基于测试性<i>D</i>矩阵的多故障诊断与维修策略

田恒; 段富海; 樊亮; 桑勇; 史萌

doi:10.13700/j.bh.1001-5965.2017.0225

基于测试性D矩阵的多故障诊断与维修策略

doi: 10.13700/j.bh.1001-5965.2017.0225

田恒¹,
段富海^1, ,,
樊亮²,
桑勇¹,
史萌²

1.
大连理工大学机械工程学院, 大连 116024
2.
中国航空工业集团公司西安飞行自动控制研究所惯性技术航空科技重点实验室, 西安 710065

基金项目:

航空科学基金 20150863003

详细信息

作者简介:
田恒男, 博士研究生。主要研究方向:故障诊断与测试性分析

段富海男, 教授, 博士生导师。主要研究方向:可靠性与测试性的设计分析

通讯作者:
段富海, E-mail: duanfh@dlut.edu.cn

中图分类号: TP206.3
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- 被引次数: 0
出版历程
- 收稿日期: 2017-04-13
- 录用日期: 2017-05-19
- 网络出版日期: 2018-04-20

Multiple fault diagnosis and maintenance strategy based on testability D matrix

1.
School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China
2.
Aviation Key Laboratory of Science and Technology on Inertia, AVIC Xi'an Flight Automatic Control Research Institute, Xi'an 710065, China

Funds:

Aeronautical Science Foundation of China 20150863003

More Information

Corresponding author: DUAN Fuhai, E-mail: duanfh@dlut.edu.cn

摘要

摘要:
针对复杂的多故障诊断问题以及多故障直接处理方法实现的难点，在测试性D矩阵基础上，提出了一种基于单故障化的多故障诊断与维修策略（MFDMSTS）。首先，在多故障假设下引入析取运算，定义了可隔离单故障和可隔离多故障，据此定义将多故障转化为单故障，并将转化的单故障与测试集组成新的D矩阵；然后，运用单故障诊断算法处理新的D矩阵，得到最优诊断树；最后，针对诊断树的不同叶子节点，提出了多故障诊断与维修策略。实例验算表明：MFDMSTS能降低平均诊断费用和平均诊断步数，并大幅降低误修率。
- 测试性D矩阵 /
- 多故障诊断 /
- 析取运算 /
- 多故障单故障化 /
- 维修策略
Abstract:
In view of the complicated multiple fault diagnosis problems and difficulties in the realization of multiple fault direct processing algorithm, on the basis of testability D matrix and single fault algorithm, a novel multiple fault diagnosis and maintenance strategy based on translating into single fault (MFDMSTS) is introduced. Firstly, under the assumption of multiple faults, disjunctive operation is introduced, and isolable single fault and isolable multiple faults are defined. According to the definitions, single fault, which composes a new D matrix with test set, is translated into from multiple faults. Secondly, single fault diagnosis algorithm is used to process the new D matrix, and the optimal diagnostic tree is obtained. Finally, a further multiple fault diagnosis and maintenance strategy is proposed for different leaf nodes in the diagnostic tree. Experimental verification demonstrates that MFDMSTS is an effective way to reduce average diagnostic cost and average diagnostic steps, and to greatly reduce the rate of maintenance error.
- testability D matrix /
- multiple fault diagnosis /
- disjunctive operation /
- translating multiple faults into single fault /
- maintenance strategy

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图 1 基于MFDMSTS和AO^*的新D矩阵诊断树

Figure 1. Diagnostic tree of new D matrix based on MFDMSTS and AO^*

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图 2 叶子节点s₉的维修诊断树

Figure 2. Maintenance diagnostic tree of leaf node s₉

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图 3 叶子节点s₁₀的维修诊断树

Figure 3. Maintenance diagnostic tree of leaf node s₁₀

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表 1 某电路系统的D矩阵^[10]

Table 1. D matrix of a circuit system^[10]

故障状态	测试					概率
故障状态	t₁	t₂	t₃	t₄	t₅	概率
f₁	0	1	0	0	1	0.014
f₂	0	0	1	1	0	0.027
f₃	1	0	0	1	1	0.125
f₄	1	1	0	0	0	0.068
f₅	1	1	1	1	0	0.146

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表 2 多故障单故障化的结果

Table 2. Results of translating multiple faults into single fault

I_FS	组合数	F_IT	故障状态	概率p(F_Sⁱ)	归一化概率p(s_i)
f₀	1	{{t₂, t₄}, {t₁, t₂, t₃}, …, {t₁, t₂, t₃, t₄, t₅}}	s₀		0.671 3
f₁	1	{{t₄, t₁}, {t₃, t₁}}	s₁	0.014 000	0.009 5
f₂	1	{{t₂, t₅}, {t₂, t₁}, {t₁, t₅}}	s₂	0.027 000	0.018 6
f₃	1	{{t₂, t₃}}	s₃	0.125 000	0.095 9
f₄	1	{{t₃, t₅}, {t₄, t₅}}	s₄	0.068 000	0.049 0
f₁f₂	1	{{t₁}}	s₅	0.000 378	0.000 3
f₂f₃	1	{{t₂}}	s₆	0.003 400	0.002 3
f₁f₄	1	{{t₃, t₄}, {t₄}}	s₇	0.000 950	0.000 6
f₁f₃f₄	3	{{t₃}}	s₈	0.010 400	0.007 0
f₂f₄f₅	5	{{t₅}}	s₉	0.162 000	0.129 8
f₁f₂f₃f₄f₅	16		s₁₀	0.022 800	0.015 7
总和	32				1.000 0

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表 3 MFDMSTS得到的新D矩阵

Table 3. New D matrix obtained by MFDMSTS

故障状态	测试					概率
故障状态	t₁	t₂	t₃	t₄	t₅	概率
s₀	0	0	0	0	0	0.671 3
s₁	0	1	0	0	1	0.009 5
s₂	0	0	1	1	0	0.018 6
s₃	1	0	0	1	1	0.095 9
s₄	1	1	0	0	0	0.049 0
s₅	0	1	1	1	1	0.000 3
s₆	1	0	1	1	1	0.002 3
s₇	1	1	0	0	1	0.000 6
s₈	1	1	0	1	1	0.007 0
s₉	1	1	1	1	0	0.129 8
s₁₀	1	1	1	1	1	0.015 7

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表 4 MFDMSTS、Sure3^*和Sure3的诊断结果对比

Table 4. Comparison of diagnosis results among MFDMSTS, Sure3^* and Sure3

算法	C_ost	N_D	FDR/%	FIR/%
MFDMSTS	2.390	3.727	100	84.75
Sure3^*	2.515	3.727	100	84.75
Sure3	2.528	4.154	100	85.46

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表 5 MFDMSTS与Sure3的维修策略对比

Table 5. Comparison of maintenance strategy between MFDMSTS and Sure3

多故障状态	组合数	s_i中的组合故障	MFDMSTS		Sure3
多故障状态	组合数	s_i中的组合故障	维修策略	误修率/%	维修策略	误修率/%
s₁, s₂, s₃, s₄, s₅, s₆, s₇	1	f₁, f₂, f₃, f₄, f₁f₄, f₂f₃	直接维修检测的故障集	0	直接维修检的故障集	0
s₈	3	f₃f₄, f₁f₃, f₁f₃f₄	维修f₃f₄，测试，维修f₁，结束	0.12	维修f₃，测试，维修f₁，测试，维修f₄	0
s₉	5	f₅, f₄f₅, f₂ f₅, f₂f₄, f₂f₄f₅	图 2	0.15	维修f₂f₄f₅	12.95

s₁₀	16	f₃f₅, f₁f₅, f₃ f₄ f₅, …, f₁f₂f₃f₄f₅	图 3	0.26	维修f₁f₂f₃f₄f₅	1.57

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表 6 某型惯导二次电源的D矩阵

Table 6. D matrix for secondary electrical power of an inertial navigation

故障状态	测试						概率
故障状态	T₁	T₂	T₃	T₄	T₅	T₆	概率
F₁	1	1	1	0	1	1	0.063
F₂	0	0	1	0	0	0	0.021
F₃	0	1	0	0	0	0	0.013
F₄	0	0	1	1	0	0	0.037
F₅	0	0	0	0	0	1	0.017
F₆	0	0	0	1	0	0	0.023
F₇	0	0	0	0	1	1	0.034
F₈	1	1	0	0	0	0	0.022
F₉	0	0	1	0	1	0	0.030

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表 7 MFDMSTS与TEAMS仿真分析结果对比

Table 7. Comparison of analysis results between MFDMSTS and TEAMS simulation

算法	C_ost	N_D	FDR/%	FIR/%	M_R-avg/%
MFDMSTS	4.22	5.45	100	82.69	0.012 8
TEAMS	4.22	5.45	100	82.69

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