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

摘要/Abstract

摘要：

针对弹药保障节点受打击后因供应任务再分配引发邻居节点吞吐量增多，被发现并打击概率增大，进而导致弹药供应链易发生级联失效的问题，提出一种用于动态识别弹药供应链关键节点的方法。首先，分析节点失效、级联失效过程，构建基于节点失效概率服从两阶段Gompertz分布的弹药供应链级联失效模型。其次，从供应能力和供应效率角度出发，选取敏捷性、稳定性、负荷度和鲁棒性构建节点重要性评价指标体系。再次，考虑当前任务完成情况和后续任务完成能力，选取阵地缺供率、供应任务完成率和供应链路存活率作为弹药供应链综合供应能力评价指标。最后，构建弹药供应链系统动力学模型，采用移除节点法对所提方法和 5 种时序网络关键节点识别方法进行验证，并从外部环境与内部参数两个维度对所提方法进行敏感性分析。结果显示，所提方法较其他方法弹药供应链综合供应能力下降最快，表明所识别节点对弹药供应影响最大、重要度最高；同时发现所提方法对弹药供应任务和敏捷性指标的变化较为敏感。结论显示，所提方法能够有效识别弹药供应链中的关键节点，有助于制定抗打击预案，提高弹药供应效能。

关键词: 关键节点分析, 级联失效, 时序网络, 系统动力学

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

中图分类号:

E 233

刘鹏华, 史宪铭, 王亚龙, 杨密芬. 考虑级联失效的弹药供应链关键节点分析[J]. 系统工程与电子技术, 2026, 48(8): 2761-2781.

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.

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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