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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。
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.
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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 1 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 a* b* 估计类型 转化形式 a b N(1, 1) 点估计型 =0.921 Beta分布
at=11.009
bt=0.945(10, 1) 20.009 1.945 N(2, 1) 点估计型 =0.913 Beta分布
at=9.910
bt=0.944(20, 2) 27.910 2.944 N(2, 2) 点估计型 =0.927 Beta分布
at=12.030
bt=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
at=13.037
bt=0.951(30, 2) 41.037 2.951 表 3 二次电源系统FMECA信息
Table 3. FMECA information of secondary power system
节点 故障率λp/(10-6h-1) 故障模式M 故障模式频数比αj/% 故障模式影响概率βj 故障模式危害度Dji① 故障影响(扩散度)Ij② 被检测难度评分等级Ej② 标识码 模式名称 N(2, 1) 3.042 M1N(2, 1) 短路 20 1 4.259 4 2 M2N(2, 1) 退化 80 0.1 1.460 4 5 N(2, 2) 0.139 M1N(2, 2) 开路 92 1 0.384 3 2 M2N(2, 2) 参漂 8 0.5 0.017 3 4 N(2, 3) 10.516 M1N(2, 3) 退化 35 0.1 2.576 5 5 M2N(2, 3) 低温不启动 10 0.1 0.736 5 1 M3N(2, 3) 漏气 15 0.1 0.946 5 3 M4N(2, 3) 开路 15 1 11.042 5 2 M5N(2, 3) 短路 25 1 18.403 5 1 N(2, 4) 0.366 M1N(2, 4) 接触不良 80 0.8 1.640 1 2 M2N(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。 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 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) M1N(2, 1) 10 2 6 4 8 4 1(2) 0(1) 6 3 M2N(2, 1) 8 2 4 1 3 N(2, 2) M1N(2, 2) 1(2) 1 0(2) 0(1) 1(2) 1 0(2) 0(1) 0(2) 0(1) M2N(2, 2) 0(1) 0(1) 0(1) 0(1) 0(1) N(2, 3) M1N(2, 3) 12 3 8 16 9 M2N(2, 3) 4 1 1 5 1 M3N(2, 3) 35 5 38 1 37 2 46 7 39 2 M4N(2, 3) 5 12 14 7 15 M5N(2, 3) 9 21 12 11 12 N(2, 4) M1N(2, 4) 1(2) 1 3 2 1(2) 1 0(2) 0(1) 2(3) 2 M2N(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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