基于部分最大可满足性问题的动态系统中最小故障检测隔离集求解方法

doi:10.13229/j.cnki.jdxbgxb.20210792

Abstract

Abstract:

Selecting fault detectability and isolability set （FDIS） that can detect and isolate all faults is an important step in model-based fault detection and isolation of dynamic systems. This step usually requires the minimal cardinality of FDIS， that is， generating minimal fault detectability and isolability set （MFDIS）. The solution time of MFDIS increases exponentially with the increase of the scale of the problem. BILP complete method is the most common and efficient method to generate MFDIS in dynamic systems， but the efficiency of this method needs to be improved， and the complete solution of large-scale cases can’t be obtained in an acceptable time. In this paper， an approach for generating MFDIS based on partial maximum satisfiability problem （PMS） is proposed for the first time. The concept of MSO equivalent set is proposed， and some MSO sets are represented by MSO equivalent set to reduce the size of the problem. Then， the MFDIS genarating problem is transformed to PMS problem to improve the solving efficiency. The experimental results show that the proposed reduction method reduces the problem size to 8.22% of the original size on average； compared with BILP method， the efficiency of the proposed method is increased by 4.72 times on average.

Key words: model-based diagnosis, fault diagnosis, sensor selection, fault diagnosability analysis, partial maximum satisfiability problem

CLC Number:

TP306

Dan-tong OUYANG,Rui SUN,Xin-liang TIAN,Li-ming ZHANG,Ping-ping LIU. Approach for generating minimal fault detectability and isolability set in dynamic system based on partial maximum satisfiability problem[J].Journal of Jilin University(Engineering and Technology Edition), 2023, 53(4): 1163-1173.

Figures/Tables 9

Fig.1

Table 1

Selected MSOs of four-tank system"

MSO	方程集	故障集
$M S O 59$	$e 2, e 5, e 6, e 8, e 12, e 13, e 14,$ $e 15, e 16, e 20$	$f 2, f 4, f 5$
$M S O 68$	$e 2, e 5, e 6, e 7, e 9, e 12, e 13,$ $e 14, e 15, e 17, e 18, e 19, e 20$	$f 2, f 3, f 5, f 6$
$M S O 79$	$e 1, e 3, e 4, e 5, e 7, e 9, e 10,$ $e 12, e 13, e 14, e 15, e 17, e 18$ $e 19, e 20$	$f 1, f 3, f 5, f 6$
$M S O 90$	$e 1, e 3, e 4, e 5, e 7, e 8, e 9,$ $e 11, e 12, e 14, e 15, e 16$	$f 1, f 3, f 4$
$M S O 151$	$e 1, e 2, e 3, e 4, e 5, e 8, e 11, e 12,$ $e 14, e 15, e 17, e 18, e 19, e 20$	$f 1, f 2, f 4, f 6$

Table 1

Table 2

Detectablity attribute of MSOs"

MSO	方程集	故障集
$M S O 1$	$e 16, e 17, e 18, e 19, e 20$	$f 6$
$M S O 2$	$e 11, e 12, e 13, e 14, e 15, e 17,$ $e 18, e 19, e 20$	$f 5, f 6$
$M S O 3$	$e 11, e 12, e 13, e 14, e 15, e 16, e 20$	$f 5$
$M S O 4$	$e 8, e 10, e 12, e 13, e 14, e 15$ $e 17, e 18, e 19, e 20$	$f 4, f 5, f 6$
$M S O 5$	$e 8, e 10, e 12, e 13, e 14, e 15, e 16,$ $e 20$	$f 4, f 5$
$M S O 6$	$e 8, e 10, e 11, e 13, e 16, e 17, e 18,$ $e 19$	$f 4, f 6$

Table 2

Fig.2

Table 3

Fig.3

Table 4

Table 5

Table 6

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硬子句		软子句
Weight	子句	Weight	子句
7	1 6 0	1	-1 0
7	1 2 0	1	-2 0
7	3 5 0	1	-3 0
7	2 3 0	1	-4 0
7	2 3 4 5 0	1	-5 0
7	5 0	1	-6 0
7	6 0

故障个数	MSO等价集平均数	约简百分比/%
7	56	99.05
8	86	98.55
9	113	98.09
10	155	97.38
11	195	96.71
12	271	95.42
13	346	94.16
14	461	92.22
15	561	90.53
16	710	88.01
17	876	85.21
18	1044	82.37

故障个数	集合覆盖规模	BILP	QMaxSAT	提升百分比
7	（42， 5 923）	21	2	9.5
8	（56， 5 923）	1 048	127	7.25
9	（72， 5 923）	1 869	243	6.69
10	（90， 5 923）	12 285	1 846	5.65
11	（110， 5 923）	24 135	4 657	4.18

Fault number	Hitting set property	SPHS	BILP	QMaxSAT	Increased efficiency
7	（42， 56.4）	18.03	0.03	0.002	14
8	（56， 74.1）	173.43	0.05	0.009	5.08
9	（72， 100.6）	32 876.34	0.09	0.06	0.56
10	（90， 173.7）	time out	0.25	0.18	0.40
11	（110， 224.8）	time out	0.53	0.37	0.45
12	（132， 284）	time out	3.22	0.67	3.80
13	（156， 341.9）	time out	11	2.56	3.30
14	（182，469.6）	time out	40	12	2.33
15	（210，540.5）	time out	288	79	2.65
16	（240，673.2）	time out	927	158	5.87
17	（272，877.6）	time out	1 462	264	4.54
18	（306，1 044）	time out	2 649	570	3.65

Approach for generating minimal fault detectability and isolability set in dynamic system based on partial maximum satisfiability problem

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