基于粗糙集和证据理论的设备状态评估方法

doi:10.3969/j.issn.1001-506X.2020.01.19

摘要/Abstract

摘要：

为准确判定复杂设备健康状态，提出一种基于粗糙集理论和证据理论的健康状态评估方法。鉴于粗糙集只能处理离散指标，首先提出一种基于动态模糊C-均值聚类算法的连续型评估指标的离散化方法；再通过基于互信息的属性约简算法对复杂设备健康状态评估指标进行约简；然后对约简的评估决策表进行处理，构建基本信度分配函数；最后利用D-S合成规则进行多指标合成得到健康状态，进一步挖掘评估指标与健康状态间的关系。实例研究及对比分析表明该方法能有效提高决策可信度，减少评估的不确定性。

关键词: 粗糙集, D-S证据理论, 健康状态评估, 模糊C-均值聚类

Abstract:

To assess the health condition of complex equipment accurately, a health condition assessment method based on rough sets and D-S evidence theory is proposed. Firstly, given that only discrete attributes could be processed by using rough sets, a discretization method for continuous attributes based on the dynamic fuzzy C-means clustering algorithm is put forward. Secondly, the reduction attributes are obtained by using the reduction algorithm based on mutual information. Thirdly, the assessment decision table is processed and the basic probability assignment function is set up. Finally, assessment indexes are fused by the evidence theory to get the health condition grade, and the relationship between assessment indexes and health conditions is mined further. The case study and comparative analysis show that this method can improve the decision credibility effectively and reduce the uncertainty of assessment.

Key words: rough set, D-S evidence theory, health condition assessment, fuzzy C-means clustering

中图分类号:

TJ07

王亮, 卢湛夷, 李卓禹. 基于粗糙集和证据理论的设备状态评估方法[J]. 系统工程与电子技术, 2020, 42(1): 141-147.

Liang WANG, Zhanyi LU, Zhuoyu LI. Condition assessment method of equipment based on rough sets and evidence theory[J]. Systems Engineering and Electronics, 2020, 42(1): 141-147.

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序号	c₁	c₂	c₃	c₄	c₅	c₆	状态
1	2.5	6.8	24.4	0.4	7.3	14.9	良好
2	3.1	7.6	25.6	0.7	6.5	13.7	良好
3	2.8	6.5	25.2	0.8	8.2	14.3	良好
4	6.8	8.1	21.8	0.9	13.6	12.1	正常
5	7.5	13.2	22.1	1.5	12.3	11.4	正常
6	7.8	12.8	22.8	1.6	11.9	9.9	正常
7	8.1	16.3	20.1	1.9	18.5	9.3	一般
8	4.2	15.9	17.8	2.4	15.8	8.1	一般
9	5.6	17.4	18.4	2.5	17.3	7.7	一般
10	8.6	19.2	13.7	3.1	22.6	6.9	恶化
11	9.4	20.1	12.2	3.3	23.4	7.3	恶化
12	8.8	18.9	14.1	2.9	25.1	5.8	恶化
13	14.4	23.1	11.5	4.2	26.3	5.4	病态
14	12.6	21.9	9.9	4.9	25.6	6.1	病态
15	13.7	22.6	10.6	5.2	27.7	5.5	病态

样本	指标	m(1)	m(2)	m(3)	m(4)	m(5)	m(Θ)
E₁	c₃	0	0	0	0.720 7	0.179 3	0.1
	c₆	0	0	0	0.657 0	0.243 0	0.1
	c₂	0	0	0	0.595 5	0.204 5	0.2
	c₄	0	0	0	0.560 5	0.239 5	0.2
E₂	c₃	0.782 7	0.117 3	0	0	0	0.1
	c₆	0.559 3	0.340 7	0	0	0	0.1
	c₂	0.371 3	0.428 7	0	0	0	0.2
	c₄	0.491 4	0.308 6	0	0	0	0.2
E₃	c₃	0	0	0.656 8	0.243 2	0	0.1
	c₆	0	0.270 7	0.629 3	0	0	0.1
	c₂	0	0	0.529 6	0.270 4	0	0.2
	c₄	0	0.144 7	0.655 3	0	0	0.2
E₄	c₃	0	0	0.656 8	0.243 2	0	0.1
	c₆	0	0.270 7	0.629 3	0	0	0.1
	c₂	0.8	0	0	0	0	0.2
	c₄	0	0.144 7	0.655 3	0	0	0.2

样本	合成指标	m(1)	m(2)	m(3)	m(4)	m(5)	m(Θ)	结果
E₁	c₃⊕c₆	0	0	0	0.864 5	0.121 3	0.014 2	4
	c₂⊕c₃⊕c₆	0	0	0	0.927	0.069 2	0.003 8	4
	c₄⊕c₃⊕c₆	0	0	0	0.917 9	0.078 2	0.003 9	4
	c₂⊕c₄⊕c₃⊕c₆	0	0	0	0.956 6	0.042 4	0.001	4
E₂	c₃⊕c₆	0.856 6	0.128 4	0	0	0	0.015	1
	c₂⊕c₃⊕c₆	0.845 9	0.149	0	0	0	0.005 1	1
	c₄⊕c₃⊕c₆	0.891 6	0.104	0	0	0	0.004 5	1
	c₂⊕c₄⊕c₃⊕c₆	0.882 4	0.116 2	0	0	0	0.001 6	1
E₃	c₃⊕c₆	0	0.044 9	0.898 2	0.040 3	0	0.016 6	3
	c₂⊕c₃⊕c₆	0	0.012 8	0.948 9	0.033 5	0	0.004 8	3
	c₄⊕c₃⊕c₆	0	0.022 1	0.963 8	0.01	0	0.004 1	3
	c₂⊕c₄⊕c₃⊕c₆	0	0.006 2	0.984 6	0.008 1	0	0.001 2	3
E₄	c₃⊕c₆	0	0.044 9	0.898 2	0.040 3	0	0.016 6	3
	c₂⊕c₃⊕c₆	0.062 3	0.042 1	0.842 3	0.037 8	0	0.015 5	3
	c₄⊕c₃⊕c₆	0	0.022 1	0.963 8	0.01	0	0.004 1	3
	c₂⊕c₄⊕c₃⊕c₆	0.016 2	0.021 8	0.948 2	0.009 8	0	0.004	3

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