An evaluation method of contribution rate based on fuzzy Bayesian networks for equipment system-of-systems architecture

doi:10.23919/JSEE.2023.000081

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (3): 574-587.doi: 10.23919/JSEE.2023.000081

• COMPLEX SYSTEMS THEORY AND PRACTICE • Previous Articles

An evaluation method of contribution rate based on fuzzy Bayesian networks for equipment system-of-systems architecture

Renjie XU¹^,²(), Xin LIU¹^,³(), Donghao CUI²(), Jian XIE¹(), Lin GONG¹^,³^,*()

¹ School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China
² College of Systems Engineering, National University of Defense Technology, Changsha 410073, China
³ Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing 314019, China

Received:2022-08-30 Online:2023-06-15 Published:2023-06-30
Contact: Lin GONG E-mail:3220200354@bit.edu.cn;xliu826@bit.edu.cn;2711548599@qq.com;xiejian@bit.edu.cn;gonglin@bit.edu.cn
About author:
XU Renjie was born in 1998. He received his B.E. degree in industrial engineering from Shihezi University, Xinjiang, China, in 2020, and M.S. degree from Beijing Institute of Technology, Beijing, China. He is currently working toward his Ph.D. degree from National University of Defense Technology, Changsha, China and visiting the School of Management, Technical University of Munich, Heilbronn, Germany. His research interests include system-of-systems resilience assessment and optimization, management science and complex system management. E-mail: 3220200354@bit.edu.cn

LIU Xin was born in 1994. He received his B.S. degree in industrial engineering and Ph.D. degree in data science from Beijing Institute of Technology and City University of Hong Kong in 2016 and 2021, respectively. He is currently an assistant professor at the School of Mechanical Engineering, Beijing Institute of Technology, Beijing, China. He was an exchange student at the Department of Mechanical Engineering, Karlsruhe Institute of Technology, Germany, in 2015. His current research interests include data mining, computational intelligence, renewable energy, and predictive modeling. E-mail: xliu826@bit.edu.cn

CUI Donghao was born in 1997. He received his B.E. degree in management from Shihezi University, Xinjiang, China, in 2020, and is currently working toward his M.S. degree with the National University of Defense Technology, Changsha, China. His research interests include data mining and complex network analysis, national security and crisis management. E-mail: 2711548599@qq.com

XIE Jian was born in 1991. He received his Ph.D. degree in mechanical engineering from Beijing Institute of Technology, Beijing, China, in 2020. He is currently an assistant professor in the School of Mechanical Engineering, Beijing Institute of Technology. He was a visiting predoctoral fellow with the Northwestern University from 2017 to 2019. His current research interests include complex network and system-of-systems engineering. E-mail: xiejian@bit.edu.cn

GONG Lin was born in 1979. He received his Ph.D. degree in mechanical engineering from Beijing Institute of Technology, Beijing, China, in 2006. He is currently an associate professor and the deputy dean of the School of Mechanical Engineering, Beijing Institute of Technology. He was a visiting scholar with the University of Southern California, USA from 2013 to 2014. His current research interests include innovative design of complex systems, big data analysis, industrial engineering, knowledge engineering, and statistical optimization. E-mail: gonglin@bit.edu.cn
Supported by:
This work was supported by the National Key Research and Development Project (2018YFB1700802), the National Natural Science Foundation of China (72071206), and the Science and Technology Innovation Plan of Hunan Province (2020RC4046).

Abstract

Abstract:

The contribution rate of equipment system-of-systems architecture (ESoSA) is an important index to evaluate the equipment update, development, and architecture optimization. Since the traditional ESoSA contribution rate evaluation method does not make full use of the fuzzy information and uncertain information in the equipment system-of-systems (ESoS), and the Bayesian network is an effective tool to solve the uncertain information, a new ESoSA contribution rate evaluation method based on the fuzzy Bayesian network (FBN) is proposed. Firstly, based on the operation loop theory, an ESoSA is constructed considering three aspects: reconnaissance equipment, decision equipment, and strike equipment. Next, the fuzzy set theory is introduced to construct the FBN of ESoSA to deal with fuzzy information and uncertain information. Furthermore, the fuzzy importance index of the root node of the FBN is used to calculate the contribution rate of the ESoSA, and the ESoSA contribution rate evaluation model based on the root node fuzzy importance is established. Finally, the feasibility and rationality of this method are validated via an empirical case study of aviation ESoSA. Compared with traditional methods, the evaluation method based on FBN takes various failure states of equipment into consideration, is free of acquiring accurate probability of traditional equipment failure, and models the uncertainty of the relationship between equipment. The proposed method not only supplements and improves the ESoSA contribution rate assessment method, but also broadens the application scope of the Bayesian network.

Key words: equipment system-of-systems architecture (ESoSA), contribution rate evaluation, fuzzy Bayesian network (FBN), fuzzy set theory

Renjie XU, Xin LIU, Donghao CUI, Jian XIE, Lin GONG. An evaluation method of contribution rate based on fuzzy Bayesian networks for equipment system-of-systems architecture[J]. Journal of Systems Engineering and Electronics, 2023, 34(3): 574-587.

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Type	Model	Model number
AWACS	Tactical AWACS	XY1 XY2
AWACS	Strategic AWACS	DY1
Reconnaissance aircraft	Tactical reconnaissance aircraft	SZ1 SZ2
Reconnaissance aircraft	Strategic reconnaissance aircraft	LZ1 LZ2
Radar	−	JY1 JY2
Ground command and control center	−	D1 D2
Battle command	−	DD1
Fighter bomber	−	JH1
Bomber	−	HZ1 HZ2 HZ3
Fighter plane	Fourth generation fighter plane	GJ1 GJ2
	Third generation fighter plane	ZJ1 ZJ2
	Second generation fighter plane	DJ1 DJ2

Intermediate node	Intermediate event name	Intermediate node	Intermediate event name
y₁	Tactical AWACS failure	y₉	Reconnaissance aircraft failure
y₂	Tactical reconnaissance aircraft failure	y₁₀	Ground command and control center failure
y₃	Strategic reconnaissance aircraft failure	y₁₁	Bomber failure
y₄	Radar failure	y₁₂	Fighter plane failure
y₅	Second generation fighter failure	y₁₃	Reconnaissance equipment structure failure
y₆	Third generation fighter plane failure	y₁₄	Decision equipment structure failure
y₇	Fourth generation fighter failure	y₁₅	Strike equipment structure failure
y₈	AWACS failure

Root node equipment	Model number	$ \tilde P({x_i} = 1) $
X₁	XY1	{0.2125,0.25,0.2875}
X₂	XY2	{0.2125,0.25,0.2875}
X₃	DY1	{0.2975,0.35,0.4025}
X₄	SZ1	{0.1275,0.15,0.1725}
X₅	SZ2	{0.1275,0.15,0.1725}
X₆	LZ1	{0.1700,0.20,0.2300}
X₇	LZ2	{0.1700,0.20,0.2300}
X₈	JY1	{0.2125,0.25,0.2875}
X₉	JY2	{0.2125,0.25,0.2875}
X₁₀	D1	{0.3230,0.38,0.4370}
X₁₁	D2	{0.3230,0.38,0.4370}
X₁₂	DD1	{0.3400,0.40,0.4600}
X₁₃	JH1	{0.1700,0.20,0.2300}
X₁₄	HZ1	{0.2125,0.25,0.2875}
X₁₅	HZ2	{0.2550,0.30,0.3450}
X₁₆	HZ3	{0.2975,0.35,0.4025}
X₁₇	DJ1	{0.1275,0.15,0.1725}
X₁₈	DJ2	{0.1275,0.15,0.1725}
X₁₉	ZJ1	{0.1275,0.15,0.1725}
X₂₀	ZJ2	{0.2125,0.25,0.2875}
X₂₁	GJ1	{0.2550,0.30,0.3450}
X₂₂	GJ2	{0.2550,0.30,0.3450}

Serial number	Root node equipment	Model number	ESoSA contribution rate/%
1	X₁	XY1	1.5539
2	X₂	XY2	1.5539
3	X₃	DY1	1.6595
4	X₄	SZ1	1.3428
5	X₅	SZ2	1.3428
6	X₆	LZ1	1.29
7	X₇	LZ2	1.29
8	X₈	JY1	1.4313
9	X₉	JY2	1.4313
10	X₁₀	D1	2.0892
11	X₁₁	D2	2.0892
12	X₁₂	DD1	3.0359
13	X₁₃	JH1	0.0571
14	X₁₄	HZ1	0.067
15	X₁₅	HZ2	0.0615
16	X₁₆	HZ3	0.1165
17	X₁₇	DJ1	0.0971
18	X₁₈	DJ2	0.0971
19	X₁₉	ZJ1	0.2517
20	X₂₀	ZJ2	0.2277
21	X₂₁	GJ1	0.1666
22	X₂₂	GJ2	0.1666

An evaluation method of contribution rate based on fuzzy Bayesian networks for equipment system-of-systems architecture

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x₁	x₂	P(y=0\| x₁, x₂)	P(y=0.5\| x₁, x₂)	P(y=1\|x₁, x₂)
0	0	1.0	0	0
0	0.5	0.1	0.2	0.7
0	1	0.1	0.1	0.8
0.5	0	0.4	0.3	0.3
0.5	0.5	0.4	0.1	0.5
0.5	1	0.1	0.2	0.7
1	0	0	0	1.0
1	0.5	0	0	1.0
1	1	0	0	1.0

Rule	X₁₄	X₁₅	X₁₆	y₁₁
Rule	X₁₄	X₁₅	X₁₆	0	0.5	1
1	0	0	0	1	0	0
2	0	0	0.5	0.3	0.6	0.1
3	0	0	1	0	0	1
4	0	0.5	0	0.3	0.6	0.1
5	0	0.5	0.5	0.2	0.6	0.2
6	0	0.5	1	0	0	1
7	0	1	0	0	0	1
8	0	1	0.5	0	0	1
9	0	1	1	0	0	1
10	0.5	0	0	0.3	0.6	0.1
11	0.5	0	0.5	0.2	0.6	0.2
12	0.5	0	1	0	0	1
13	0.5	0.5	0	0.2	0.6	0.2
14	0.5	0.5	0.5	0.1	0.3	0.6
15	0.5	0.5	1	0	0	1
16	0.5	1	0	0	0	1
17	0.5	1	0.5	0	0	1
18	0.5	1	1	0	0	1
19	1	0	0	0	0	1
20	1	0	0.5	0	0	1
21	1	0	1	0	0	1
22	1	0.5	0	0	0	1
23	1	0.5	0.5	0	0	1
24	1	0.5	1	0	0	1
25	1	1	0	0	0	1
26	1	1	0.5	0	0	1
27	1	1	1	0	0	1