Resilience based importance measure analysis for SoS

doi:10.21629/JSEE.2019.05.10

Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (5): 920-930.doi: 10.21629/JSEE.2019.05.10

• Systems Engineering • Previous Articles Next Articles

Resilience based importance measure analysis for SoS

Xing PAN^1,*(), Huixiong WANG¹(), Yanjing YANG^1,²(), Guozhong ZHANG³()

¹ School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
² China Railway Signal and Communication Corporation, Beijing 100070, China
³ Institute of Systems Engineering, China State Shipbuilding Corporation, Beijing 100036, China

Received:2019-03-06 Online:2019-10-08 Published:2019-10-09
Contact: Xing PAN E-mail:panxing@buaa.edu.cn;wanghuixiong@buaa.edu.cn;yangyanjing@crscu.com.cn;18911990023@189.cn
About author:PAN Xing was born in 1979. He received his B.S. degree in mechanical engineering, and Ph.D. degree in systems engineering from Beihang University (BUAA), Beijing, China, in 2000, and 2005, respectively. From 2005 to 2009, he was an assistant professor with the School of Reliability and Systems Engineering, Beihang University, Beijing, China. Since 2009, he has been an associate professor. From 2012 to 2013, he was a visiting scholar at the Department of Systems and Industrial Engineering, University of Arizona, Tucson, USA. His research interests include reliability engineering, systems engineering, and system risk analysis. E-mail: panxing@buaa.edu.cn|WANG Huixiong was born in 1995. He received his B.S. degree in safety science from School of Reliability and Systems Engineering, Beihang University, in 2018. He is currently a master student in the same school. His interests of research include systems engineering and complex network. E-mail: wanghuixiong@buaa.edu.cn|YANG Yanjing was born in 1991. He received his B.S. degree in material engineering from Yanshan University in 2015, and M.S. degree in industrial engineering from Beihang University in 2018. Since 2018, he has been an assistant engineer at China Railway Signal and Communication Corporation. His research interests include signal system engineering and system and systems engineering (SoSE). E-mail: yangyanjing@crscu.com.cn|ZHANG Guozhong was born in 1979. He is a senior engineer with the Institute of Systems Engineering, China State Shipbuilding Corporation. His research interest is system of systems engineering (SoSE). E-mail: 18911990023@189.cn
Supported by:
the National Natural Science Foundation of China(71571004);This work was supported by the National Natural Science Foundation of China (71571004)

Abstract

Abstract:

In a system of systems (SoS), resilience is an important factor in maintaining the functionality, stability, and enhancing the operation effectiveness. From the perspective of resilience, this paper studies the importance of the SoS, and a resilience-based importance measure analysis is conducted to provide suggestions in the design and optimization of the structure of the SoS. In this paper, the components of the SoS are simplified as four kinds of network nodes: sensor, decision point, influencer, and target. In this networked SoS, the number of operation loops is used as the performance indicator, and an approximate algorithm, which is based on eigenvalue of the adjacency matrix, is proposed to calculate the number of operation loops. In order to understand the performance change of the SoS during the attack and defense process in the operations, an integral resilience model is proposed to depict the resilience of the SoS. From different perspectives of enhancing the resilience, different measures, parameters and the corresponding algorithms for the resilience importance of components are proposed. Finally, a case study on an SoS is conducted to verify the validity of the network modelling and the resilience-based importance analysis method.

Key words: system of systems (SoS), resilience, network mo-delling, importance measure analysis, operation loop

Xing PAN, Huixiong WANG, Yanjing YANG, Guozhong ZHANG. Resilience based importance measure analysis for SoS[J]. Journal of Systems Engineering and Electronics, 2019, 30(5): 920-930.

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Type	Notation	Number
Sensor (S)	$S_{1}$, $S_{2}$, $S_{3}$, $S_{4}$, $S_{5}$, $ S_{6}$, $S_{7}$, $S_{8}$	8
Decision point (D)	$D_{1}$, $D_{2}$, $D_{3}$	3
Influencer (I)	$I_{1}$, $ I_{2}$, $I_{3}$, $I_{4}$, $I_{5}$, $I_{6}$, $ I_{7}$, $I_{8}$	8
Target (T)	$T_{1}$, $T_{2}$, $T_{3}$, $T_{4}$	4

Connection	Notation	Probability
Target$ \to $Sensor	$P_{TS}$	0.4
Sensor$ \to $Decision point	$P_{SD}$	0.6
Decision point$ \to $Decision point	$P_{DD}$	0.6
Decision point$ \to $Influencer	$P_{DI}$	0.6
Influencer$ \to $Target	$P_{IT}$	0.3

Node	$S_{1}$	$D_{1}$	$I_{1}$	$S_{8}$	$S_{4}$	$I_{5}$
Degree	5	15	2	6	3	2
MTTR	1.6	2	1.4	1.6	1.6	1.4

Measure	Normal	Adding node $S$	Adding node $D$	Adding node $I$
$R$	0.641 6	0.741 5	0.851 1	0.701 5
RIM		0.155 6	0.3264	0.093 2

Measure	Normal	$S_{1}$ functioning normally	$D_{1}$ functioning normally	$I_{1}$ functioning normally
$R$	0.781 0	0.840 0	0.886 2	0.832 7
RIM		0.075 5	0.134 7	0.066 2

Resilience based importance measure analysis for SoS

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Measure	No recovery	Recovering $S_{1 }$ only	Recovering $D_{1}$ only	Recovering $I_{1 }$ only
$R$	0.605 2	0.637 2	0.698 6	0.653 9
RIM		0.052 9	0.154 2	0.080 4

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