基于层次Bayesian网络及后验风险准则的故障样本量确定方法
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摘要
针对现有测试性验证方法对装备系统结构考虑不足,且在双方风险约束条件下所确定的故障样本量过大问题,提出一种基于层次Bayesian网络和后验风险准则的故障样本量确定方法。根据装备系统结构建立测试性验证方法的层次Bayesian网络模型,并以故障检测率作为Bayesian网络的传递参数;提出Bayesian网络不确定性推理算法,充分融合各层次测试性先验信息,同时基于偏度-峰度检验的拟合分布选取方法推导出系统故障检测率联合先验分布;进一步结合系统成败型数据确定其后验分布,基于后验样本数据集和Bayes后验风险准则设计故障样本量确定算法,通过实例进行分析。结果表明,与经典验证方法、传统Bayesian方法相比,所提方法在相同双方指标约束下能有效降低样本量。
The existing testability verification methods take insufficient account of the equipment system structure and need a large number of fault sample size under both-sides' risk constraints. A fault sample size determination method based on hierarchical Bayesian network and posterior risk criteria is proposed.A hierarchical Bayesian network model of testability verification method is established according to the structure of an equipment system. In hierarchical Bayesian network model,the failure detection rate is used as the transmission parameter of the Bayesian network. Bayesian network reasoning algorithm is proposed to fully fuse the priori information of each level,and the joint prior distribution of fault detection rates is deduced based on fitting distribution selection method for skewness-kurtosis test. The posterior distribution is determined with the binomial data of the system. A fault sample size determination algorithm is established based on the posterior sample data and Bayesian posterior risk criteria,and is validated by an example. Compared with the classical and traditional Bayesian verification methods,the proposed method can reduce the sample size effectively under the same both-sides' risk constraints.
The existing testability verification methods take insufficient account of the equipment system structure and need a large number of fault sample size under both-sides' risk constraints. A fault sample size determination method based on hierarchical Bayesian network and posterior risk criteria is proposed.A hierarchical Bayesian network model of testability verification method is established according to the structure of an equipment system. In hierarchical Bayesian network model,the failure detection rate is used as the transmission parameter of the Bayesian network. Bayesian network reasoning algorithm is proposed to fully fuse the priori information of each level,and the joint prior distribution of fault detection rates is deduced based on fitting distribution selection method for skewness-kurtosis test. The posterior distribution is determined with the binomial data of the system. A fault sample size determination algorithm is established based on the posterior sample data and Bayesian posterior risk criteria,and is validated by an example. Compared with the classical and traditional Bayesian verification methods,the proposed method can reduce the sample size effectively under the same both-sides' risk constraints.
引文
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[15]刘钰,韩峰,陆希成,等.电子系统电磁脉冲易损性评估的分层贝叶斯网络模型[J].电子学报,2016,44(11):2695-2703.LIU Y,HAN F,LU X C,et al. EMP susceptibility modeling and assessment of electronic system based on hierarchical Bayesian networks[J]. Acta Electronica Sinica,2016,44(11):2695-2703.(in Chinese)
[16]马德仲,周真,于晓洋,等.基于模糊概率的多状态贝叶斯网络可靠性分析[J].系统工程与电子技术,2012,34(12):2607-2611.MA D Z,ZHOU Z,YU X Y,et al. Reliability analysis of multistate Bayesian networks based on fuzzy probability[J]. Systems Engineering and Electronics,2012,34(12):2607-2611.(in Chinese)
[17]王晓伟,孙波,吕英军,等.基于贝叶斯网络的系统测试性建模与分析[J].中国测试,2011,37(5):90-93.WANG X W,SUN B,LUY J,et al. Model and analysis of system testability based on Bayesian networks[J]. China Measurement&Test,2011,37(5):90-93.(in Chinese)
[18] GYFTODIMOS E,FLACH P A. Hierarchical Bayesian networks:an approach to classification and learning for structured data[M]∥George A. Vouros,Themistoklis Panayiotopoulos. Methods and Applications of Artificial Intelligence. NY,US:Springer,2004:291-300.
[19]章溢,吕凤虎.峰度与偏度系数的近似经验贝叶斯估计[J].江西师范大学学报,2016,40(4):358-362.ZHANG Y,LUF H. The approximate empirical Bayesian estimation of kurtosis and skewness coefficient[J]. Journal of Jiangxi Normal University,2016,40(4):358-362.(in Chinese)
[20]王超.虚实结合的测试性试验与综合评估技术[D].长沙:国防科学技术大学,2014.WANG C. Testability test and intergrated evaluation technology with virtual-physical test[D]. Changsha:National University of Defense Technology,2014.(in Chinese)
[21]雷华军,秦开宇.确定测试性验证试验方案的贝叶斯方法[J].系统工程与电子技术,2012,34(12):2612-2616.LEI H J,QIN K Y. Bayesian method for determination of testability demonstration test scheme[J]. Systems Engineering and Electronics,2012,34(12):2612-2616.(in Chinese)
[2]田仲.测试性验证方法研究[J].航空学报,1995,16(增刊1):65-70.TIAN Z. Study of testability demonstration methods[J]. Acta Aeronautica et Astronautica Sinica,1995,16(S1):65-70.(in Chinese)
[3]陈然,连光耀,张西山.基于序贯回归的小样本测试性验证试验方案[J].航空动力学报,2018,33(2):305-311.CHEN R,LIAN G Y,ZHANG X S. A small sample testability verification test scheme based on sequential and regression analysis[J]. Journal of Aerospace Power,2018,33(2):305-311.(in Chinese)
[4]邓露,许爱强,李文海,等.基于Bayesian理论的测试性验证试验方案[J].南京理工大学学报,2014,38(6):775-780.DENG L,XU A Q,LI W H,et al. Testability demonstration test schem based on Bayesian theory[J]. Journal of Nanjing University of Science and Technology,2014,38(6):775-780.(in Chinese)
[5] Department of Defense. Maintainability verification/demonstration/evaluation:MIL-STD-471A-1973[S]. Washington, DC,US:Department of Defense,1973.
[6]中国人民解放军总装备部.装备测试性工作通用要求:GJB2547A—2012[S].北京:中国人民解放军总装备部,2012.The PLA General Armaments Department. General requirement for materiel testability program:GJB2547A—2012[S]. Beijing:the PLA General Armaments Department,2012.(in Chinese)
[7]李天梅,邱静,刘冠军.利用研制阶段试验数据制定测试性验证试验方案新方法[J].机械工程学报,2009,45(8):52-57.LI T M,QIU J,LIU G J. New methodology for determining testability integrated test scheme with test data in the development stages[J]. Journal of Mechanical Engineering,2009,45(8):52-57.(in Chinese)
[8]汤巍,景博,黄以锋.小子样变总体下的Bayes测试性验证方法[J].系统工程与电子技术,2014,36(12):2566-2570.TANG W,JING B,HUANG Y F. Testability verification method based on Bayes theory under small sample and varying population circumstance[J]. Systems Engineering and Electronics,2014,36(12):2566-2570.(in Chinese)
[9]尹园威,尚朝轩,蔡金燕,等.装备测试性增长过程的贝叶斯验证方法[J].振动.测试与诊断,2016,36(3):488-491.YIN Y W,SHANG C X,CAI J Y,et al. Bayes verification method based on equipment testability growth[J]. Journal of Vibration,Measurement&Diagnosis,2016,36(3):488-491.(in Chinese)
[10]王敏,杨江平,卢雷,等.利用分系统数据制定整机测试性验证试验方案[J].现代防御技术,2015,43(5):213-217.WANG M,YANG J P,LU L,et al. Determining testability demonstration test scheme with subsystem data[J]. Modern Defence Technology,2015,43(5):213-217.(in Chinese)
[11]张西山,黄考利,闫鹏程,等.基于验前信息的测试性验证试验方案确定方法[J].北京航空航天大学学报,2015,41(8):1505-1512.ZHANG X S,HUANG K L,YAN P C,et al. Method of confirming testability verification test scheme based on prior information[J]. Journal of Beijing University of Aeronautics and Astronantics,2015,41(8):1505-1512.(in Chinese)
[12]常春贺,杨江平,曹鹏举.基于研制信息的测试性验证试验方案研究[J].航空学报,2012,33(11):2057-2064.CHANG C H,YANG J P,CAO P J. Study on the scheme of testability demonstration test based on development information[J]. Acta Aeronautica et Astronautica Sinica,2012,33(11):2057-2064.(in Chinese)
[13] WANG C,QIU J,LIU G J,et al. Testability demonstration with component level data from virtual and physical tests[J]. Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2015,229(2):265-272.
[14]郑应荣.系统级层次化测试性建模与分析[D].哈尔滨:哈尔滨工业大学,2014.ZHENG Y R. Testability modeling and analysis of hierarchical system[D]. Harbin:Harbin Institute of Technology,2014.(in Chinese)
[15]刘钰,韩峰,陆希成,等.电子系统电磁脉冲易损性评估的分层贝叶斯网络模型[J].电子学报,2016,44(11):2695-2703.LIU Y,HAN F,LU X C,et al. EMP susceptibility modeling and assessment of electronic system based on hierarchical Bayesian networks[J]. Acta Electronica Sinica,2016,44(11):2695-2703.(in Chinese)
[16]马德仲,周真,于晓洋,等.基于模糊概率的多状态贝叶斯网络可靠性分析[J].系统工程与电子技术,2012,34(12):2607-2611.MA D Z,ZHOU Z,YU X Y,et al. Reliability analysis of multistate Bayesian networks based on fuzzy probability[J]. Systems Engineering and Electronics,2012,34(12):2607-2611.(in Chinese)
[17]王晓伟,孙波,吕英军,等.基于贝叶斯网络的系统测试性建模与分析[J].中国测试,2011,37(5):90-93.WANG X W,SUN B,LUY J,et al. Model and analysis of system testability based on Bayesian networks[J]. China Measurement&Test,2011,37(5):90-93.(in Chinese)
[18] GYFTODIMOS E,FLACH P A. Hierarchical Bayesian networks:an approach to classification and learning for structured data[M]∥George A. Vouros,Themistoklis Panayiotopoulos. Methods and Applications of Artificial Intelligence. NY,US:Springer,2004:291-300.
[19]章溢,吕凤虎.峰度与偏度系数的近似经验贝叶斯估计[J].江西师范大学学报,2016,40(4):358-362.ZHANG Y,LUF H. The approximate empirical Bayesian estimation of kurtosis and skewness coefficient[J]. Journal of Jiangxi Normal University,2016,40(4):358-362.(in Chinese)
[20]王超.虚实结合的测试性试验与综合评估技术[D].长沙:国防科学技术大学,2014.WANG C. Testability test and intergrated evaluation technology with virtual-physical test[D]. Changsha:National University of Defense Technology,2014.(in Chinese)
[21]雷华军,秦开宇.确定测试性验证试验方案的贝叶斯方法[J].系统工程与电子技术,2012,34(12):2612-2616.LEI H J,QIN K Y. Bayesian method for determination of testability demonstration test scheme[J]. Systems Engineering and Electronics,2012,34(12):2612-2616.(in Chinese)