基于故障树的复杂装备模糊贝叶斯网络推理故障诊断

doi:10.12305/j.issn.1001-506X.2021.05.12

Abstract

Abstract:

The small-lot and customized attributes of complex equipment determines that there are relatively many uncertainties in the process of its life cycle, so potential fault hazard of complex equipment is inevitable, and the fault diagnosis of complex equipment is particularly important. Therefore, a fuzzy Bayesian network inference model for complex equipment fault diagnosis based on fault tree is proposed. First, the fault tree model for complex equipment is established by analyzing its structural composition. Secondly, the fault tree transformation method is used to construct the Bayesian network topology structure based on fault tree. Then, in view of lacking of structural data of complex equipment and the uncertainty of expert scoring, the fuzzy set theory is used to determine the parameters such as conditional probability. Finally, a case study is carried out, and the fault nodes (potential faults) of the cases are diagnosed by using causal inference and diagnostic inference in fuzzy Bayesian network inference, which is proved effective. The research results not only solves the problem that it is not practical to construct the optimal network by using search function in Bayesian network, but also solves the problem of data deficiencies of complex equipment and uncertainty of expert scoring by using fuzzy set theory. The proposed model is suitable not only for determining fault in process diagnosis, but also recognizing potential risk in advance diagnosis, and also play a role in the detection and evaluation of the improvement effect of faults (or potential faults) nodes.

Key words: fault tree, complex equipment, fuzzy Bayesian network, fault diagnose

CLC Number:

Hongzhuan CHEN, Aijia ZHAO, Tengjiao LI, Congcong CAI, Shuo CHENG, Chunli XU. Fuzzy Bayesian network inference fault diagnosis of complex equipment based on fault tree[J]. Systems Engineering and Electronics, 2021, 43(5): 1248-1261.

Figures/Tables 19

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类型	名称	符号	含义
事件	底事件		底事件是构成故障树最底层级的事件, 也就是无法进一步细化的系统中最基本的组成事件, 包括基本事件与非基本事件
	基本事件		基本事件是分析中能够清晰掌握其发生规律, 容易针对性改正, 且无需再查明其发生原因的事件
	非基本事件		非基本事件是故障树分析中未探明的事件, 原则上需要进一步控明其原因, 但暂时无法获取发生原因或没有必要掌握其原因的事件, 非基本事件对系统的影响微乎其微, 定性分析或定量计算时一般可以忽略不计
	结果事件		结果事件是故障树分析中逻辑门的输出事件, 包括顶事件和中间事件
	顶事件		顶事件在故障树中代表系统整体故障的事件或状态, 是故障树分析中的结果, 也是系统模型中最不希望出现的状态
	中间事件		中间事件是构成故障树模型中顶事件和底事件以外的中间层级的事件
	开关事件		开关事件是指在正常工作条件下必然发生或必然不发生的事件
	条件事件		条件事件是规定逻辑门是否起作用的限制事件
逻辑门	与门		与门表示所有输入事件都发生时, 输出事件才发生
	或门		或门表示只要有一个输入事件发生, 输出事件就发生
	异或门		异或门表示只有单个输入事件发生时, 输出事件才发生
	表决门		r/n表决门表示在n个输入事件中至少有r个事件发生, 输出事件才发生

u₂₁	P(u₁₁)	P(u₂₂\|u₁₁)	P(u₂₁\|u₁₁)
T	a	b	c
F	1-a	1-b	1-c

u₂₁	u₂₂	P(u₃₁\|u₂₁, u₂₂)
T	T	d
F	T	e
T	F	f
F	F	g

符号	含义	举例说明
T_ijk	T_ijk=μ_{v_k}(u_ij)代表节点u_ij发生的第k个评语等级的隶属度	T₁₂₃表示复杂装备贝叶斯网络中故障层第2个节点的故障发生可能性为“一般”的隶属度
$ {r_{\overline i \overline j k}}$	${r_{\overline i \overline j k}} = {\mu _{{v_k}}}\left( {{u_{\overline i \overline j }}} \right) $代表节点u_ij不发生的第k个评语等级的隶属度	r_{${\rm{\bar 1}}$${\rm{\bar 2}}$${\rm{\bar 3}}$}表示复杂装备贝叶斯网络中故障层第2个节点的故障不发生可能性为“一般”的隶属度
r_{iji^′j^′k}	$r_{i j i^{\prime} j^{\prime} k}=\mu_{v_{k}}\left(u_{i^{\prime} j^{\prime}}, u_{i j}\right) $代表节点u_ij与节点u_i^′j^′同时发生的第k个评语等级的隶属度	r₁₂₃₄₅表示复杂装备贝叶斯网络中故障层第2个节点与状态层第4个件节点同时发生故障的可能性为“很低”的隶属度
$r_{{i^\prime }{j^\prime }\mid ijk}^\prime $	$r_{{i^\prime }{j^\prime }\mid ijk}^\prime =\mu_{v_{k}}\left(u_{i^{\prime} j^{\prime}}, u_{i j}\right)$代表节点u_ij发生引发节点$u_{i^{\prime} j^{\prime}} $发生的第k个评语等级的隶属度	r₁₂₃₄₅^′表示复杂装备贝叶斯网络中故障层第2个节点故障发生导致状态层第4个件节点发生故障的可能性为“很低”的隶属度

故障	符号	先验概率
热压罐漏压	A	0.07
检具故障	B	0.05
碳纤破损	C	0.07
蜂窝超尺寸	D	0.17
铺贴故障	E	0.87
机加量偏差	F	0.12
装配出错	G	0.06
设备故障	H	-
材料故障	I	-
操作故障	J	-
复合材料故障	K	-

事件概率	可能性/%
事件概率	90~100	80~90	70~80	60~70	50~60	40~50	30~40	20~30	10~20	0~10
P(H=1\|A=1, B=0)	11	1	-	-	-	-	-	-	-	-
P(H=1\|A=0, B=1)	-	-	-	-	-	-	-	4	6	2
P(I=1\|C=1, D=0)	-	-	-	-	-	-	-	6	5	1
P(I=1\|C=0, D=1)	-	-	-	-	-	-	-	1	3	8
P(J=1\|E=1, F=1, G=0)	1	7	4	-	-	-	-	-	-	-
P(J=1\|E=1, F=0, G=1)	-	7	5	-	-	-	-	-	-	-
P(J=1\|E=1, F=0, G=0)	-	-	-	-	1	6	3	2	-	-
P(J=1\|E=0, F=1, G=1)	-	-	-	-	-	1	7	3	1	-
P(J=1\|E=0, F=1, G=0)	-	-	-	-	-	-	1	5	6	-
P(J=1\|E=0, F=0, G=1)	-	-	-	-	-	-	-	5	7	-
P(K=1\|H=1, I=1, J=0)	9	3	-	-	-	-	-	-	-	-
P(K=1\|H=1, I=0, J=1)	10	2	-	-	-	-	-	-	-	-
P(K=1\|H=1, I=0, J=0)	3	4	5	-	-	-	-	-	-	-
P(K=1\|H=0, I=1, J=1)	2	5	5	-	-	-	-	-	-	-
P(K=1\|H=0, I=1, J=0)	-	-	-	-	-	1	10	1	-	-
P(K=1\|H=0, I=0, J=1)	-	8	3	1	-	-	-	-	-	-

Fuzzy Bayesian network inference fault diagnosis of complex equipment based on fault tree

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故障	征兆	关联强度(条件概率)
热压罐漏压A 检具故障B	设备故障H	P(H=1\|A=1, B=1)=1 P(H=0\|A=1, B=1)=0
		P(H=1\|A=1, B=0)=0.941 7 P(H=0\|A=1, B=0)=0.058 3
		P(H=1\|A=0, B=1)=0.166 7 P(H=0\|A=0, B=1)=0.833 3
		P(H=1\|A=0, B=0)=0 P(H=0\|A=0, B=0)=1
碳纤破损C 蜂窝超尺寸D	材料故障I	P(I=1\|C=1, D=1)=1 P(I=0\|C=1, D=1)=0
		P(I=1\|C=1, D=0)=0.191 7 P(I=0\|C=1, D=0)=0.808 3
		P(I=1\|C=0, D=1)=0.091 7 P(I=0\|C=0, D=1)=0.908 3
		P(I=1\|C=0, D=0)=0 P(I=1\|C=0, D=0)=1
铺贴故障E 机加量偏差F 装配出错G	操作故障J	P(J=1\|E=1, F=1, G=1)=1 P(J=0\|E=1, F=1, G=1)=0
		P(J=1\|E=1, F=1, G=0)=0.82 5 P(J=0\|E=1, F=1, G=0)=0.17 5
		P(J=1\|E=1, F=0, G=1)=0.808 3 P(J=0\|E=1, F=0, G=1)=0.191 7
		P(J=1\|E=1, F=0, G=0)=0.4 P(J=0\|E=1, F=0, G=0)=0.6
		P(J=1\|E=0, F=1, G=1)=0.316 7 P(J=0\|E=0, F=1, G=1)=0.683 3
		P(J=1\|E=0, F=1, G=0)=0.208 3 P(J=0\|E=0, F=1, G=0)=0.791 7
		P(J=1\|E=0, F=0, G=1)=0.191 7 P(J=0\|E=0, F=0, G=1)=0.808 3
		P(J=1\|E=0, F=0, G=0)=0 P(J=0\|E=0, F=0, G=0)=1
设备故障H 材料故障I 操作故障J	复合材料报废K	P(K=1\|H=1, I=1, J=1)=1 P(K=0\|H=1, I=1, J=1)=0
		P(K=1\|H=1, I=1, J=0)=0.92 5 P(K=0\|H=1, I=1, J=0)=0.07 5
		P(K=1\|H=1, I=0, J=1)=0.933 3 P(K=0\|H=1, I=0, J=1)=0.066 7
		P(K=1\|H=1, I=0, J=0)=0.833 3 P(K=0\|H=1, I=0, J=0)=0.166 7
		P(K=1\|H=0, I=1, J=1)=0.825 P(K=0\|H=0, I=1, J=1)=0.175
		P(K=1\|H=0, I=1, J=0)=0.35 P(K=0\|H=0, I=1, J=0)=0.65
		P(K=1\|H=0, I=0, J=1)=0.808 3 P(K=0\|H=0, I=0, J=1)=0.191 7
		P(K=1\|H=0, I=0, J=0)=0 P(K=0\|H=0, I=0, J=0)=1

条件概率	专家编号
条件概率	1	2	3	4	5	6	7	8	9	10	11	12	均值
P(H=1\|A=1, B=1)=1	1	1	1	1	1	1	1	1	1	1	1	1	1
P(H=1\|A=1, B=0)=1	0.9	0.8	1	1	1	1	1	1	1	1	1	1	0.975 0
P(H=1\|A=0, B=1)=0.2	0	0	0.3	0.3	0.25	0.25	0.1	0.2	0.1	0.15	0.1	0.1	0.154 2
P(H=1\|A=0, B=0)=0	0	0	0	0	0	0	0	0	0	0	0	0	0
P(I=1\|C=1, D=1)=1	1	1	1	1	1	1	1	1	1	1	1	1	1
P(I=1\|C=1, D=0)=0.2	0.1	0.2	0.1	0.2	0.2	0.3	0.3	0.2	0.25	0.1	0	0.25	0.183 3
P(I=1\|C=0, D=1)=0.1	0	0.3	0	0.1	0	0.1	0	0.2	0	0	0.05	0.05	0.066 7
P(I=1\|C=0, D=0)=0	0	0	0	0	0	0	0	0	0	0	0	0	0
P(J=1\|E=1, F=1, G=1)=1	1	1	1	1	1	1	1	1	1	1	1	1	1
P(J=1\|E=1, F=1, G=0)=0.8	0.8	0.7	0.75	0.9	0.9	0.9	0.85	0.9	0.9	0.9	0.7	0.8	0.833 3
P(J=1\|E=1, F=0, G=1)=0.8	0.9	0.85	0.85	0.8	0.8	0.8	0.7	0.8	0.8	0.9	0.7	0.8	0.809 1
P(J=1\|E=1, F=0, G=0)=0.4	0.3	0.4	0.35	0.35	0.4	0.5	0.5	0.5	0.5	0.4	0.3	0.6	0.409 1
P(J=1\|E=0, F=1, G=1)=0.3	0.3	0.5	0.2	0.35	0.2	0.4	0.3	0.3	0.4	0.1	0.3	0.2	0.295 8
P(J=1\|E=0, F=1, G=0)=0.2	0.3	0.1	0.3	0.4	0.1	0.2	0.2	0.15	0.1	0.2	0.1	0.3	0.204 2
P(J=1\|E=0, F=0, G=1)=0.2	0.3	0.15	0.2	0.15	0.3	0.1	0.1	0.2	0.2	0.1	0.2	0.1	0.181 8
P(J=1\|E=0, F=0, G=0)=0	0	0	0	0	0	0	0	0	0	0	0	0	0
P(K=1\|H=1, I=1, J=1)=1	1	1	1	1	1	1	1	1	1	1	1	1	1
P(K=1\|H=1, I=1, J=0)=0.9	1	0.85	0.95	1	1	1	0.95	0.8	1	0.9	0.8	1	0.937 5
P(K=1\|H=1, I=0, J=1)=0.9	1	0.85	1	0.9	0.8	1	0.9	0.9	1	1	1	1	0.945 8
P(K=1\|H=1, I=0, J=0)=0.8	0.9	0.85	1	0.7	0.8	1	0.8	0.9	1	0.7	0.7	0.7	0.837 5
P(K=1\|H=0, I=1, J=1)=0.9	0.8	0.85	0.85	0.9	0.7	1	0.8	0.8	0.9	0.7	1	0.7	0.833 3
P(K=1\|H=0, I=1, J=0)=0.3	0.3	0.45	0.3	0.4	3	0.2	0.4	0.3	0.35	0.3	0.3	0.35	0.554 2
P(K=1\|H=0, I=0, J=1)=0.8	0.9	0.75	0.9	0.8	0.7	0.9	0.8	0.7	0.6	0.9	0.9	0.9	0.812 5
P(K=1\|H=0, I=0, J=0)=0	0	0	0	0	0	0	0	0	0	0	0	0	0

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