Reliability evaluation method of high-reliability products based on improved evidence fusion

doi:10.11772/j.issn.1001-9081.2022060867

Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (7): 2140-2146.DOI: 10.11772/j.issn.1001-9081.2022060867

• Artificial intelligence • Previous Articles Next Articles

Reliability evaluation method of high-reliability products based on improved evidence fusion

Sirui WANG, Shijuan CHENG(), Feimeng YUAN

School of Mathematics，Southwest Jiaotong University，Chengdu Sichuan 611756，China

Received:2022-06-16 Revised:2022-09-24 Accepted:2022-09-26 Online:2022-10-08 Published:2023-07-10
Contact: Shijuan CHENG
About author:WANG Sirui， born in 1998， M. S. candidate. Her research interests include reliability theory and engineering， information fusion.
CHENG Shijuan， born in 1973， Ph. D.， associate professor. Her research interests include reliability theory and engineering， information fusion.
YUAN Feimeng， born in 1998， M. S. candidate. Her research interests include reliability theory and engineering， information fusion.
Supported by:
Humanities and Social Science Research Foundation of Ministry of Education(20XJAZH009)

基于改进证据融合的高可靠产品可靠性评估方法

王思蕊, 程世娟(), 袁非梦

西南交通大学数学学院，成都 611756

通讯作者: 程世娟
作者简介:王思蕊（1998—），女，四川绵阳人，硕士研究生，主要研究方向：可靠性理论与工程、信息融合；
程世娟（1973—），女，山东临沂人，副教授，博士，主要研究方向：可靠性理论与工程、信息融合；
袁非梦（1998—），女，河南新乡人，硕士研究生，主要研究方向：可靠性理论与工程、信息融合。
基金资助:
教育部人文社会科学研究规划基金资助项目(20XJAZH009)

Abstract

Abstract:

In the reliability evaluation of many high-reliability and high-value products， product reliability often cannot be accurately evaluated due to the lack of objective test data. Aiming at this problem， a reliability evaluation method for high-reliability products based on improved evidence fusion was proposed in order to make full use of reliability information from different sources. Firstly， combining the characteristics of reliability engineering， the modified weight of each evidence was determined by the consistency of the evidence at credal level， pignistic level and the uncertainty of the evidence itself. Secondly， the optimal comprehensive weight was obtained by linear combination of each weight vector based on game theory. Finally， the Dempster’s combination rule was used to fuse the modified evidence， and the probability distribution of the product reliability index was obtained through the Pignistic probability transformation formula to complete the product reliability evaluation. The reliability evaluation results of one electronic device show that compared with the results of Jiang’s combination method and Yang’s combination method， which also consider multi-dimensional weight modification， the credibility of the conflict interval given by the proposed method is reduced by 69.6% and 54.6% respectively， and the credibility of the overall frame of discrimination given by the proposed method is reduced by 5.6% and 3.7% respectively. Therefore， in the application of reliability engineering， the performance of the proposed method in solving evidence conflict and reducing the uncertainty of fusion results is better than that of the comparison methods， and this method can fuse multi-source reliability information effectively and improve the credibility of the results of product reliability evaluation.

Key words: Dempster-Shafer (D-S) evidence theory, information fusion, modified weight, game theory, reliability evaluation

摘要：

对许多高可靠、高价值的产品进行可靠性评估时，常由于客观试验数据缺乏导致无法对产品可靠性进行准确评估。针对这个问题，为充分利用不同来源的可靠性信息，提出一种基于改进证据融合的高可靠产品可靠性评估方法。首先，结合可靠性工程特点，分别由各证据在信度层、决策层的一致性以及证据自身的不确定度来确定证据修正权重；其次，基于博弈论原理对各权重向量进行线性组合，从而得到最优综合权重；最后，利用Dempster组合规则融合修正后的证据，并通过Pignistic概率转化公式得到产品可靠性指标的概率分布，以完成产品可靠性评估。某电子设备的可靠度评估结果显示，所提方法相较于同样考虑多维权重修正的Jiang组合方法和Yang组合方法，赋予冲突区间的信度分别减小了69.6%、54.6%，赋予整个识别框架的信度分别减小了5.6%、3.7%。因此，在可靠性工程应用中，所提方法化解证据冲突、降低融合结果不确定性的表现优于对比方法，能够有效融合多源可靠性信息，提高产品可靠性评估结果可信度。

关键词: D-S证据理论, 信息融合, 修正权重, 博弈论, 可靠性评估

CLC Number:

TP391.1

Sirui WANG, Shijuan CHENG, Feimeng YUAN. Reliability evaluation method of high-reliability products based on improved evidence fusion[J]. Journal of Computer Applications, 2023, 43(7): 2140-2146.

王思蕊, 程世娟, 袁非梦. 基于改进证据融合的高可靠产品可靠性评估方法[J]. 《计算机应用》唯一官方网站, 2023, 43(7): 2140-2146.

Figures/Tables 8

Fig. 1 Improved evidence fusion process

Fig. 2 Probability density of reliability transformed by confidence interval

Fig. 3 Reliability evaluation flowchart based on improved evidence fusion

Tab. 1 Similarity weights defined based on consistency of evidence at credal level

$m i$	$d i j i ≠ j$	$d i$	$s u p m i$	$w a i$
$m 1$	$d 12 = 0.856 6, d 13 = 0.496 9, d 14 = 0.560 6$	1.914 1	0.978 4	0.265 6
$m 2$	$d 21 = 0.856 6, d 23 = 0.833 3, d 24 = 0.838 1$	2.528 0	0.740 8	0.201 1
$m 3$	$d 31 = 0.496 9, d 32 = 0.833 3, d 34 = 0.542 6$	1.872 8	1.000 0	0.271 4
$m 4$	$d 41 = 0.560 6, d 42 = 0.838 1, d 43 = 0.542 6$	1.941 3	0.964 7	0.261 9

Tab. 1 Similarity weights defined based on consistency of evidence at credal level

$m i$	$d i j i ≠ j$	$d i$	$s u p m i$	$w a i$
$m 1$	$d 12 = 0.856 6, d 13 = 0.496 9, d 14 = 0.560 6$	1.914 1	0.978 4	0.265 6
$m 2$	$d 21 = 0.856 6, d 23 = 0.833 3, d 24 = 0.838 1$	2.528 0	0.740 8	0.201 1
$m 3$	$d 31 = 0.496 9, d 32 = 0.833 3, d 34 = 0.542 6$	1.872 8	1.000 0	0.271 4
$m 4$	$d 41 = 0.560 6, d 42 = 0.838 1, d 43 = 0.542 6$	1.941 3	0.964 7	0.261 9

Tab. 2 Similarity weights defined based on consistency of evidence at pignistic level

$m i$	$S i m i j i ≠ j$	$S u p m i$	$w b i$
$m 1$	$S i m 12 = 0.028 6, S i m 13 = 0.941 7, S i m 14 = 0.596 8$	1.561 7	0.357 3
$m 2$	$S i m 21 = 0.028 6, S i m 23 = 0.045 3, S i m 24 = 0.000 1$	0.074 0	0.016 9
$m 3$	$S i m 31 = 0.596 8, S i m 32 = 0.045 3, S i m 34 = 0.580 4$	1.567 4	0.357 4
$m 4$	$S i m 41 = 0.596 8, S i m 42 = 0.000 1, S i m 43 = 0.580 4$	1.177 3	0.268 4

Tab. 2 Similarity weights defined based on consistency of evidence at pignistic level

$m i$	$S i m i j i ≠ j$	$S u p m i$	$w b i$
$m 1$	$S i m 12 = 0.028 6, S i m 13 = 0.941 7, S i m 14 = 0.596 8$	1.561 7	0.357 3
$m 2$	$S i m 21 = 0.028 6, S i m 23 = 0.045 3, S i m 24 = 0.000 1$	0.074 0	0.016 9
$m 3$	$S i m 31 = 0.596 8, S i m 32 = 0.045 3, S i m 34 = 0.580 4$	1.567 4	0.357 4
$m 4$	$S i m 41 = 0.596 8, S i m 42 = 0.000 1, S i m 43 = 0.580 4$	1.177 3	0.268 4

Tab. 3 Reliability weights defined based on evidence uncertainty

$m i$	$E d i$	$w c i$	$m i$	$E d i$	$w c i$
$m 1$	1.537 8	0.288 5	$m 3$	1.250 9	0.354 7
$m 2$	2.875 0	0.154 3	$m 4$	2.191 8	0.202 4

Tab. 3 Reliability weights defined based on evidence uncertainty

$m i$	$E d i$	$w c i$	$m i$	$E d i$	$w c i$
$m 1$	1.537 8	0.288 5	$m 3$	1.250 9	0.354 7
$m 2$	2.875 0	0.154 3	$m 4$	2.191 8	0.202 4

Tab. 4 BPA after fusing by different methods

方法	各命题BPA
方法	m（ $[0.4,0.5]$ ）	m（ $[0.6,0.8]$ ）	m（ $[0.65,0.8]$ ）	m（ $[0.65,0.85]$ ）	m（ $[0.7,0.8]$ ）	m（ $[0,1]$ ）
传统D-S方法	0.076 9	0.028 9	0.124 9	0.041 7	0.717 8	0.009 8
基于信度层证据一致性修正	0.097 7	0.123 5	0.031 6	0.114 7	0.183 8	0.448 7
基于决策层证据一致性修正	0.006 3	0.166 9	0.061 1	0.149 6	0.207 5	0.408 6
基于证据不确定度修正	0.070 0	0.134 9	0.048 8	0.159 5	0.146 4	0.440 4
文献［12］方法	0.090 4	0.127 6	0.033 3	0.116 7	0.185 0	0.447 0
文献［22］方法	0.060 6	0.132 2	0.042 8	0.142 0	0.184 1	0.438 3
本文方法	0.027 5	0.155 5	0.055 8	0.151 3	0.187 8	0.422 1

Tab. 4 BPA after fusing by different methods

方法	各命题BPA
方法	m（ $[0.4,0.5]$ ）	m（ $[0.6,0.8]$ ）	m（ $[0.65,0.8]$ ）	m（ $[0.65,0.85]$ ）	m（ $[0.7,0.8]$ ）	m（ $[0,1]$ ）
传统D-S方法	0.076 9	0.028 9	0.124 9	0.041 7	0.717 8	0.009 8
基于信度层证据一致性修正	0.097 7	0.123 5	0.031 6	0.114 7	0.183 8	0.448 7
基于决策层证据一致性修正	0.006 3	0.166 9	0.061 1	0.149 6	0.207 5	0.408 6
基于证据不确定度修正	0.070 0	0.134 9	0.048 8	0.159 5	0.146 4	0.440 4
文献［12］方法	0.090 4	0.127 6	0.033 3	0.116 7	0.185 0	0.447 0
文献［22］方法	0.060 6	0.132 2	0.042 8	0.142 0	0.184 1	0.438 3
本文方法	0.027 5	0.155 5	0.055 8	0.151 3	0.187 8	0.422 1

Fig. 4 Probability distribution curves of reliability obtained by different methods

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Reliability evaluation method of high-reliability products based on improved evidence fusion

基于改进证据融合的高可靠产品可靠性评估方法

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