Accountable capability improvement based on interpretable capability evaluation using belief rule base

doi:10.23919/JSEE.2024.000095

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (5): 1231-1244.doi: 10.23919/JSEE.2024.000095

收稿日期:2022-12-26 出版日期:2024-10-18 发布日期:2024-11-06

Accountable capability improvement based on interpretable capability evaluation using belief rule base

Xuan LI¹(), Jiang JIANG¹(), Jianbin SUN¹(), Haiyue YU¹(), Leilei CHANG¹^,²^,*()

¹ College of Systems Engineering, National University of Defense Technology, Changsha 410073, China
² China-Austria Belt and Road Joint Laboratory on Artificial Intelligence and Advanced Manufacturing, Hangzhou Dianzi University, Hangzhou 310018, China

Received:2022-12-26 Online:2024-10-18 Published:2024-11-06
Contact: Leilei CHANG E-mail:xlhunan@126.com;jiangjiangnudt@163.com;sunjianbin@nudt.edu.cn;haiyue_nudt@163.com;leileichang@hotmail.com
About author:
LI Xuan was born in 1982. She received her Ph.D. degree from National University of Defense Technology, Changsha, China, in 2017. She is an associate professor of the Big Data and Decision Lab in National University of Defense Technology. Her research interests include big data analysis, data engineering and application in the military background. E-mail: xlhunan@126.com

JIANG Jiang was born in 1980. He received his Ph.D. degree from National University of Defense Technology, Changsha, China, in 2011. He is an associate professor with National University of Defense Technology. His research interests include capability evaluation, risk assessment, and design of technology systems in the military background. E-mail: jiangjiangnudt@163.com

SUN Jianbin was born in 1989. He received his Ph.D. degree from National University of Defense Technology, Changsha, China, in 2018. He is an associate professor with National University of Defense Technology. His research interests include system of systems engineering management and decision analysis under uncertainty. E-mail: sunjianbin@nudt.edu.cn

YU Haiyue was born in 1991. He received his Ph.D. degree in management science and engineering from National University of Defense Technology, Changsha, China, in 2020. He is now a lecturer in management science and engineering with College of Systems Engineering at National University of Defense Technology. His main research interests include reliability modeling and evaluation of complex systems under uncertainty, testing, and evaluation of the intelligent system. E-mail: haiyue_nudt@163.com

CHANG Leilei was born in 1985. He received his Ph.D. degree from National University of Defense Technology, Changsha, China, in 2014. He is an associate professor with Hangzhou Dianzi University. He was a research fellow at Nanyang Technological University. His research interests include capability evaluation and improvement in the military background, and evaluation approaches in other theoretical and practical practices. E-mail: leileichang@hotmail.com
Supported by:
This work was supported by the National Natural Science Foundation of China (72471067; 72431011; 72471238; 72231011; 62303474; 72301286), and the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK239909299001-010).

摘要/Abstract

Abstract:

A new approach is proposed in this study for accountable capability improvement based on interpretable capability evaluation using the belief rule base (BRB). Firstly, a capability evaluation model is constructed and optimized. Then, the key sub-capabilities are identified by quantitatively calculating the contributions made by each sub-capability to the overall capability. Finally, the overall capability is improved by optimizing the identified key sub-capabilities. The theoretical contributions of the proposed approach are as follows. (i) An interpretable capability evaluation model is constructed by employing BRB which can provide complete access to decision-makers. (ii) Key sub-capabilities are identified according to the quantitative contribution analysis results. (iii) Accountable capability improvement is carried out by only optimizing the identified key sub-capabilities. Case study results show that “Surveillance”, “Positioning”, and “Identification” are identified as key sub-capabilities with a summed contribution of 75.55% in an analytical and deducible fashion based on the interpretable capability evaluation model. As a result, the overall capability is improved by optimizing only the identified key sub-capabilities. The overall capability can be greatly improved from 59.20% to 81.80% with a minimum cost of 397. Furthermore, this paper also investigates how optimizing the BRB with more collected data would affect the evaluation results: only optimizing “Surveillance” and “Positioning” can also improve the overall capability to 81.34% with a cost of 370, which thus validates the efficiency of the proposed approach.

Key words: accountable capability improvement, interpretable capability evaluation, belief rule base (BRB)

. [J]. Journal of Systems Engineering and Electronics, 2024, 35(5): 1231-1244.

Xuan LI, Jiang JIANG, Jianbin SUN, Haiyue YU, Leilei CHANG. Accountable capability improvement based on interpretable capability evaluation using belief rule base[J]. Journal of Systems Engineering and Electronics, 2024, 35(5): 1231-1244.

图/表 17

参考文献 27

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Number	Sub-capability	Representative index	Type	Range
1	Surveillance (S)	Maximum surveillance distance/km	Benefit	[0, 4000]
2	Positioning (P)	Position precision coefficient/km	Cost	[0.1 4]
3	Identification (I)	Target identification belief level	Benefit	[0, 1]
4	Tracking (T)	Target track filtering precision	Cost	[0, 2.5]
5	Anti-jamming (AJ)	Disturbance suppression ration	Benefit	[0, 1]

Number	θ	IF (sub-capabilities)					THEN (overall capability)/%			Comment
Number	θ	S	P	I	T	AJ	High	Medium	Low	Comment
1	1	0	4	0	2.5	0	0	0	100	Least optimal condition
2	1	4000	0.1	1	0	1	100	0	0	Optimal condition
3	1	3000	1.5	0.6	1.2	0.8	70	30	0	Under influence
4	1	1500	3	0.3	2	0.4	40	40	20	Under influence
5	1	2000	2.5	0.4	1.8	0.5	50	30	20	Under influence
6	1	2500	2	0.5	1.6	0.6	50	40	10	Under influence

Rules	Matching degree calculation						Weight calculation
	Matching degree of a single sub-capability					Integrated matching degree	Initial weight	Weight
	S	P	I	T	AJ	Integrated matching degree	Initial weight	Weight
Rule 1	0.6	0	0	0	0	0.12	1	0.12
Rule 2	0	0	0	0.2	0	0.04	1	0.04
Rule 3	0.4	0	0	0	0.5	0.18	1	0.18
Rule 4	0	0	0.2	0.8	0	0.20	1	0.20
Rule 5	0	0.4	0.8	0	0	0.24	1	0.24
Rule 6	0	0.6	0	0	0.5	0.22	1	0.22

Sub-capabilities	Rule 1	Rule 2	Rule 3	Rule 4	Rule 5	Rule 6
S	0.6	0	0.4	0	0	0
P	0	0	0	0	0.4	0.6
I	0	0	0	0.2	0.8	0
T	0	0.2	0	0.8	0	0
AJ	0	0	0.5	0	0	0.5

Rule	High	Medium	Low
Rule 1	1	0	0
Rule 2	0	0	1
Rule 3	0.0334	0.2806	0.6860
Rule 4	0.2789	0.4637	0.2574
Rule 5	0.3667	0.4005	0.2328
Rule 6	0.3896	0.3457	0.2647

Accountable capability improvement based on interpretable capability evaluation using belief rule base

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Sub-capability	Contribution to the overall capability being scaled as “high”
S	0.3451
P	0.2140
I	0.1964
T	0.1255
AJ	0.1190

Scheme number	Key sub-capability			Overall capability/%			Cost
Scheme number	Surveillance	Positioning	Identification	High	Medium	Low	Cost
1	3600	1.80	0.50	61.05	25.44	13.51	52
2	3650	1.80	0.60	67.17	24.99	7.84	112
3	3650	1.50	0.60	69.70	25.46	4.84	142
4	3700	1.50	0.70	71.61	23.09	5.30	202
5	3750	0.80	0.70	75.83	18.38	5.79	322
6	3800	0.80	0.80	78.42	15.74	5.84	382
7	3800	0.80	0.90	80.67	13.57	5.76	392
8	3800	0.80	0.95	81.84	12.52	5.64	397

Scheme number	Key sub-capabilities		Overall capability/%			Cost
Scheme number	S	P	High	Medium	Low	Cost
1	3650	1.20	73.25	15.55	11.20	150
2	3700	1.00	77.40	13.58	9.02	220
3	3750	0.75	80.82	10.44	8.74	295
4	3800	0.50	81.34	10.30	8.36	370

Capability	Status of sub-capabilities	Overall capability (“high”)/%	Cost
Present capability (before capability improvement)	S=3 600 km; P=2.20 km; I=0.38; T=2.10; AJ=0.70	59.20	NA
Overall capability improved by initial BRB	S=3 600 km; P=2.20 km; I=0.38; T=2.10; AJ=0.70	81.84	397
Overall capability improved by optimized BRB	S=3 600 km; P=2.20 km; I=0.38; T=2.10 AJ=0.70	80.82	295
Overall capability improved by optimized BRB	S=3 600 km; P=2.20 km; I=0.38; T=2.10 AJ=0.70	81.34	370

Approach	Parameter setting	MAE	Analytical step	Adoptable
Initial BRB	Six rules, three scales in the capability evaluation results.	3.44e-03	Yes	Yes
Optimized BRB		6.25e-03	Yes	Yes
BPNN	The number of layers is 2, the number of neurons is 10, the epoch is 1000, the goal is 0, the transfer function is tansig	3.23e-03	No	No
SVM	Kernal function is RBF, C=0.2	1.41e-02	No	No

Number	θ	IF (sub-capabilities)					THEN (overall capability)/%
Number	θ	S	P	I	T	AJ	High	Medium	Low
1	0.8923	0	4	0	2.5	0	0	0	100
2	0.7964	1258	3.47	0.42	2.34	0.38	29.87	33.67	36.46
3	0.8623	1789	2.89	0.59	2.03	0.49	48.52	27.19	24.29
4	0.4364	2347	2.33	0.71	1.77	0.63	62.58	26.67	10.75
5	0.5188	2875	1.78	0.85	1.16	0.78	81.13	14.73	4.14
6	0.7638	4000	0.1	1	0	1	100	0	0