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

系统工程与电子技术 ›› 2021, Vol. 43 ›› Issue (5): 1248-1261.doi: 10.12305/j.issn.1001-506X.2021.05.12

基于故障树的复杂装备模糊贝叶斯网络推理故障诊断

陈洪转^1,*(), 赵爱佳¹(), 李腾蛟¹(), 蔡匆聪¹(), 程硕¹(), 徐春丽^1,²()

1. 南京航空航天大学经济与管理学院, 江苏南京 211106
2. 南京铖联激光科技有限公司, 江苏南京 210039

收稿日期:2020-07-26 出版日期:2021-05-01 发布日期:2021-04-27
通讯作者: 陈洪转 E-mail:13813922476@163.com;15295556236@163.com;18561379757@163.com;51861195@qq.com;17312303672@163.com;xuchunli@3dimi.com
作者简介:陈洪转(1977—), 女, 教授, 博士, 主要研究方向为复杂装备研制管理、供应链管理、质量管理。E-mail: 13813922476@163.com|赵爱佳(1992—), 男, 硕士研究生, 主要研究方向为复杂装备管理、质量管理。E-mail: 15295556236@163.com|李腾蛟(2000—), 男, 本科, 主要研究方向为工业工程。E-mail: 18561379757@163.com|蔡匆聪(2000—), 女, 本科, 主要研究方向为工业工程。E-mail: 51861195@qq.com|程硕(1996—), 男, 硕士研究生, 主要研究方向为复杂装备管理、军民融合。E-mail: 17312303672@163.com|徐春丽(1980—), 女, 硕士研究生, 主要研究方向为复杂装备管理、供应链管理。E-mail: xuchunli@3dimi.com
基金资助:
国家社会科学规划基金(19BJY094);教育部人文社会科学规划基金(18YJA630008);中央高校基本科研业务费专项资金(NP2019202);质量管理主题创新区项目资助课题

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

Hongzhuan CHEN^1,*(), Aijia ZHAO¹(), Tengjiao LI¹(), Congcong CAI¹(), Shuo CHENG¹(), Chunli XU^1,²()

1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2. Nanjing CenLaser Laser Technology Company Limited, Nanjing 210039, China

Received:2020-07-26 Online:2021-05-01 Published:2021-04-27
Contact: Hongzhuan CHEN E-mail:13813922476@163.com;15295556236@163.com;18561379757@163.com;51861195@qq.com;17312303672@163.com;xuchunli@3dimi.com

摘要/Abstract

摘要：

复杂装备的小批量、个性化定制属性, 注定了其生命周期过程中存在着相对较多的不确定性, 故障隐患必不可免, 故障诊断尤为重要。因此，提出基于故障树的复杂装备模糊贝叶斯网络推理故障诊断模型。首先, 通过分析复杂装备的结构组成, 建立复杂装备的故障树模型。其次, 利用故障树转化法, 构建基于故障树的贝叶斯网络拓扑结构。然后, 针对复杂装备结构数据缺乏和专家打分的不确定性, 通过模糊集合论方法确定条件概率等参数。最后, 进行案例研究, 利用模糊贝叶斯网络推理中的因果推理和诊断推理, 诊断出案例中的故障(潜在故障)节点, 证明了所提方法的有效性。研究成果不仅解决了贝叶斯网络中利用搜索函数构建最优网络不符合实际的问题, 也通过模糊集合论解决了复杂装备数据缺乏和专家打分不确定性的不足。所提模型不仅适应于过程诊断中故障的确定, 同时也适用于事前诊断中潜在风险的识别, 而且对于故障(或潜在故障)节点的改善效果还能起到检测评估的作用。

关键词: 故障树, 复杂装备, 模糊贝叶斯网络, 故障诊断

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

中图分类号:

陈洪转, 赵爱佳, 李腾蛟, 蔡匆聪, 程硕, 徐春丽. 基于故障树的复杂装备模糊贝叶斯网络推理故障诊断[J]. 系统工程与电子技术, 2021, 43(5): 1248-1261.

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.

图/表 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	-	-	-	-	-	-

基于故障树的复杂装备模糊贝叶斯网络推理故障诊断

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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