针对扩展动态故障树的约束分析方法

doi:10.11959/j.issn.1000-436x.2017156

通信学报 ›› 2017, Vol. 38 ›› Issue (9): 159-166.doi: 10.11959/j.issn.1000-436x.2017156

针对扩展动态故障树的约束分析方法

吴奇烜¹,马建峰¹,孙聪¹,张帅¹,张双²,郑涛²

¹ 西安电子科技大学网络与信息安全学院，陕西西安 710071
² 中国航空工业集团公司西安航空计算技术研究所，陕西西安 710068

修回日期:2017-03-30 出版日期:2017-09-01 发布日期:2017-10-18
作者简介:吴奇烜（1992-），男，陕西商洛人，西安电子科技大学硕士生，主要研究方向为系统可靠性分析、信息流安全。|马建峰（1963-），男，陕西西安人，西安电子科技大学教授、博士生导师，主要研究方向为密码学、无线和移动安全等。|孙聪（1982-），男，陕西兴平人，博士，西安电子科技大学副教授，主要研究方向为信息流安全、可信软件。|张帅（1990-），男，江苏沛县人，西安电子科技大学硕士生，主要研究方向为大型富媒体系统架构的设计。|张双（1976-），男，陕西汉中人，中国航空工业集团公司西安航空计算技术研究所研究员，主要研究方向为计算机网络与机载信息安全技术。|郑涛（1988-），男，陕西岐山人，中国航空工业集团公司西安航空计算技术研究所工程师，主要研究方向为计算机网络与机载信息安全技术。
基金资助:
国家自然科学基金资助项目(61303033);国家自然科学基金资助项目(U1405255);国家高技术研究发展计划（“863”计划）基金资助项目(2015AA017203);陕西省自然科学基础研究计划基金资助项目(2016JM6034);航空科学基金资助项目(20141931001);工信部某专项科研基金资助项目(MJ-2014-S-37)

Constraint analysis for extended dynamic fault tree

Qi-xuan WU¹,Jian-feng MA¹,Cong SUN¹,Shuai ZHANG¹,Shuang ZHANG²,Tao ZHENG²

¹ School of Cyber Engineering,Xidian University,Xi’an 710071,China
² Aeronautical Computing Technique Research Institute,Aviation Industry Corporation of China,Xi’an 710068,China

Revised:2017-03-30 Online:2017-09-01 Published:2017-10-18
Supported by:
The National Natural Science Foundation of China(61303033);The National Natural Science Foundation of China(U1405255);The National High Technol-ogy Research and Development Program of China (863 Program)(2015AA017203);The Natural Science Basis Research Plan in Shaanxi Province of China(2016JM6034);The Aviation Science Foundation of China(20141931001);The Special Research Foundation of MIIT(MJ-2014-S-37)

摘要/Abstract

摘要：

提出延时门机制对动态故障树进行扩展，用于对子系统失效延时传播到上层系统进行建模，并通过扩展动态贝叶斯网络对包含延时门的动态故障树进行求解。还提出并实现了一种基于可满足性模理论的扩展动态故障树求解算法，支持由非确定性的基本事件概率范围约束求解系统的最优化失效率。通过对实际系统的分析、求解及与现有工具的对比，说明分析方法的有效性，并通过对实际系统的分析给出了基本事件概率约束和延时门参数对系统整体失效率的影响。

关键词: 延时门, 动态故障树, 动态贝叶斯网络, 可满足性模理论

Abstract:

As a new extension of dynamic fault trees,time delay gate was proposed.This new mechanism can be used to model the time delay on the fault propagation from the lower level subsystems to the higher level system.The dynamic Bayesian networks was extend to solve the dynamic fault trees containing time delay gates.An algorithm based on SMT to support the optimized failure distribution under the nondeterministic range constraint of basic events was also proposed.The effectiveness is shown by comparison with existing tools on analyzing and solving real systems,and the effects of range constraints and gate parameter on the failure distribution of systems is illustrated.

Key words: time delay gate, dynamic fault tree, dynamic Bayesian network, satisfiability modulo theory

中图分类号:

TP311.5

吴奇烜,马建峰,孙聪,张帅,张双,郑涛. 针对扩展动态故障树的约束分析方法[J]. 通信学报, 2017, 38(9): 159-166.

Qi-xuan WU,Jian-feng MA,Cong SUN,Shuai ZHANG,Shuang ZHANG,Tao ZHENG. Constraint analysis for extended dynamic fault tree[J]. Journal on Communications, 2017, 38(9): 159-166.

图/表 8

表1

各种功能门的动态贝叶斯网络上层事件条件概率计算式"

门结构	门输出概率计算式
AND	P(AND#=1)=P(A#=1)P(B#=1)
OR	P(OR#=1)=1–(1–P(A#=1))(1–P(B#=1))
PDEP	P(X#=1)=πP(Tr#=1)+P(Tr#=0)(P(X=0)F(Δt,X)+P(X=1))，
	其中，X=A,B
SP	P(B#=1)=(P(A=0)α+P(A=1))P(B=0)F(Δt,B)+P(B=1)
	P(SP#=1)=P(A#=1)P(B#=1)
PAND	P(PAND#=1)=P(PAND=1)+ $\frac{P (A # = 1) + P (A = 1)}{2 (P (B # = 1)}$ –P(B=1))
RB	P(RB#=1)=P(A#=1)–P(RB=1)+P(RB=1)(1–R(Δt,A)P(trigger))
	P(A#=1)=P(A=0)F(Δt,A)+P(RB=1)

表1

图1

图2

表2

图3

图4

图5

图6

参考文献 18

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门结构	门输出概率计算式
	P(RB#=1)=P(A#=1) – P(RB=1) + P(RB=1) ·
RB'	(1 – R(Δt,A)(1 – P(TD#=1))P(trigger))
	P(A#=1)=P(A=0)F(Δt,A) + P(RB=1)
	P(FO₀#=1)=P(A#=1)
TD	P(FO_i#=1)=P(FO_i-1=1)C,0≤i≤n
	P(TD#=1)=P(FO_n#=1)

针对扩展动态故障树的约束分析方法

Constraint analysis for extended dynamic fault tree

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