摘要
轿车车身制造偏差是影响产品质量、制造成本和市场占有率等的重要因素之一，因此车身装配偏差的诊断与控制方法一直受到学术界和工业界高度重视。车身产品由数百个薄板零件在数十个工位上焊装而成，一方面装配过程中零件、夹具、焊接、操作等偏差源因素众多，对最终装配质量的影响关系极其复杂；另一方面车身批量生产中通常只对若干装配工位的有限测点进行抽样检测，无法观测到装配过程中各类偏差输入、传递与输出的完备信息。由于装配系统的复杂性和观测信息的不完备性，使得各类偏差源与车身装配质量之间的影响关系难以准确描述，故障诊断的溯源结果呈现出一定的不确定性。传统基于模式匹配的诊断方法主要用于解决完备信息下单个夹具定位失效模式引起的偏差诊断问题，而实际生产中偏差源诊断受到检测样本小、信息不完备的制约，特别是多偏差源的诊断仍然依赖工程经验，诊断结论准确性差、诊断验证周期长、偏差控制成本高。
贝叶斯网络理论是不确定知识表达与诊断推理的有效方法之一。它一方面可以将车身装配偏差间复杂影响关系以不确定的概率模型形式进行表达；另一方面能够对工程经验、设计知识等先验信息和当前检测数据进行多源信息融合，从而实现不完备信息下装配偏差关系模型的学习更新，不断提高故障诊断准确性。与传统基于经典统计理论的方法相比，贝叶斯网络在检测样本小、信息不完备条件下的复杂系统故障诊断中具有显著优势。
本文将贝叶斯网络理论应用到车身装配偏差诊断的不确定性问题，提出基于贝叶斯网络的装配偏差影响关系建模与诊断方法。针对小数据集下贝叶斯网络模型构建的难题，提出基于先验信息与检测数据等多源信息融合的模型学习方法,并给出了多偏差源诊断推理、偏差源可诊断性、观测节点优化等系统方法，最后结合工程应用案例验证了本文所提出方法的可靠性。本文主要研究内容及创新成果如下：
(1)车身装配偏差诊断问题的贝叶斯网络表达方法
针对车身装配过程的偏差源诊断问题，引入不确定性建模的贝叶斯网络方法，对车身装配偏差的影响关系进行表达。首先通过对装配偏差源与质量检测特征的提取，获得贝叶斯网络的输入输出节点；然后结合大样本下贝叶斯网络学习方法，给出了装配偏差影响关系的贝叶斯网络模型表达形式;最后结合车身装配过程小样本检测等特殊性问题，分析了上述贝叶斯网络模型在进行实际偏差源诊断时需解决的问题。
(2)车身装配偏差贝叶斯网络的多源信息融合建模
针对小数据集下复杂偏差影响关系的贝叶斯网络建模难题，提出基于多源信息融合的贝叶斯网络建模方法。首先结合工程经验、设计阶段装配偏差仿真结果等先验信息，提出从偏差敏感度矩阵到贝叶斯网络初始结构与先验参数的映射方法，建立初始贝叶斯网络模型；然后通过节点先验分布与检测数据的融合，实现网络结构关系与各节点条件概率的迭代更新。在此基础上，提出基于信息熵的测点组评价方法，结合偏差源的可诊断性分析和有效独立准则，实现了面向偏差源可诊断性的观测节点优化。
(3)基于贝叶斯网络的多装配偏差源诊断方法研究
针对车身多级装配过程多偏差源诊断的需求，提出小样本下证据变量值获取以及多偏差源诊断推理方法。首先研究小样本下基于贝叶斯估计的装配质量评价方法，获得偏差源概率推理中的证据变量值；然后通过贝叶斯网络的最大后验假设和最大后验概率问题的求解，实现车身装配过程多偏差源问题的故障诊断；最后结合对贝叶斯网络诊断结果的分类，分析了不完备质量检测以及噪声等因素对诊断准确率的影响，验证了贝叶斯网络诊断方法的有效性。
(4)工程应用
在上述研究基础上，结合某车型装配车间的实际情况，在侧围总成装配、前围下部总成装配等案例的偏差源诊断中开展应用研究，详细描述了从输入输出节点定义、贝叶斯网络模型构建、观测节点质量评价到后验概率推理的车身装配偏差诊断过程，验证了贝叶斯网络方法解决多偏差源诊断问题的有效性与模型在线迭代学习的可行性。
本文面向汽车车身装配过程的偏差控制，研究基于贝叶斯网络的装配偏差建模方法，实现了小样本检测环境下车身装配多偏差源的诊断，不仅为汽车车身装配过程精度控制提供新的理论方法与技术指导，对飞机、列车等复杂产品的装配精度控制也具有借鉴意义。
The dimensional variation of auto bodies is one of the most important factors thataffect the product quality, manufacturing cost and the market shares, so the techniqueson the root cause diagnosis and process control are paid great attention to by bothresearchers and manufacturers. The auto body is assembled with hundreds ofcompliant sheet metal parts in dozens of assembly stations. In the assembly process,different variation sources such as incoming parts, tooling, welding etc, will affect theassembly variation. The relationship between variation sources and the assemblyvariation are extremely complicated. Besides, the measurement data about the processare always small samples in some limited stations, which only provide incompleteinformation for the process monitoring and diagnosis. The traditional fault diagnosismethods, such as pattern matching method, are different to diagnose the root cause ofthe assembly variations by considering the incomplete measurement data. In realassembly process, variation sources diagnosis is still mainly relying on theengineering experience.
The Bayesian network theory is one of the most effective methods for knowledgerepresentation and uncertain reasoning. It can describe the complex relationshipbetween root causes and assembly deviation with an uncertain probability model. Onthe other hand, multi-source information, such as engineering experience, designknowledge and also the measurement data can be incorporated into the model to avoidthe shortcomings of small sample data. Compared with the traditional statisticmethods, Bayesian networks have a significant advantage for assembly variationdiagnosis under incomplete measurement data set.
In this paper, Bayesian networks are used to solve the fault diagnosis problem inthe auto body assembly process. The Bayesian network model is used to illustrate thecausal relationships between the root cause nodes and the sensor nodes. A newmodeling method under small sample data set by considering multi-sourceinformation is proposed. Based on the diagnostic model, the methods on probabilityreasoning, diagnosability of the root nodes and optimal sensor placement aredeveloped. At last, the assembly diagnostic cases are studied. The results andcomparative analysis showed the proposed methods are effective and reliable.
The main contents are shown as follows:
(1) Description of the dimensional variation source diagnosis problem in theassembly process with Bayesian networks
For the diagnosis problem in the assembly process, the Bayesian network theoryis introduced to describe the causal relationship of the assembly deviations. At first,the root nodes and sensors nodes of the diagnostic network are acquired by extractingthe key characteristics in the assembly process. Afterwards, the directed acyclic graphand conditional probability tables are learned based on the learning algorithms underlarge data sets. Furthermore, the probability reasoning methods based on thediagnostic Bayesian network and the variation sources diagnosis procedures arepresented. At last, the further studies concerning the small sample problem in the realmeasurement process are proposed.
(2) The Bayesian network modeling of the causal relationship of theassembly variation by considering multi-source information
For the Bayesian network modeling problem under the small sample data set, anew method based on multi-source information fusion is proposed. At first, theoriginal Bayesian network structure and conditional probabilities are acquired basedon the mapping of the variation simulation results which are obtained in the variationdesign stage. Furthermore, the diagnostic model is updated by incorporated with thenew measurement data set. The causal relationships are updated based on theconditional independence test method, and the corresponding parameters of thenetwork nodes are updated based on Bayesian estimation approach. At last, on thebasis on constructing the diagnostic information matrix, the effective independencemethod is used for optimal sensor placement in the auto body assembly process.
(3) Multiple fault diagnosis in the auto body assembly process based onBayesian networks
Multiple fault diagnosis in the multi-station assembly process is always different.Based on the above Bayesian network model, methods on the process monitoring forevidence variables, diagnostic reasoning and diagnostic capability analysis are studied.At first, under small sample data condition, a parameter estimation method based onBayesian approach is presented. The estimation results are used as evidence states ofthe sensor nodes for probability reasoning. Afterwards, the diagnostic methods andprocedures based on the Bayesian network are proposed by updating the posteriorprobability of the root nodes. At last, by classifying the diagnosis results, thesensitivity analysis by considering the number of evidence variables and measurementnoises is performed to evaluate the diagnostic performance of Bayesian networks.
(4) Application to the assembly variation source diagnosis
Based on the above theoretical research, the diagnostic method based on Bayesiannetworks is applied in the real assembly cases. The corresponding programmingmodule for assembly process monitoring is developed. The side frame and front areaassembly cases are studied for fixture fault diagnosis and optimal sensor placement. The results showed the Bayesian network method for multiple fault diagnosis in theauto body process is practicable and effective.
This paper presented a framework of Bayesian network model and fault diagnosisin the auto body assembly process, which provides a practicable variation sourcesdiagnosis method under small sample data sets. The proposed methods in this papercan not only be used in dimensional quality improvement of auto bodies, but also canbe applied to aircraft, train bodies and other mechanical products for assembly qualityimprovement.
引文
[1]林忠钦.汽车车身制造质量控制技术[M].北京:机械工业出版社,2005.
[2] JD Power, Initial quality survey1997for automobiles, JD Power and Associated,1997.
[3] Shi, J. Stream of variation modeling and analysis for multistage manufacturingprocesses [M]. CRC Press,2006.
[4]林忠钦,连军,倪军等.基于小样本的车身装配尺寸质量动态高精度评价方法[J].机械工程学报,2001,37(11):62-65.
[5]王华.小样本采样条件下车身焊装检测数据分析与处理研究[D].上海:上海交通大学,2003.
[6]马少平,朱小燕.人工智能[M].北京:清华大学出版社,2004.
[7] Norvig, S. and Russell, P. Artificial intelligence: a modern approach [M].Prentice Hall,2004.
[8] Wittwer, J. W., Chase K. W. and Howell L. L. The direct linearization methodapplied to position error in kinematic linkages [J]. Mechanism and MachineTheory,2004,39(7):681-693.
[9] Gao, J., Chase, K. W., Magleby, S. P. Comparison of assembly tolerance analysisby the direct linearization and modified Monte Carlo simulation methods [C].Proceeding of ASME design engineering technical conference,1995,53-60.
[10] Marler, J. D. Nonlinear tolerance analysis using the direct linearization method[D]. M.S. thesis. Provo UT: Brigham Young University,1988.
[11] DeMeter, E. C. Restraint Analysis of Fixtures which Rely on Surface Contact [J],ASME Journal of Engineering for Industry,1994,116(2):207-215.
[12] Weill, R., Darel, I., Laloum, M. The Influence of Fixture Positioning Errors onthe Geometric Accuracy of Mechanical Parts [C], Proceedings of CIRPConference on PE&MS,1991,215-225.
[13] Cai, W., Hu S. J., Yuan, J. X. A Variational Method of Robust FixtureConfiguration Design for3-D Work pieces [J], ASME Journal of ManufacturingScience and Engineering,1997,119(4):593-602.
[14] Liao, Y. J. and Hu S. J. An integrated model of a fixture workpiece system forsurface quality prediction [J]. International Journal of Advanced ManufacturingTechnology,2001,17(11):810-818.
[15] Cao, J. Variation analysis for rigid workpiece locating considering quadraticeffects using the method of moments [C], ASME International Conference onManufacturing Science and Engineering, Ypsilanti, MI,2006.
[16] Takezawa, N. An Improved method for establishing the process wise qualitystandard [R]. Reports of Statistical and Applied Research. Japanese Union ofScientists and Engineers,1980,27(3):63-76.
[17] Hsieh, C. and Kong, P. Simulation and optimization of assembly processesinvolving flexible parts [J], Journal of Vehicle Design,1997,18(5):455-465.
[18] Liu, S. and Hu, S. J. An offset finite element model and its application inpredicting sheet metal assembly variation [J], International Journal of MachineTools and Manufacturing,1995,35(11):1545-1557.
[19] Liu, S. C. and Hu, S. J. Variation simulation for deformable sheet metalassemblies using Finite Element Methods [J]. Journal of Manufacturing Scienceand Engineering.1997,119(3):369-374.
[20] Camelio, J., Hu, S. J. and Marin, S. P. Compliant assembly variation analysisusing component geometric covariance [J]. Journal of Manufacturing Scienceand Engineering.2004,126:355-360.
[21] Xie, K. Variation propagation analysis on compliant assemblies consideringcontact interaction [J]. Journal of Manufacturing Science and Engineering,2007,129(5),934-942.
[22]邢彦锋.基于装配质量分析的车身零部件装配顺序优化研究[D].上海:上海交通大学.2008.
[23]于奎刚.车身柔性薄板装配过程建模及稳健设计研究[D].上海:上海交通大学,2011.
[24] Apley, D. W. and Shi J. Diagnosis of multiple fixture faults in panel assembly [J],ASME Journal of Manufacturing Science and Engineering,1998,120(4):793-801.
[25] Chang, M. and Gossard, D.C. Computation method for diagnosis ofvariation-related assembly problem [J]. International Journal of ProductionResearch,1998,36(11):2985-2995.
[26] Camelio, J. Hu, S.J. and Yim, H. Sensor placement for effective diagnosis ofmultiple faults in fixturing of compliant parts [J]. Journal of ManufacturingScience and Engineering,2005,127(1),68-74.
[27] Lawless, J. F., Machay, R. J., Robinson J. A. Analysis of variation transmission inmanufacturing processes [J], Journal of Quality Technology,1999,31(2):131-154.
[28] Fong, D.T. and Lawlwss, J.F. The Analysis of Process VariationTransmission with Multivariate Measurement [J], Statistical Sinica,1998,8:151-161.
[29] Hu, S.J. Stream of variation theory for automotive body assembly [C], Annals ofthe CIRP,1997,46(1),1-6.
[30] Jin, J. and Shi J. State space modeling of sheet metal assembly for dimensionalcontrol [J], ASME Transactions, journal of manufacturing science andengineering,1999,121,756-762.
[31] Ding, Y., Ceglarek, D. and Shi J. Modeling and diagnosis of multistagemanufacturing processes part I-state space model [C], Proceedings of the2000Japan/USA Symposium on Flexible Automation, Ann Arbor,2000,7:23-26.
[32]田兆青.轿车车身装配偏差流的状态空间建模方法及应用基础研究[D].上海:上海交通大学,2008.
[33] Camelio, J., Hu, S. J. and Ceglarek, D. Modeling variation propagation ofmulti-station assembly systems with compliant parts [J]. Journal of MechanicalDesign.2003,125(4):673-681.
[34] Ding, Y., Ceglarek D. and Shi, J. Fault diagnosis of multi-station manufacturingprocesses by using state space approach [J], ASME Journal of ManufacturingScience and Engineering,2002,124(2):313-322.
[35] Ding, Y., Shi, J. and Ceglarek, D. Diagnosability analysis of multi-stationmanufacturing processes [J]. ASME Journal of Manufacturing Science andEngineering,2002,124(1):1-13.
[36] Zhou, S., Chen Y. and Shi, J. Statistical estimation and testing for variation rootcause determination of multistage manufacturing processes [J]. IEEETransactions on Automation Science and Engineering,2004,1(1):73-83.
[37] Tian, Z., Lai, X. and Lin, Z. Diagnosis of multiple fixture faults inmultiple-station manufacturing processes based on state space approach [J],Journal of Tsinghua Science and Technology,2004,9(6):628-634.
[38] Khan, A., Ceglarek, D., Shi, J. and Ni, J. Sensor optimization for fault diagnosisin single fixture systems: a methodology [J], ASME Journal of ManufacturingScience and Engineering,1999,121(1):109-117.
[39] Khan, A. and Ceglarek, D. Sensor optimization for fault diagnosis inmulti-fixture assembly systems with distributed sensing [J]. Journal ofManufacturing Science and Engineering.2000,122(1):215-226.
[40] Ding, Y., Kim, P. and Ceglarek, D. Optimal Sensor Distribution for variationDiagnosis in Multistation Assembly Processes [J]. IEEE Transaction of Roboticsand Automation,2003,19(4):543–556.
[41] Lai, X., Tian, Z. and Lin Z., A simplified method for optimal sensor distributionfor process fault diagnosis in multistation assembly processes [J]. Journal ofManufacturing Science and Engineering.2008,130(5):051002-051013.
[42] Hu, S. J., Wu, S. W. Identifying root cause of variation in automobile bodyassembly using principal component analysis [J], Transactions of NAMRI,1992,20:311-316.
[43] Roan, C., Hu S. J. and Wu S. M. Computer aided identification of root cause ofvariation in automobile body assembly [J], ASME Journal of ManufacturingScience and Engineering,1993,64:391-400.
[44] Ceglarek, D. and Shi, J. Fixture failure diagnosis for auto-body assembly usingpattern recognition [J], ASME Journal of Engineering for Industry,1996,118:55-66.
[45] Rong, Q., Ceglarek, D. and Shi, J. Dimensional fault diagnosis for compliantbeam structure assemblies [J]. Journal of Engineering for Industry,2000,122(4),773-780.
[46]胡敏,来新民.主成分分析方法在轿车装配尺寸偏差中的应用研究[J].中国机械工程,2002,6(3):461-463.
[47] Liu, Y. and Hu, S.J. Assembly fixture fault diagnosis using designated componentanalysis [J]. Journal of Manufacturing Science and Engineering,2005,127(2):358-368.
[48] Schwarz, S. A. and Lu, S. Representation, acquisition, and manipulation ofprobabilistic attribute values to support engineering decision making [J]Transaction of NAMRI,1993, XX,261-267.
[49]傅晓锦,张新华.零件加工偏差原因诊断专家系统[J].机械设计与制造工程,1999,5(28):36-38.
[50]高清,郑曦东,马玉林等.零件加工质量偏差原因诊断专家系统的研究[J].1996,28(1):102-107.
[51]杨鸿鹏,林志航.基于集成诊断模型加工质量的智能诊断系统研究,西安交通大学学报,1997,31(9):1-5.
[52] Ceglarek, D., Shi, J. and Wu, S. M. A knowledge-based diagnostic approach forthe launch of the auto-body assembly process [J]. ASME Journal of Engineeringfor Industry,1997,116(4):491-499.
[53]钟秉林,黄仁.机械故障诊断学[M].北京:机械工业出版社,1997.
[54] Feret, P. and Glasgow, I. Combining cased-based and model-based resoning frothe diagnosis of complex devices [J]. Applied Intelligence,1997,3(7):57-78.
[55]陈朝阳,张代胜,任佩红.汽车故障诊断专家系统的现状与发展趋势[J].机械工程学报,2003,39(11):1-6.
[56]杨昌昊.基于不确定性理论的机械故障智能诊断方法研究[D].合肥,中国科学技术大学,2009.
[57]赵秀恒,王清印,王义闹.不确定性系统理论及其在预测与决策中的应用[M].北京:冶金工业出版社,2010.
[58]张文修,梁怡.不确定性信息推理[M].西安:西安交通大学出版社,1996:157-207.
[59] Pearl, J. Probabilistic Reasoning in Intelligent Systems: Networks of PlausibleInference [C]. Morgan Kaufmann, San Mateo, CA,1988.
[60]张连文,郭海鹏.贝叶斯网引论[M].北京:科学出版社,2006.
[61]张德利.基于贝叶斯网络的故障智能诊断方法研究[D].华北电力大学,2008.
[62] James O. Berger. Statistical decision theory and Bayesian analysis [M]. SpringerPress,2010.
[63] Rish, I. An empirical study of the na ve Bayes classifier [R].41-46.
[64] Heckerman, D. A tutorial on learning with Bayesian networks [J]. Studies inComputational Intelligence,2008,156:33-82.
[65]吴喜之.统计决策论及贝叶斯分析[M].北京:上海统计出版社,1998.
[66]茆诗松.贝叶斯统计[M],北京:中国统计出版社,1999.
[67]李剑川.贝叶斯网络故障诊断与维修决策方法及应用研究[D].长沙:国防科技大学,2002.
[68] Howard, R. and Matheson, J.E. Influence diagrams, Readings of on the principlesand applications of decision analysis [C]. Strategic Decisions Group, Menlo Park,CA.1984,721-762.
[69]吕泽华.模糊集理论的新拓展及其应用研究[D].武汉:华中科技大学,2007.
[70]龚雯，基于模糊理论的机械加工偏差源智能诊断方法研究，组合机床与自动化加工技术，2003,9，33-35.
[71] Shafer, G. A mathematics theory of evidence [D]. Princeton: Princeton UniversityPress,1976,20-46.
[72]朱大奇,于盛林.基于D-S证据推理的数据融合算法及其在电路故障诊断中的应用[J].电子学报，2002，30(2):221-223.
[73]彭敏放，何怡刚，王耀南.基于神经网络与证据理论的模拟电路故障诊断[J]，电路与系统学报,2005,10(l):35-39.
[74] Smets, P. The transferable belief model for expert judgments and reliabilityproblems [J]. Reliability Engineering and system safety,1992,38:59-66.
[75]徐晓滨.不确定性信息处理的随机集方法及在系统可靠性评估与故障诊断中的应用[D].上海:上海海事大学,2009.
[76]高晓康.粗糙集理论研究及其在工程和医学诊断中的应用[D].上海:同济大学,2007.
[77]冯林.基于粗糙集理论的不确定信息处理与知识获取方法研究[D].成都:西南交通大学,2004.
[78] Judea, P. Bayesian networks [R]. Handbook of Brain Theory and NeuralNetworks, R-277, MIT Press,2001.
[79] Heckerman, D. and Geiger D. Learning Bayesian networks: the combination ofknowledge and statistical data [J]. Machine Learning,2005,20(3):197-243.
[80] Li, J. and Shi, J. Knowledge discovery from observational data for processcontrol using causal Bayesian network [J]. IIE Transaction,2007,39(1):681-690.
[81] Zhang, N., Poole, D. Exploiting causal independence in Bayesian networkinference [J]. Journal of Artificial Intelligence Research,1996,5,301-328.
[82] Fiedman, N., Murphy, K., Russell, S. Learning the stucture of dynamicprobabilistic networks [C]. In UAI’98Proceedings of the Fourteenth conferenceon Uncertainty in artificial Intelligence, San Francisco,1998,139-147.
[83] Cooper, G.F. and Herskovits E. A Bayesian method for the induction ofprobabilistic networks from data [J]. Machine Learning,1992,9(4):309-347.
[84] Heckerman, D. A tutorial on learning with Bayesian networks [J]. Studies inComputational Intelligence,2008,156:33-82.
[85] Remco, R. B. Bayesian Network Classifiers in Weka [R].2004.
[86] Friedman, N. and Goldszmidt, M. Learning Bayesian networks with localstructure [C]. Proceedings of the Twelfth Conference on Uncertainty in ArtificialIntelligence, Portland, Oregon,1996,252–262.
[87] Friedman, N. and Koller, D. Being Bayesian about network: A Bayesianapproach to structure discovery in Bayesian network [J]. Machine learning,2003,50(1-2):95-125.
[88]刘大有,王飞,卢奕南等.基于遗传算法的Bayesian网络结构学习研究[J].计算机研究与发展,2001,38(8):916-922.
[89]黄友平.贝叶斯网络研究[D].北京:中国科学院研究生院,2005.
[90] Spirtes, P. and Meek, C. Learning Bayesian networks with discrete variablesfrom data [C]. AAAI KDD-95Proceedings.1995,294-299.
[91] Cheng, J., Bell, D., Liu, W.R. Learning Bayesian net-works from data: Anefficient approach based on in-formation theory [J]. Artificial Intelligence,2002,137(1-2):43-90.
[92]王双成,苑森淼.具有丢失数据的贝叶斯网络结构学习研究[J].软件学报,2004,15(7):1030-1041.
[93] Sahami, M., Dumais, S. and Heckerman, D. A Bayesian approach to filteringjunk e-mail. in learning for categorization [R]. Madison, Wisconsin: AAAITechnical Report WS98-05,1998.
[94] Neil, M. and Tranham, E. Using Bayesian networks to predict Oprisk [J].Operational Risks&Regulation,2002,1:8-10.
[95] Liu, E. and Zhang D. Diagnosis of component failures in the space shuttle marineengines using Bayesian belief networks: a feasibility study [J]. InternationalJournal on Artificial Intelligence Tools,2003,12:355-374.
[96] Kipersztok, O., Dildy G.A. Evidence-based Bayesian networks approach toairplane maintenance [C]. Proceeding of the2002Neural Networks.2002,3:2887-2891.
[97] Romessis, C. and Mathioudakis, K. Bayesian network approach for gas path faultdiagnosis [J]. Journal of Engineering for Gas Turbines and Power,2006,128(1):64-72.
[98] Huang, Y., McMurran, R., Dhadyalla G.. Probability based vehicle fault diagnosis:Bayesian network method [J]. Journal of Intelligent Manufacturing,2008,19(3):301-311.
[99] Wolbrecht, E., Ambrosio, B., Paasch B. Monitoring and diagnosis of amulti-stage manufacturing process using Bayesian Networks [J]. ArtificialIntelligence for Engineering Design, Analysis and Manufacturing,2000,14(1):53–67.
[100] Dey, S. and Stori, J.A.A Bayesian network approach to root cause diagnosis ofprocess variations [J]. International Journal of Machine Tool Manufacture,2005,45(1):75-91.
[101]李俭川，胡茑庆，秦国军，温熙森.贝叶斯网络理论及其在设备故障诊断中的应用[J].中国机械工程，2003,14(10):896-900.
[102]张晓丹.汽车发动机故障诊断中不确定问题的贝叶斯网络解法[D].沈阳:东北大学,2005.
[103]傅军,贺炜.贝叶斯网络在柴油机动力装置故障诊断中的应用[J].上海海运学院学报,2001,22(3):68-71.
[104]杨志波,董明.动态贝叶斯网络在设备剩余寿命预测中的应用研究[J].计算机集成制造系统,2007,13(9):1811-1815.
[105]华斌.贝叶斯网络在水电机组状态检修中的应用研究[D].武汉:华中科技大学,2004.
[106]徐宾刚，屈梁生，陶肖明.转子故障贝叶斯诊断网络的研究.机械工程学报.2004,40(1):68-72.
[107]张连文,袁世宏.隐结构模型与中医辨证[R]. HKUST-CS04-12,香港科技大学,2004.
[108]杜世昌.多源多工序加工系统偏差流建模、诊断和控制系统研究[D].上海:上海交通大学,2008.
[109] Lanterman A D., Schwarz, Wallace, and Rissanen: Intertwining themes intheories of model selection [J]. International Statistical Review,2001,69:185-212.
[110]宫秀军.贝叶斯学习理论及其应用研究[D].中国科学院研究生院,2002.
[111] Dougherty, J., Kohavi, R., Sahami M. Supervised and unsuperviseddiscretization of continuous features [C], In Proceedings of the12th InternationalConference on Machine Learning, Los Altos, CA, Morgan Kaufman, California,CA,1995,194–202.
[112]刘银华,金隼.基于小数据集贝叶斯网络建模的装配偏差源诊断[J].上海交通大学学报,2012,46(5):701-705.
[113]蒙哥马利，傅珏生.实验设计与分析[M],上海:人民邮电出版社,2009.
[114] Kammer, C., Brillhart, R.D. Optimal sensor placement for modal identificationusing system-realization methods [J], Journal of Guidance, Control andDynamics,1996,19(3),729-731.
[115]李东升,李宏男,王国新,任亮.传感器布设中有效独立法的简捷快速算法[J].防灾减灾工程学报.2009,29(1):103-108.
[116] Efron, B. Computers and the Theory of Statistics: Thinking the Unthinkable [R].SIAM Review.1979.
[117] Menassa, R. J. and Devries, W. R. Optimization methods applied to selectingsupport positions in fixture design, ASME Journal of Engineering for Industry,1991,113:412-418.