故障样本量确定与分配一体化设计方案

王康; 史贤俊; 韩旭; 龙玉峰

doi:10.13700/j.bh.1001-5965.2019.0184

故障样本量确定与分配一体化设计方案

doi: 10.13700/j.bh.1001-5965.2019.0184

海军航空大学, 烟台 264001

详细信息

作者简介:
王康男, 博士研究生。主要研究方向:装备测试性设计、验证与评估

史贤俊男, 博士, 教授, 博士生导师。主要研究方向:导弹自动测试技术, 装备测试性设计、验证与评估

通讯作者:
史贤俊，E-mail:sxjaa@sina.com

中图分类号: V240.2;TJ06
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出版历程
- 收稿日期: 2019-04-23
- 录用日期: 2019-07-19
- 网络出版日期: 2020-01-20

Integrated design scheme for fault sample size determination and allocation

Naval Aviation University, Yantai 264001, China

More Information

Corresponding author: SHI Xianjun, E-mail:sxjaa@sina.com

摘要

摘要:
针对当前测试性验证领域未能考虑故障样本量确定和样本分配2个环节的相互联系，以及现有样本分配方案对影响因子的选择没有统一的框架，导致确定的故障样本量和样本分配不合理的问题，提出了一种故障样本量确定与分配一体化设计方案。首先，以层次Bayes网络模型为框架，融合各节点测试性指标先验信息得到顶层测试性指标的融合分布，并建立故障样本量确定流程；其次，引入结构重要度作为样本分配影响因子，同时结合故障模式影响及危害性分析（FMECA）信息确定节点和故障模式的样本分配影响因子，提出基于节点和故障模式的二次分配框架实施样本分配；最后，通过实际案例进行对比分析。结果表明：相比其他样本分配方案，所提方案能充分考虑系统结构及其先验信息，进而实现了故障样本量确定和分配一体化方案的设计，保证了所确定的故障样本量和分配的合理性，具备更好的工程适用性。
- 测试性验证 /
- 故障样本量 /
- 样本分配 /
- 层次Bayes网络 /
- 先验信息 /
- 故障模式
Abstract:
For the current testability verification field, the relationship between the fault sample size determination and the sample allocation is not taken into consideration, and the existing sample allocation schemes have no uniform framework for the selection of the impact factor, which lead to the problem that the determined sample size and sample allocation are unreasonable, so an integrated design scheme for fault sample size determination and allocation is proposed. Firstly, the prior information of each node's testability indicators was integrated to obtain the fusion distribution of top-level testability indicators, which could be used to establish a fault sample size determination process based on the hierarchical Bayes network model. Secondly, the structural importance was introduced as the sample allocation influence factor. At the same time, the failure modes, effect and criticality analysis (FMECA) information was used to determine the sample allocation influence factor of the nodes and the failure modes. Then the secondary allocation framework based on the nodes and failure modes was proposed to implement the sample allocation. Finally, a comparative analysis was carried out through actual cases. The results show that, compared with other sample allocation schemes, the proposed scheme can fully consider the system structure and its prior information, and realize the integrated design for fault sample size determination and allocation, which ensures the reasonable sample size and allocation with better engineering applicability.
- testability verification /
- fault sample size /
- sample allocation /
- hierarchical Bayes network /
- prior information /
- failure mode

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图 1 系统结构模型向一体化设计模型的转化示意图

Figure 1. Schematic diagram of transformation from system structure model to integrated design model

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图 2 二次电源系统一体化设计模型

Figure 2. Integrated design model of secondary power system

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图 3 节点N_{(1, 1)}不同先验分布概率密度曲线

Figure 3. Probability density curves of different prior distribution at node N_{(1, 1)}

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表 1 一体化设计模型的CPT

Table 1. CPT of integrated design model

N_{(2, 1)}		0								1
N_{(2, 2)}		0				1				0				1
N_{(2, 3)}		0		1		0		1		0		1		0		1
N_{(2, 4)}		0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1
N_{(1, 1)}	0
N_{(1, 1)}	1

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表 2 节点先验信息

Table 2. Prior information of each node

节点	继承先验超参数		专家信息融合		成败型数据	自先验超参数
节点	a^*	b^*	估计类型	转化形式	成败型数据	a	b
N_{(1, 1)}			点估计型 =0.921	Beta分布 a_t=11.009 b_t=0.945	(10, 1)	20.009	1.945
N_{(2, 1)}			点估计型 =0.913	Beta分布 a_t=9.910 b_t=0.944	(20, 2)	27.910	2.944
N_{(2, 2)}			点估计型 =0.927	Beta分布 a_t=12.030 b_t=0.947	(24, 0)	36.030	0.947
N_{(2, 3)}	31.2	3.6	区间估计型[0.861, 0.932]	成败型数据(211, 21)	(28, 3)	246.2	27.6
N_{(2, 4)}			点估计型 =0.932	Beta分布 a_t=13.037 b_t=0.951	(30, 2)	41.037	2.951

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表 3 二次电源系统FMECA信息

Table 3. FMECA information of secondary power system

节点	故障率λ_p/(10^－6h^-1)	故障模式M		故障模式频数比α_j/%	故障模式影响概率β_j	故障模式危害度D_ji^①	故障影响(扩散度)I_j^②	被检测难度评分等级E_j^②
节点	故障率λ_p/(10^－6h^-1)	标识码	模式名称		故障模式影响概率β_j	故障模式危害度D_ji^①	故障影响(扩散度)I_j^②	被检测难度评分等级E_j^②
N_{(2, 1)}	3.042	M₁^{N_{(2, 1)}}	短路	20	1	4.259	4	2
N_{(2, 1)}	3.042	M₂^{N_{(2, 1)}}	退化	80	0.1	1.460	4	5
N_{(2, 2)}	0.139	M₁^{N_{(2, 2)}}	开路	92	1	0.384	3	2
N_{(2, 2)}	0.139	M₂^{N_{(2, 2)}}	参漂	8	0.5	0.017	3	4
N_{(2, 3)}	10.516	M₁^{N_{(2, 3)}}	退化	35	0.1	2.576	5	5
		M₂^{N_{(2, 3)}}	低温不启动	10	0.1	0.736	5	1
		M₃^{N_{(2, 3)}}	漏气	15	0.1	0.946	5	3
		M₄^{N_{(2, 3)}}	开路	15	1	11.042	5	2
		M₅^{N_{(2, 3)}}	短路	25	1	18.403	5	1
N_{(2, 4)}	0.366	M₁^{N_{(2, 4)}}	接触不良	80	0.8	1.640	1	2
N_{(2, 4)}	0.366	M₂^{N_{(2, 4)}}	开路	20	1	0.512	1	2
注：①指故障模式危害度, 通过文献[13]求解；②指本文以扩散度表征故障影响，可通过文献[27]求解。

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表 4 不同样本分配方式结果对比

Table 4. Result comparison of different sample allocation methods

节点	故障模式M	基于故障率的样本分配^[12]		基于危害度的样本分配^[13]		基于故障属性的样本分配^[27]		基于多因子的样本分配^[15]		一体化设计方案
节点	故障模式M	节点	故障模式	节点	故障模式	节点	故障模式	节点	故障模式	节点	故障模式
N_{(2, 1)}	M₁^{N_{(2, 1)}}	10	2	6	4	8	4	1(2)	0(1)	6	3
N_{(2, 1)}	M₂^{N_{(2, 1)}}	10	8	6	2	8	4	1(2)	1	6	3
N_{(2, 2)}	M₁^{N_{(2, 2)}}	1(2)	1	0(2)	0(1)	1(2)	1	0(2)	0(1)	0(2)	0(1)
N_{(2, 2)}	M₂^{N_{(2, 2)}}	1(2)	0(1)	0(2)	0(1)	1(2)	0(1)	0(2)	0(1)	0(2)	0(1)
N_{(2, 3)}	M₁^{N_{(2, 3)}}		12		3		8		16		9
	M₂^{N_{(2, 3)}}		4		1		1		5		1
	M₃^{N_{(2, 3)}}	35	5	38	1	37	2	46	7	39	2
	M₄^{N_{(2, 3)}}		5		12		14		7		15
	M₅^{N_{(2, 3)}}		9		21		12		11		12
N_{(2, 4)}	M₁^{N_{(2, 4)}}	1(2)	1	3	2	1(2)	1	0(2)	0(1)	2(3)	2
N_{(2, 4)}	M₂^{N_{(2, 4)}}		0(1)		1		0(1)		0(1)		0(1)
注：(·)内数字为基于式(29)校正后的样本量。

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