考虑级联失效的弹药供应链关键节点分析

doi:10.12305/j.issn.1001-506X.2026.08.22

Abstract

Abstract:

After the ammunition support node is attacked, the throughput of neighbor nodes increases due to the supply task redistribution, and the probability of being found and attacked increases, which leads to the problem that the ammunition supply chain is prone to cascading failure. A method for dynamic identification of key nodes in the ammunition supply chain is proposed. Firstly, analyze the node failure and cascading failure processes, and construct a cascading failure model of the ammunition supply chain based on the fact that the node failure probability follows a two-stage Gompertz distribution. Secondly, from the perspectives of supply capacity and supply efficiency, the evaluation index system of node importance is constructed by selecting agility, stability, load degree and robustness. Thirdly, considering the current task completion status and the subsequent task completion capacity, the position shortage rate, the supply task completion rate and the survival rate of the supply chain are selected as the comprehensive supply capacity evaluation indices for the ammunition supply chain. Finally, a dynamic model of the ammunition supply chain system is constructed. The proposed method and five key node identification methods of temporal network are verified by using the node removal method, and the sensitivity analysis of the proposed method is conducted from two dimensions: external environment and internal parameters. The results show that compared with other methods, the comprehensive supply capacity of the ammunition supply chain of the proposed method decreases the fastest, indicating that the identified nodes have the greatest impact and the highest importance on ammunition supply. At the same time, it is found that the proposed method is relatively sensitive to changes in ammunition supply tasks and agility indices. The conclusion shows that the proposed method can effectively identify the key nodes in the ammunition supply chain, which is helpful for formulating anti-strike contingency plans and improving the efficiency of ammunition supply.

Key words: key node analysis, cascading failure, temporal network, system dynamics

CLC Number:

E 233

Penghua LIU, Xianming SHI, Yalong WANG, Mifen YANG. Analysis of key nodes in the ammunition supply chain considering cascading failure[J]. Systems Engineering and Electronics, 2026, 48(8): 2761-2781.

Figures/Tables 27

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Table 1

Table 2

Fig.7

Table 3

Table 4

Table 5

Fig.8

Table 6

Fig.9

Fig.10

Fig.11

Table 7

Table 8

Table 9

Fig.12

Fig.13

Fig.14

Table 10

Table 11

Table 12

Fig.15

References 45

1	刘昊邦, 史宪铭, 华斌, 等. 基于DoDAF的弹药供应保障体系构建与效能评估[J]. 兵器装备工程学报, 2023, 44 (1): 80- 85，174.
	LIU H B, SHI X M, HUA B, et al. Construction and effectiveness evaluation of ammunition supply support system based on DoDAF[J]. Journal of Ordnance Equipment Engineering, 2023, 44 (1): 80- 85，174.
2	刘洪娟, 叶层程, 邓群, 等. 军事物流基础设施网络级联失效抗毁性研究[J]. 军事交通学报, 2022, 1 (4): 28- 33.
	LIU H J, YE C C, DENG Q, et al. Research on cascading failure invulnerability of military logistics infrastructure network[J]. Journal of Military Transportation, 2022, 1 (4): 28- 33.
3	王琮, 沈会良, 夏永祥, 等. 装备保障体系关键节点分析[J]. 系统工程与电子技术, 2022, 44 (10): 3134- 3142.
	WANG C, SHEN H L, XIA Y X, et al. Key node analysis of equipment support system[J]. Systems Engineering and Electronics, 2022, 44 (10): 3134- 3142.
4	熊志华, 姚智胜. 轨道交通网络级联失效影响范围研究[J]. 交通运输系统工程与信息, 2020, 20 (1): 12- 18.
	XIONG Z H, YAO Z S. Impact scope of cascading failure in rail transit network[J]. Journal of Transportation Systems Engineering and Information Technology, 2020, 20 (1): 12- 18.
5	郝羽成, 李成兵, 魏磊. 考虑节点过载的复杂网络级联失效模型[J]. 系统工程与电子技术, 2018, 40 (10): 2282- 2287. doi: 10.3969/j.issn.1001-506X.2018.10.19
	HAO Y C, LI C B, WEI L. Cascading failure model for complex networks considering node overload[J]. Systems Engineering and Electronics, 2018, 40 (10): 2282- 2287. doi: 10.3969/j.issn.1001-506X.2018.10.19
6	YIN R R, LI L H, WANG Y M, et al. Robustness of networks with dependence clusters against hybrid cascading failure induced by fluctuating load[J]. Physica A: Statistical Mechanics and its Applications, 2025, 660: 130367.
7	刘凤增, 肖兵, 刘俊杰, 等. 级联失效下非对称依赖网络鲁棒性研究[J]. 国防科技大学学报, 2021, 43 (1): 49- 56.
	LIU F Z, XIAO B, LIU J J, et al. Robustness of interdependent asymmetric networks under cascading failures[J]. Journal of National University of Defense Technology, 2021, 43 (1): 49- 56.
8	李淑敏, 王旭. 欠载级联失效对网络抗毁性的影响——以生鲜农产品供应链网络为例[J]. 科学技术与工程, 2022, 22 (18): 7746- 7756.
	LI S M, WANG X. Impact of underload cascading failure on network invulnerability: case study of fresh agricultural product supply chain network[J]. Science Technology and Engineering, 2022, 22 (18): 7746- 7756.
9	FU X W, YANG Y S. Modeling and analyzing cascading failures for internet of things[J]. Information Sciences, 2021, 545, 753- 770. doi: 10.1016/j.ins.2020.09.054
10	GJORGIEV B, SANSAVINI G. Identifying and assessing power system vulnerabilities to transmission asset outages via cascading failure analysis[J]. Reliability Engineering & System Safety, 2022, 217, 108085.
11	LU Q C, ZhANG L, XU P C, et al. Modeling network vulnerability of urban rail transit under cascading failures: a coupled map lattices approach[J]. Reliability Engineering & System Safety, 2022, 221, 108320.
12	许波桅, 唐灿璇, 李军军. 级联失效下海港-陆港集装箱运输网络鲁棒性分析[J]. 交通运输系统工程与信息, 2023, 23 (3): 265- 279.
	XU B W, TANG C X, LI J J. Robustness analysis of seaport-dry port container transportation network under cascading failure[J]. Journal of Transportation Systems Engineering and Information Technology, 2023, 23 (3): 265- 279.
13	王威, 狄鹏, 胡斌. 基于随机行走介数的级联失效模型[J]. 系统工程与电子技术, 2012, 34 (9): 1914- 1917.
	WANG W, DI P, HU B. Cascading failure model based on random walk betweenness[J]. Systems Engineering and Electronics, 2012, 34 (9): 1914- 1917.
14	王宏宇, 吴纬, 魏艳艳. 基于超网络模型武器装备体系抗毁性分析[J]. 系统工程与电子技术, 2017, 39 (8): 1782- 1787.
	WANG H Y, WU W, WEI Y Y. Invulnerability analysis of weapon equipment system-of-systems based on supernetwork model[J]. Systems Engineering and Electronics, 2017, 39 (8): 1782- 1787.
15	冯芬玲, 蔡明旭, 贾俊杰. 基于多层复杂网络的中欧班列运输网络关键节点识别研究[J]. 交通运输系统工程与信息, 2022, 22 (6): 191- 200.
	FENG F L, CAI M X, JIA J J. Key node identification in China-Europe railway express transportation network based on multi-layer complex network[J]. Journal of Transportation Systems Engineering and Information Technology, 2022, 22 (6): 191- 200.
16	BAEK E C, HYON R, LÓPEZ K, et al. In-degree centrality in a social network is linked to coordinated neural activity[J]. Nature Communications, 2022, 13, 1118. doi: 10.1038/s41467-022-28432-3
17	LIAO H Y, YI J Y, CAI S N, et al. Changes in degree centrality of network nodes in different frequency bands in Parkinson’s disease with depression and without depression[J]. Frontiers in Neuroscience, 2021, 15, 638554. doi: 10.3389/fnins.2021.638554
18	WU X, CAO W, WANG J, et al. A spatial interaction incorporated betweenness centrality measure[J]. PloS One, 2022, 17 (5): e0268203. doi: 10.1371/journal.pone.0268203
19	LIU Z F, YE J X, ZOU Z N. Closeness centrality on uncertain graphs[J]. ACM Transactions on the Web, 2023, 17 (4): 1- 29.
20	谢丽霞, 孙红红, 杨宏宇, 等. 基于K-shell的复杂网络关键节点识别方法[J]. 清华大学学报（自然科学版）, 2022, 62 (5): 849- 861.
	XIE L X, SUN H H, YANG H Y, et al. K-shell based method for identifying key nodes in complex networks[J]. Journal of Tsinghua University （Science and Technology）, 2022, 62 (5): 849- 861.
21	KIM H, ANDERSON R. Temporal node centrality in complex networks[J]. Physical Review E, 2012, 85 (2): 026107. doi: 10.1103/PhysRevE.85.026107
22	WANG Z Q, PEI X B, WANG Y B, et al. Ranking the key nodes with temporal degree deviation centrality on complex networks[C]//Proc.of the 29th Chinese Control and Decision Conference, 2017: 1484−1489.
23	YE Z H, ZHAN X X, ZHOU Y Z, et al. Identifying vital nodes on temporal networks: an edge-based k-shell decomposition[C]//Proc.of the 36th Chinese Control Conference, 2017: 1402−1407.
24	洪成, 蒋沅, 严玉为, 等. 基于层间邻域信息熵的时序网络节点重要性评估方法[J]. 复杂系统与复杂性科学, 2024, 21 (1): 20- 27，42.
	HONG C, JIANG Y, YAN Y W, et al. Node importance evaluation in temporal networks based on inter-layer neighborhood information entropy[J]. Complex Systems and Complexity Science, 2024, 21 (1): 20- 27，42.
25	王亭, 张永, 周明妮, 等. 融合网络拓扑结构特征与客流量的城市轨道交通关键节点识别研究[J]. 交通运输系统工程与信息, 2022, 22 (6): 201- 211.
	WANG T, ZHANG Y, ZHOU M N, et al. Key node identification in urban rail transit combining network topology and passenger flow[J]. Journal of Transportation Systems Engineering and Information Technology, 2022, 22 (6): 201- 211.
26	HE Z Y, ABBES A, JAHANSHAHI H, et al. Fractional-order discrete-time SIR epidemic model with vaccination: chaos and complexity[J]. Mathematics, 2022, 10 (2): 165. doi: 10.3390/math10020165
27	AVRAM F, ADENANE R, KETCHESON D I. A review of matrix SIR arino epidemic models[J]. Mathematics, 2021, 9 (13): 1513. doi: 10.3390/math9131513
28	LI B, ESKANDARI Z. Dynamical analysis of a discrete-time SIR epidemic model[J]. Journal of the Franklin Institute, 2023, 360 (12): 7989- 8007. doi: 10.1016/j.jfranklin.2023.06.006
29	ABDY M, SIDE S, ANNAS S, et al. An SIR epidemic model for COVID-19 spread with fuzzy parameter: the case of Indonesia[J]. Advances in Difference Equations, 2021, 2021, 105. doi: 10.1186/s13662-020-03162-2
30	LI B, ESKANDARI Z, AVAZZADEH Z. Dynamical behaviors of an SIR epidemic model with discrete time[J]. Fractal and Fractional, 2022, 6 (11): 659. doi: 10.3390/fractalfract6110659
31	NAIK P A, ESKANDARI Z, MADZVAMUSE A, et al. Complex dynamics of a discrete-time seasonally forced SIR epidemic model[J]. Mathematical Methods in the Applied Sciences, 2023, 46 (6): 7045- 7059. doi: 10.1002/mma.8955
32	秦长江, 吴克宇, 成清, 等. 基于杀伤网贡献率的动态体系节点重要度评估[J]. 系统工程与电子技术, 2023, 45 (6): 1732- 1742.
	QIN C J, WU K Y, CHENG Q, et al. Dynamic system-of-systems node importance evaluation based on kill-web contribution rate[J]. Systems Engineering and Electronics, 2023, 45 (6): 1732- 1742.
33	赵美, 王海丹, 王立欣, 等. 基于系统动力学的战时弹药供应链可靠性仿真分析[J]. 装甲兵工程学院学报, 2013, 27 (6): 13- 17.
	ZHAO M, WANG H D, WANG L X, et al. Reliability simulation analysis of wartime ammunition supply chain based on system dynamics[J]. Journal of Academy of Armored Force Engineering, 2013, 27 (6): 13- 17.
34	JOHNSON J. Automating the OODA loop in the age of intelligent machines: reaffirming the role of humans in command-and-control decision-making in the digital age[J]. Defence Studies, 2023, 23 (1): 43- 67. doi: 10.1080/14702436.2022.2102486
35	KRESS M. On the attrition of attacking missiles by defensive interceptors[J]. Naval Research Logistics, 1991, 38 (1): 29- 46.
36	RICHARDS M. Fundamentals of radar signal processing[M]. 2nd ed. New York: McGraw-Hill Education, 2014.
37	ROTMAN S , ADAR E, GU R. Statistical detection of targets in clutter using optical sensors[J]. Optical Engineering, 1991, 30(6): 811–819.
38	DELL R F, EAGLE J N. Optimizing defense of a border[J]. Military Operations Research, 2000, 5 (3): 27- 40.
39	CAI K, WU L F. Using grey Gompertz model to explore the carbon emission and its peak in 16 provinces of China[J]. Energy and Buildings, 2022, 277, 112545. doi: 10.1016/j.enbuild.2022.112545
40	CLARK R . Intelligence analysis: a target-centric approach[M]. 6th ed. Washington D.C.: Congressional Quarterly Press, 2020.
41	WANG J L, GUO X. The Gompertz model and its applications in microbial growth and bioproduction kinetics: past, present and future[J]. Biotechnology Advances, 2024, 72: 108335.
42	单子丹, 侯成, 陈佳鑫, 等. 级联失效下考虑节点过载的作业车间云网络鲁棒性研究[EB/OL]. [2025-04-20]. https://www.cnki.com.cn/Article/CJFDTotal-JSJJ20240426007.htm
	SHAN Z D, HOU C, CHEN J X, et al. Robustness of job-shop cloud network considering node overload under cascading failure[EB/OL]. [2025-04-20]. https://www.cnki.com.cn/Article/CJFDTotal-JSJJ20240426007.htm
43	高磊, 高军, 刘晓蕾. 战时弹药供应链系统结构设计[J]. 火力与指挥控制, 2014, 39 (7): 155- 159，163.
	GAO L, GAO J, LIU X L. Structural design of wartime ammunition supply chain system[J]. Fire Control & Command Control, 2014, 39 (7): 155- 159，163.
44	XIAO F, LI J, WEI B. Cascading failure analysis and critical node identification in complex networks[J]. Physica A: Statistical Mechanics and its Applications, 2022, 596, 127117. doi: 10.1016/j.physa.2022.127117
45	SANCHEZ-OCAMPO A, RAMIREZ J M, PATERNINA M R A, et al. Critical nodes detection and dynamic vulnerability analysis in power grids[C]//Proc. of the IEEE 7th Student Conference on Electric Machines and Systems, 2024.

节点	装卸载作业线数量	节点	装卸载作业线数量
${E_1}$	2	${D_2}$	3
${E_2}$	2	${D_3}$	3
${E_3}$	2	${D_4}$	3
${E_4}$	2	${C_1}$	4
${D_1}$	3	${C_2}$	4

阵地	最小值/发	最大值/发	期望/发	方差	随机种子
F₁	0	200	100	2500	1
F₂	10	200	100	2500	1
F₃	10	200	100	2500	1
F₄	10	200	100	2500	1

节点	库容	初始库存	节点	库容	初始库存
F₁	600	600	D₁	2 000	2 000
F₂	600	600	D₂	2 000	2 000
F₃	600	600	D₃	2300	2300
F₄	600	600	D₄	2 000	2 000
E₁	1000	1000	C₁	5000	5000
E₂	1200	1200	C₂	5000	5000
E₃	1000	1000	B	6000	6000
E₄	1000	1000	—	—	—

排序	TC		TB		TDD		TK		INE		N法
排序	节点	值	节点	值	节点	值	节点	值	节点	值	节点	值
1	${D_4}$	2.026	${E_2}$	0.133	${E_4}$	4.165	${D_2}$	4	${D_1}$	4.698	${C_1}$	0.650
2	${E_2}$	1.299	${D_4}$	0.108	${E_3}$	3.843	${D_4}$	4	${D_2}$	4.473	${C_2}$	0.590
3	${D_3}$	1.014	${D_2}$	0.094	${D_2}$	2.923	${D_1}$	4	${E_1}$	4.282	${D_3}$	0.446
4	${D_2}$	0.965	${D_3}$	0.079	${D_3}$	2.380	${C_1}$	4	${E_3}$	4.282	${E_2}$	0.436
5	${D_1}$	0.849	${E_4}$	0.072	${E_2}$	1.244	${E_4}$	3	${E_4}$	4.282	${D_2}$	0.422
6	${E_4}$	0.790	${D_1}$	0.068	${E_1}$	0.753	${E_3}$	2	${D_3}$	4.241	${D_1}$	0.420
7	${E_1}$	0.736	${E_3}$	0.032	${D_4}$	0.753	${D_3}$	0	${E_2}$	3.970	${E_3}$	0.403
8	${E_3}$	0.736	${E_1}$	0.032	${C_2}$	0.619	${E_2}$	0	${C_1}$	3.738	${E_4}$	0.395
9	${C_1}$	0.694	${C_2}$	0.031	${D_1}$	0.499	${E_1}$	0	${C_2}$	3.258	${D_4}$	0.391
10	${C_2}$	0.658	${C_1}$	0.016	${C_1}$	0.276	${C_2}$	0	${D_4}$	1.573	${E_1}$	0.382

移除节点个数	TC法	TB法	TDD法	TK法	INE法	N法
0	0.694	0.694	0.694	0.694	0.694	0.694
1	0.613	0.602	0.657	0.613	0.613	0.592
2	0.550	0.552	0.564	0.573	0.550	0.452
3	0.425	0.420	0.525	0.491	0.464	0.407
4	0.399	0.387	0.439	0.464	0.440	0.377
5	0.378	0.372	0.412	0.431	0.431	0.348
6	0.332	0.352	0.384	0.383	0.383	0.319
7	0.311	0.328	0.344	0.357	0.357	0.293
8	0.280	0.302	0.321	0.333	0.333	0.271
9	0.258	0.257	0.257	0.258	0.251	0.255
10	0.233	0.233	0.233	0.233	0.233	0.233

Analysis of key nodes in the ammunition supply chain considering cascading failure

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 27

References 45

Related Articles 15

Recommended Articles

Metrics

Comments

节点	运输时间
节点	${F_1}$	${F_2}$	${F_3}$	${F_4}$	${E_1}$	${E_2}$	${E_3}$	${E_4}$	${D_1}$	${D_2}$	${D_3}$	${D_4}$	${C_1}$	${C_2}$	$B$
${E_1}$	2	2	3	3	0	—	—	—	3	3	4	5	—	—	—
${E_2}$	2	2	4	4	—	0	—	—	4	3	4	4	—	—	—
${E_3}$	3	3	2	2	—	—	0	—	4	5	3	3	—	—	—
${E_4}$	3	4	2	2	—	—	—	0	5	5	3	3	—	—	—
${D_1}$	10	11	17	18	3	4	4	5	0	—	—	—	6	—	—
${D_2}$	11	10	16	17	3	3	5	5	—	0	—	—	6	—	—
${D_3}$	18	17	10	12	4	4	3	3	—	—	0	—	—	6	—
${D_4}$	16	17	10	10	5	4	3	3	—	—	—	0	—	7	—
${C_1}$	16	16	—	—	—	—	—	—	6	6	—	—	0	—	9
${C_2}$	—	—	16	16	—	—	—	—	—	—	6	7	—	0	9
$B$	—	—	—	—	—	—	—	—	—	—	—	—	9	9	0

想定	阵地	最小值/发	最大值/发	期望/发	方差	随机种子
初始想定	F₁	0	200	100	2500	1
	F₂	10	200	100	2500	1
	F₃	10	200	100	2500	1
	F₄	10	200	100	2500	1
想定1	F₁	0	300	200	2500	1
	F₂	10	300	200	2500	1
	F₃	10	300	200	2500	1
	F₄	10	300	200	2500	1
想定2	F₁	0	200	160	2500	1
	F₂	10	200	80	2500	1
	F₃	10	200	80	2500	1
	F₄	10	200	80	2500	1
想定3	F₁	0	200	80	2500	1
	F₂	10	200	160	2500	1
	F₃	10	200	80	2500	1
	F₄	10	200	80	2500	1
想定4	F₁	0	200	80	2500	1
	F₂	10	200	80	2500	1
	F₃	10	200	160	2500	1
	F₄	10	200	80	2500	1
想定5	F₁	0	200	80	2500	1
	F₂	10	200	80	2500	1
	F₃	10	200	80	2500	1
	F₄	10	200	160	2500	1

想定	Jaccard（k=3）	Jaccard（k=5）	Spearman
想定1	0.5	0.429	0.394
想定2	0.5	0.667	0.406
想定3	0.5	1.000	0.830
想定4	0.5	0.667	0.455
想定5	1.0	0.667	0.806

分组	方案	敏捷性	稳定性	负荷度	鲁棒性
—	初始方案	0.100	0.500	0.300	0.100
单指标主导实验	方案1.1	0.700	0.100	0.100	0.100
	方案1.2	0.100	0.700	0.100	0.100
	方案1.3	0.100	0.100	0.700	0.100
	方案1.40	0.100	0.100	0.100	0.700
	方案1.5	0.250	0.250	0.250	0.250
局部权重变动实验	方案2.1	0.000	0.556	0.333	0.111
	方案2.2	0.200	0.444	0.267	0.089
	方案2.3	0.300	0.389	0.233	0.078
	方案3.1	0.140	0.300	0.420	0.140
	方案3.2	0.080	0.600	0.240	0.080
	方案3.3	0.060	0.700	0.180	0.060
	方案4.1	0.143	0.714	0.100	0.143
	方案4.2	0.086	0.429	0.400	0.086
	方案4.3	0.071	0.357	0.500	0.071
	方案5.1	0.111	0.556	0.333	0.000
	方案5.2	0.089	0.444	0.267	0.200
	方案5.3	0.078	0.389	0.233	0.300

分组	方案	节点排序
分组	方案	1	2	3	4	5	6	7	8	9	10
—	初始方案	${C_1}$	${C_2}$	${D_3}$	${E_2}$	${D_2}$	${D_1}$	${E_3}$	${E_4}$	${D_4}$	${E_1}$
单指标主导实验	方案1.1	${E_3}$	${E_2}$	${E_1}$	${E_4}$	${D_3}$	${D_2}$	${D_4}$	${D_1}$	${C_1}$	${C_2}$
	方案1.2	${C_1}$	${C_2}$	${D_3}$	${D_2}$	${D_1}$	${D_4}$	${E_2}$	${E_3}$	${E_4}$	${E_1}$
	方案1.3	${C_1}$	${E_2}$	${C_2}$	${E_3}$	${D_3}$	${E_4}$	${E_1}$	${D_2}$	${D_1}$	${D_4}$
	方案1.4	${E_2}$	${E_3}$	${E_4}$	${E_1}$	${D_3}$	${D_2}$	${D_1}$	${D_4}$	${C_1}$	${C_2}$
	方案1.5	${E_2}$	${E_3}$	${C_1}$	${E_4}$	${E_1}$	${C_2}$	${D_3}$	${D_2}$	${D_1}$	${D_4}$
局部权重变动实验	方案2.1	${C_1}$	${C_2}$	${D_3}$	${D_2}$	${D_1}$	${E_2}$	${D_4}$	${E_3}$	${E_4}$	${E_1}$
	方案2.2	${C_1}$	${C_2}$	${E_2}$	${E_3}$	${E_4}$	${D_3}$	${E_1}$	${D_2}$	${D_1}$	${D_4}$
	方案2.3	${E_2}$	${C_1}$	${E_3}$	${C_2}$	${E_4}$	${E_1}$	${D_3}$	${D_2}$	${D_1}$	${D_4}$
	方案3.1	${C_1}$	${C_2}$	${E_2}$	${D_3}$	${E_3}$	${E_4}$	${E_1}$	${D_2}$	${D_1}$	${D_4}$
	方案3.2	${C_1}$	${C_2}$	${D_3}$	${E_2}$	${D_2}$	${D_1}$	${D_4}$	${E_3}$	${E_1}$	${E_4}$
	方案3.3	${C_1}$	${C_2}$	${D_3}$	${D_2}$	${D_1}$	${D_4}$	${E_2}$	${E_3}$	${E_4}$	${E_1}$
	方案4.1	${C_1}$	${C_2}$	${E_2}$	${D_3}$	${D_4}$	${D_2}$	${D_1}$	${E_3}$	${E_1}$	${E_4}$
	方案4.2	${C_1}$	${C_2}$	${D_3}$	${E_2}$	${D_2}$	${D_1}$	${E_3}$	${E_4}$	${D_4}$	${E_1}$
	方案4.3	${C_1}$	${C_2}$	${E_2}$	${D_3}$	${E_3}$	${D_2}$	${D_1}$	${E_4}$	${D_4}$	${E_1}$
	方案5.1	${C_1}$	${C_2}$	${D_3}$	${E_2}$	${D_2}$	${D_1}$	${E_3}$	${D_4}$	${E_1}$	${E_4}$
	方案5.2	${C_1}$	${C_2}$	${D_3}$	${E_2}$	${D_2}$	${D_1}$	${E_3}$	${D_4}$	${E_4}$	${E_1}$
	方案5.3	${C_1}$	${C_2}$	${D_3}$	${E_2}$	${D_2}$	${D_1}$	${E_3}$	${E_4}$	${E_1}$	${D_4}$

[1]	Gang HU, Kai KANG, Junjie HU, Xiang XU, Yongjun REN. Identification of evolution of node importance order structure based on super-adjacency matrix columns of arc-directed weighted temporal networks [J]. Systems Engineering and Electronics, 2026, 48(3): 970-985.
[2]	Zhe WANG, Jianhua LI, Dong KANG. Robustness of two-layer heterogeneous interdependent network model for networked information system of system [J]. Systems Engineering and Electronics, 2021, 43(4): 961-969.
[3]	Guowei CHEN, Yujing ZHOU, Lei REN. SD optimization of equipment cost structure facing system performance maximization [J]. Systems Engineering and Electronics, 2021, 43(4): 1022-1029.
[4]	Xing PAN, Dujun ZUO, Yuedong ZHANG. Contribution rate evaluation method of equipment system-of-systems based on system dynamics [J]. Systems Engineering and Electronics, 2021, 43(1): 112-120.
[5]	Chao WANG, Jilian GUO, Anwei SHEN. Analysis of cascading failures of interdependent networks based on asymmetric dependency [J]. Systems Engineering and Electronics, 2020, 42(5): 1093-1101.
[6]	Xiaogang QI, Doudou ZHAI, Xuexing LIU. Analysis of anti-ship force loss at sea based on system dynamics [J]. Systems Engineering and Electronics, 2020, 42(4): 836-842.
[7]	LIU Yupeng, YANG Yutao, YAN Xiangbin, TIAN Yaoli, LI Yijun. System dynamics model of stakeholders in manned spaceflight space applications [J]. Systems Engineering and Electronics, 2019, 41(12): 2807-2819.
[8]	ZHOU Zhongliang, CHENG Yue, KOU Tian, GUO Pengcheng. Air penetration combat forces plan evaluation method based on two stage DEA model [J]. Systems Engineering and Electronics, 2018, 40(4): 797-804.
[9]	LIU Hao, ZHOU Jun, ZHANG Shiwei. Launch dynamics of airborne missile with large maneuvering flight [J]. Systems Engineering and Electronics, 2018, 40(10): 2305-2310.
[10]	HAO Yucheng, LI Chengbing, WEI Lei. Cascading failure model of complex networks considering overloaded nodes [J]. Systems Engineering and Electronics, 2018, 40(10): 2282-2287.
[11]	CUI Wenyan, MENG Xiangru, KANG Qiaoyan, LI Jizhen. Optimization of cascading invulnerability on weighted complex networks based on composite edge weight model [J]. Systems Engineering and Electronics, 2017, 39(2): 355-361.
[12]	ZHANG Jie-yong, YI Kan, WANG Heng, ZHANG Jin-feng, ZHOU Xiang-xiang. Dynamic robustness measure method considering cascading failure for C⁴ISR system structure [J]. Systems Engineering and Electronics, 2016, 38(9): 2072-2079.
[13]	LUO Kai, ZHANG Ming-zhi, WU Xi. Key nodes analysis model for space information temporal network based on operation loop [J]. Systems Engineering and Electronics, 2016, 38(7): 1572-1576.
[14]	LU Yu-liang, YANG Bin. Analysing and modeling cascading failures for inter-domain routing system [J]. Systems Engineering and Electronics, 2016, 38(1): 172-178.
[15]	ZHANG Chao,ZHANG Feng-ming,WANG Ying,WU Hu-sheng. Method to analyse the robustness of aviation communication network based on complex networks [J]. Systems Engineering and Electronics, 2015, 37(1): 180-184.