A dependency matrix processing algorithm to prioritize high incidence faults

doi:10.23919/JSEE.2025.000092

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (4): 962-971.doi: 10.23919/JSEE.2025.000092

• SYSTEMS ENGINEERING • Previous Articles

A dependency matrix processing algorithm to prioritize high incidence faults

Jiashuo ZHANG¹(), Derong CHEN¹(), Peng GAO¹^,*(), Jin’gang ZHANG²(), Yulong ZHANG³()

¹ School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China
² Beijing Institute of Astronautical System Engineering, Beijing 100076, China
³ Beijing Electro-Mechanical Engineering Institution, Beijing 100074, China

Received:2024-02-20 Online:2025-08-18 Published:2025-09-04
Contact: Peng GAO E-mail:18631209081@163.com;asd18832209082@163.com;gaopeng@bit.edu.cn;dsa18832209082@163.com;Mr.yulongzhang@foxmail.com
About author:
ZHANG Jiashuo was born in 1993. He received his B.M. degree from Beijing Institute of Technology in 2019. He is pursuing his Ph.D. degree in Beijing Institute of Technology. His research interests include system testability design and safety system testing. E-mail: 18631209081@163.com

CHEN Derong was born in 1966. She received her Ph.D. degree from Beijing Institute of Technology, in 2002. She is currently a professor in the School of Mechatronical Engineering, Beijing Institute of Technology. Her research interests include vision measurement and data compression and system diagnosis. E-mail: asd18832209082@163.com

GAO Peng was born in 1982. He received his Ph.D. degree from Tsinghua University in 2018. He is currently an assistant professor in the School of Mechatronical Engineering, Beijing Institute of Technology. His research interests include testability modelling and anomaly detection techniques. E-mail: gaopeng@bit.edu.cn

ZHANG Jin’gang was born in 1986. He received his M.S. degree from Tsinghua University, Beijing, China, in 2011. He is currently a senior engineer in Beijing Institute of Astronautical System Engineering. His research interests include measurement, measurement and control, and communication. E-mail: dsa18832209082@163.com

ZHANG Yulong was born in 1996. He received his M.S. degree from Beijing Institute of Technology, in 2021. He is currently working in Beijing Electro-Mechanical Engineering Institution. His research interests include target detection, electromechanical coupling, observation and control technology. E-mail: Mr.yulongzhang@foxmail.com

Abstract

Abstract:

The operational readiness test (ORT), like weapon testing before firing, is becoming more and more important for systems used in the field. However, the test requirement of the ORT is distinctive. Specifically, the rule of selecting test items should be changed in different test turns, and whether there is a fault is more important than where the fault is. The popular dependency matrix (D-matrix) processing algorithms becomes low efficient because they cannot change their optimizing direction and spend unnecessary time on fault localization and isolation. To this end, this paper proposes a D-matrix processing algorithm named piecewise heuristic algorithm for D-matrix (PHAD). Its key idea is to use a piecewise function comprised of multiple different functions instead of the commonly used fixed function and switch subfunctions according to the test stage. In this manner, PHAD has the capability of changing optimizing direction, precisely matching the variant test requirements, and generating an efficient test sequence. The experiments on the random matrixes of different sizes and densities prove that the proposed algorithm performs better than the classical algorithms in terms of expected test cost (ETC) and other metrics. More generally, the piecewise heuristic function shows a new way to design D-matrix processing algorithm and a more flexible heuristic function to meet more complicated test requirements.

Key words: fault diagnosis, heuristic function, operational readiness test, piecewise function, testability

Jiashuo ZHANG, Derong CHEN, Peng GAO, Jin’gang ZHANG, Yulong ZHANG. A dependency matrix processing algorithm to prioritize high incidence faults[J]. Journal of Systems Engineering and Electronics, 2025, 36(4): 962-971.

Figures/Tables 9

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References 17

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Fault state	Test				$p\left( {{f_i}} \right)$
Fault state	${t_1}$	${t_2}$	${t_3}$	${t_4}$	$p\left( {{f_i}} \right)$
${f_0}$	1	0	0	0	0.88
${f_1}$	0	1	0	0	0.10
${f_2}$	0	0	1	0	0.01
${f_3}$	0	0	0	1	0.01

Condition	Dimension	Density/%
Condition 1	21×20	10
Condition 2	21×20	60
Condition 3	61×60	10
Condition 4	61×60	60

Condition	Dimension	Density/%	N	Condition	Dimension	Density/%	N
Condition 1	21×20	10	2	Condition 7	61×60	10	2
Condition 2	21×20	10	3	Condition 8	61×60	10	5
Condition 3	21×20	10	4	Condition 9	61×60	10	8
Condition 4	21×20	60	2	Condition 10	61×60	60	2
Condition 5	21×20	60	3	Condition 11	61×60	60	5
Condition 6	21×20	60	4	Condition 12	61×60	60	8

Density/%	Expected test cost
	N=3				N is dynamic
	PHAD-IG	PHAD-WFD	IG	WFD	PHAD-IG	PHAD-WFD	IG	WFD
10	3.1781	3.3340	3.1781	3.5102	3.2173	3.2997	3.2322	3.6136
20	2.2698	2.2679	2.2994	2.4368	2.2666	2.2754	2.3281	2.4186
30	1.7661	1.7510	2.0003	1.8555	1.8217	1.7451	2.0021	1.8306
40	1.4574	1.4554	1.9466	1.5424	1.5641	1.4744	1.9564	1.5351
50	1.3038	1.3038	1.9528	1.3516	1.3785	1.3024	1.9473	1.3420
60	1.1854	1.1854	1.9345	1.2177	1.2699	1.1927	1.9320	1.2256
70	1.1004	1.1004	1.9039	1.1255	1.1764	1.1025	1.9017	1.1189
80	1.0349	1.0349	1.6743	1.0518	1.0867	1.0410	1.6952	1.0612
90	1.0008	1.0008	1.4082	1.0030	1.0011	1.0011	1.4129	1.0055

Density/%	Expected test cost
	N=8				N is dynamic
	PHAD-IG	PHAD-WFD	IG	WFD	PHAD-IG	PHAD-WFD	IG	WFD
10	4.1622	4.2195	4.1627	4.5409	4.1413	4.2053	4.1492	4.5666
20	2.5308	2.5307	2.5758	2.7115	2.5370	2.5737	2.5799	2.6982
30	1.9480	1.9480	2.0771	2.0356	1.9556	1.9645	2.0809	2.0608
40	1.6234	1.6234	1.9875	1.6859	1.6595	1.6298	1.9857	1.6709
50	1.4076	1.4076	1.9801	1.4553	1.4973	1.4262	1.9801	1.4550
60	1.2604	1.2604	1.9762	1.2934	1.3347	1.2653	1.9748	1.2985
70	1.1550	1.1550	1.8916	1.1745	1.2333	1.1544	1.8905	1.1714
80	1.0752	1.0752	1.6375	1.0869	1.1166	1.0803	1.6088	1.0958
90	1.0133	1.0133	1.3512	1.0190	1.0341	1.0168	1.3479	1.0248

A dependency matrix processing algorithm to prioritize high incidence faults

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