yin Zhihong, Yu Keping, et al. A fuzzy logic-based intelligent multiattribute routing scheme for two-layered SDVNs[J]. IEEE Transactions on Network and Service Management, 2022, 19(4): 4189-4200. doi: 10.1109/TNSM.2022.3202741
[24]	Hornik K, Stinchcombe M, White H. Multilayer feedforward networks are universal approximators[J]. Neural Networks, 1989, 2(5): 359-366. doi: 10.1016/0893-6080(89)90020-8
[25]	LeCun Y, Bengio Y, Hinton G. Deep learning[J]. Nature, 2015, 521(7553): 436-444. doi: 10.1038/nature14539
[26]	Xu Bing, Wang Naiyan, Chen Tianqi, et al. Empirical evaluation of rectified activations in convolutional network[DB/OL]. arXiv preprint arXiv: 1505.00853, 2015.
[27]	Nitta T, Kuroe Y. Hyperbolic gradient operator and hyperbolic back-propagation learning algorithms[J]. IEEE transactions on neural networks and learning systems, 2017, 29(5): 1689-1702.
[28]	Freitas A A. Comprehensible classification models: a position paper[J]. ACM SIGKDD Explorations Newsletter, 2013, 15(1): 1-10.
[29]	Lakkaraju H, Bach S H, Leskovec J. Interpretable decision sets: a joint framework for description and prediction[C]//Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2016: 1675-1684.
[30]	Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1985, SMC-15(1): 116-132. doi: 10.1109/TSMC.1985.6313399
[31]	Fritzke B. Fast learning with incremental RBF networks[J]. Neural Processing Letters, 1994, 1(1): 2-5. doi: 10.1007/BF02312392
[32]	Jin Yaochu, Sendhoff B. Extracting interpretable fuzzy rules from RBF networks[J]. Neural Processing Letters, 2003, 17(2): 149-164. doi: 10.1023/A:1023642126478
[33]	Morán A, Parrilla L, Roca M, et al. Digital implementation of radial basis function neural networks based on stochastic computing[J]. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2023, 13(1): 257-269. doi: 10.1109/JETCAS.2022.3231708
[34]	Su Bowen, Zhang Fan, Huang Panfeng. Stability analysis and RBF neural network control of second-order nonlinear satellite system[J]. IEEE Transactions on Aerospace and Electronic Systems, 2023, 59(4): 4575-4589. doi: 10.1109/TAES.2023.3243582
[35]	Wang Jinpeng, Zhou Yang, Guan Xin, et al. A hybrid predicting model for the daily photovoltaic output based on fuzzy clustering of meteorological data and joint algorithm of GAPS and RBF neural network[J]. IEEE Access, 2022, 10: 30005-30017. doi: 10.1109/ACCESS.2022.3159655
[36]	Liu Xin, He Hai. Fault diagnosis for TE process using RBF neural network[J]. IEEE Access, 2021, 9: 118453-118460. doi: 10.1109/ACCESS.2021.3107360
[37]	Fan Fenglei, Wang Ge. Fuzzy logic interpretation of quadratic networks[J]. Neurocomputing, 2020, 374: 10-21. doi: 10.1016/j.neucom.2019.09.001
[38]	Fang Baofu, Zheng Caiming, Wang Hao, et al. Two-stream fused fuzzy deep neural network for multiagent learning[J]. IEEE Transactions on Fuzzy Systems, 2023, 31(2): 511-520. doi: 10.1109/TFUZZ.2022.3214001
[39]	Xu Tao, Zhao Youqun, Wang Qiuwei, et al. An adaptive inverse model control method of vehicle yaw stability with active front steering based on adaptive RBF neural networks[J]. IEEE Transactions on Vehicular Technology, 2023, 72(11): 13873-13887.
[40]	Han Honggui, Wu Xiaolong, Zhang Lu, et al. Self-organizing RBF neural network using an adaptive gradient multiobjective particle swarm optimization[J]. IEEE Transactions on Cybernetics, 2019, 49(1): 69-82. doi: 10.1109/TCYB.2017.2764744