Optimal selection of tests for fault detection and isolation in multi-operating mode system

doi:10.21629/JSEE.2019.02.20

Abstract

Abstract:

The complex systems are often in the structure of multi-operating modes, and the components implementing system functions are different under different operation modes, which results in the problems that components often fail in different operating modes, faults can be only detected in specified operating modes, tests can be available in specified operating modes, and the cost and efficiency of detecting and isolating faults are different under different operating modes and isolation levels. Aiming at these problems, an optimal test selection method for fault detection and isolation in the multi-operating mode system is proposed by using the fault pair coding and rollout algorithm. Firstly, the faults in fault-test correlation matrices under different operating modes are combined to fault-pairs, which is used to construct the fault pair-test correlation matrices under different operating modes. Secondly, the final fault pair-test correlation matrix of the multioperating mode system is obtained by operating the fault pair-test correlation matrices under different operating modes. Based on the final fault pair-test correlation matrix, the necessary tests are selected by the rollout algorithm orderly. Finally, the effectiveness of the proposed method is verified by examples of the optimal test selection in the multi-operating mode system with faults isolated to different levels. The result shows that the proposed method can effectively mine the fault detection and isolation ability of tests and it is suitable for the optimal test selection of the multi-operating mode system with faults isolated to the replacement unit and specific fault.

Key words: operating mode, test optimization, fault pair coding, fault detection, fault isolation

Yuanhong LIU. Optimal selection of tests for fault detection and isolation in multi-operating mode system[J]. Journal of Systems Engineering and Electronics, 2019, 30(2): 425-434.

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Fault	Operating mode 1				Operating mode 2					Operating mode N
Fault	t₁₁	t₁₂	⋯	t_1K	t₂₁	t₂₂	⋯	t_2K	⋯	t_N1	t_N2	⋯	t_NK
f⁰	0	0	⋯	0	0	0	⋯	0	⋯	0	0	⋯	0	p₀
f₁	d₁₁¹	d₁₂¹	⋯	d_1K¹	d₁₁²	d₁₂²	⋯	d_1K²	⋯	d₁₁^N	d₁₂^N	⋯	d_1K^N	p₁
⋮	⋮	⋮	⋱	⋮	⋮	⋮	⋱	⋮	⋱	⋮	⋮	⋱	⋮	⋮
f_m	d_m1¹	d_m2¹	⋯	d_mK¹	d_m1²	d_m2²	⋯	d_mK²	⋯	d_m1^N	d_m2^N	⋯	d_mK^N	p_m

Fault	Subject unit	Operating mode 1							Operating mode 2							Probability
Fault	Subject unit	t₁₁	t₁₂	t₁₃	t₁₄	t₁₅	t₁₆	t₁₇	t₂₁	t₂₂	t₂₃	t₂₄	t₂₅	t₂₆	t₂₇	Probability
f₀	U₀	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.700 0
f₁	U₁	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0.030 2
f₂	U₂	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0.050 5
f₃	U₂	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0.013 2
f₄	U₂	1	1	1	1	0	1	0	1	1	0	0	0	0	0	0.054 4
f₅	U₃	1	1	1	1	1	0	0	0	1	1	0	0	0	0	0.002 4
f₆	U₃	0	0	0	0	1	0	1	0	0	0	0	0	0	0	0.021 3
f₇	U₃	0	0	0	0	1	1	1	0	0	0	0	0	0	0	0.003 6
f₈	U₄	0	0	0	0	0	1	1	0	0	0	0	0	0	0	0.007 5
f₉	U₄	0	0	0	0	1	0	1	0	0	1	1	0	0	0	0.063 4
f₁₀	U₄	0	0	0	0	0	1	1	1	0	0	1	0	0	0	0.053 5

Test name	T₁	T₂	T₃	T₄	T₅	T₆	T₇
Test cost	1	1	1	1	1	1	0.5

Serial number	Fault pair	T₁	T₂	T₃	T₄	T₅	T₆	T₇	Probability
1	(f₀ f₁)	0	0	0	0	0	1	0	0.021 14
2	(f₀ f₂)	0	1	0	1	0	0	0	0.035 35
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
45	(f₅ f₁₀)	1	1	1	1	1	1	1	0.000 13
46	(f₆ f₇)	0	0	0	0	0	1	0	0.000 08
47	(f₆ f₈)	0	0	0	0	1	1	0	0.000 16
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
49	(f₆ f₁₀)	1	0	0	1	1	1	0	0.001 14
50	(f₇ f₈)	0	0	0	0	1	0	0	0.000 03
51	(f₇ f₉)	0	0	1	1	0	1	0	0.000 23
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
55	(f₉ f₁₀)	1	0	1	0	1	1	0	0.003 39

Serial number	Fault pair	T₁	T₂	T₃	T₄	T₅	T₆	T₇	Probability
1	(f₀ f₁)	0	0	0	0	0	1	0	0.021 14
2	(f₀ f₂)	0	1	0	1	0	0	0	0.035 35
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
26	(f₃ f₅)	1	1	1	1	0	0	0	0.000 03
27	(f₃ f₆)	0	0	0	0	0	1	1	0.000 05
28	(f₃ f₇)	0	0	0	0	0	1	1	0.000 05
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
43	(f₆ f₁₀)	1	0	0	1	1	1	0	0.001 14
44	(f₇ f₈)	0	0	0	0	1	0	0	0.000 03
45	(f₇ f₉)	0	0	1	1	0	1	0	0.000 23
46	(f₇ f₁₀)	1	0	0	1	1	0	0	0.003 19