关键基础设施安全资源配置优化研究

doi:10.16265/j.cnki.issn1003-3033.2026.02.0519

摘要/Abstract

摘要：

为提高关键基础设施安全资源配置的合理性与有效性,解决传统方法在安全资源分配均衡性与防护效能方面的不足,基于前景理论(PT)、敌手入侵序列图(ASD)和Stackelberg博弈理论,构建关键基础设施安全资源配置优化模型。首先,通过构建ASD-Stackelberg博弈模型求解关键基础设施内部安全资源的最优空间配置;其次,引入PT理论刻画攻防双方的有限理性特征,确定最优安全资源投入阈值;最后,以核电厂安防系统为案例开展实证研究。结果表明:相较于传统经验配置方法,文中所建模型输出的最优资源配置方案,能够使核电厂整体安防效能提升25.9%,且能够准确找出最优安全资源投入量。该结果证实模型在求解最优配置方案方面的有效性与可行性,且其在提升安全防护能力方面具有显著优越性。

关键词: 关键基础设施, 安全资源配置, 前景理论(PT), 敌手入侵序列图(ASD), Stackelberg博弈模型

Abstract:

In order to improve the rationality and effectiveness of critical infrastructure security resource allocation, and solve the shortcomings of traditional methods in the balance of security resource allocation and protection effectiveness, an optimization model of critical infrastructure security resource allocation was constructed based on PT, ASD and Stackelberg game theory. Firstly, the ASD-Stackelberg game model was constructed to solve the optimal spatial allocation of security resources within critical infrastructure. Secondly, the PT theory was introduced to describe the bounded rationality characteristics of both attack and defense sides, and the optimal security resource investment threshold was determined. Finally, the nuclear power plant security system was taken as a case study. The verification and analysis results show that compared with the traditional empirical configuration method, the optimal resource allocation scheme output by this model has significantly improved the overall security effectiveness of nuclear power plants by 25.9%, and can accurately identify the optimal amount of security resource investment. This result not only confirms the effectiveness and feasibility of the model in solving the optimal configuration scheme, but also quantitatively establishes its significant superiority in enhancing security protection capabilities.

Key words: critical infrastructure, security resource allocation, prospect theory(PT), adversary intrusion sequence diagram (ASD), Stackelberg game model

中图分类号:

X956生活安全

黄积成, 陈文静, 贾楠. 关键基础设施安全资源配置优化研究[J]. 中国安全科学学报, 2026, 36(2): 218-226.

HUANG Jicheng, CHEN Wenjing, JIA Nan. Research on security resource allocation optimization of critical infrastructure[J]. China Safety Science Journal, 2026, 36(2): 218-226.

图/表 11

图1

图2

图3

表1

图4

表2

表3

表4

不同安全资源投入时的最优安全资源配置及最短路径代价

策略	Z+z	x₁	x₂	x₃	x₄	x₅		x₆	x₇	x₈	路径代价
$S d 0$	800	157.0	165.0	169.0	25.0	56.0		25.0	32.0	169.0	214.0
$S d 1$	880	183.9	188.0	188.0	27.5	27.5		27.5	49.6	188.0	238.0
$S d 2$	960	200.3	205.0	205.0	30.0	33.2		30.0	50.8	205.2	259.6
$S d 3$	1 040	214.3	222.1	222.1	32.5	52.0		32.5	42.4	222.1	281.1
$S d 4$	1 120	219.8	231.6	237.3	35.0	78.7		35.0	45.3	237.3	300.5
$S d 5$	1 200	247.4	256.3	256.3	37.5	59.0		37.5	49.8	256.3	322.5
$S d 6$	1 280	251.2	264.7	271.2	40.0	90.0		40.0	51.9	271.2	343.4
$S d 7$	1 360	282.0	291.0	291.0	42.5	66.2		42.5	51.0	291.9	367.6
$S d 8$	1 440	296.9	307.6	307.6	45.0		71.0	45.0	59.3	307.6	389.3
$S d 9$	1 520	313.2	324.6	324.6	47.5		76.0	47.5	62.0	324.6	410.9
$S d 10$	1 600	329.9	341.7	341.7	50.0		78.7	50.0	66.4	341.7	432.5

表4

表5

不同安全资源投入下攻击者前景效用价值

防御策略	$S d 0$	$S d 1$	$S d 2$	$S d 3$	$S d 4$	$S d 5$
效用价值	155.0	126.7	101.0	76.8	54.9	27.6
防御策略	$S d 6$	$S d 7$	$S d 8$	$S d 9$	$S d 10$	—
效用价值	6.0	-22.1	-45.6	-68.9	-94.4	—

表5

表6

不同安全资源投入下防御者前景效用价值

防御策略	$S d 0$	$S d 1$	$S d 2$	$S d 3$	$S d 4$	$S d 5$
效用价值	414.5	426.4	430.4	430.6	423.2	427.4
防御策略	$S d 6$	$S d 7$	$S d 8$	$S d 9$	$S d 10$	—
效用价值	427.7	0	0	0	0	—

表6

图5

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策略	路径	路径代价
S_a1	x₀→x₂→x₅→x₇→x₈/T	170
S_a2	x₀→x₂→x₅→x₆→x₈/T	175
S_a3	x₀→x₁→x₅→x₇→x₈/T	185
S_a4	x₀→x₃→x₄→x₇→x₈/T	185
S_a5	x₀→x₁→x₅→x₆→x₈/T	190
S_a6	x₀→x₃→x₅→x₇→x₈/T	195
S_a7	x₀→x₃→x₄→x₆→x₈/T	200
S_a8	x₀→x₃→x₅→x₆→x₈/T	200
S_a9	x₀→x₂→x₄→x₇→x₈/T	220
S_a10	x₀→x₁→x₄→x₇→x₈/T	235
S_a11	x₀→x₂→x₄→x₆→x₈/T	235
S_a12	x₀→x₁→x₄→x₆→x₈/T	250