基于Petri网的顺序离散事件机电系统故障诊断方法的研究
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摘要
随着现代科学技术的飞速发展,自动化装备的功能日益强大,结构日趋复杂,故障的发生也逐渐频繁,同时在许多大型复杂机电系统中存在着大量具有瞬时性,异步性,并带有顺序动作特点的离散事件机电系统。这类顺序离散事件机电系统有其自身的特点,但缺乏相关的研究手段,为了适应系统可靠性和稳定性的要求,有必要对这类顺序离散事件机电系统的故障诊断方法进行研究。
研究归纳了顺序离散事件机电系统的主要类型,分析了顺序离散事件机电系统的故障特点,研究了其相应的建模方法。基于顺序离散事件机电系统的行为特点,分析了Petri网作为系统建模工具的依据,并在此基础上对三种主要类型建立基本Petri网模型,同时将时间统计信息引入Petri网,对顺序离散事件机电系统建立赋时Petri网模型。提出了基于Bayes试验方法的故障诊断算法,对变迁的时间统计量进行显著性检验,结合系统的先验和后验概率,在模块化故障诊断思想的指导下,分层定位至故障源。分析了在该算法下两类错误的概率,探讨了在最小误诊率的情况下,阈值概率的最优化问题,并推导了其计算方法。研究了微钻检测机的工作特点,分析了其作为顺序离散事件机电系统故障诊断实验平台的可行性。在故障诊断的基础上,研究了故障预测的方法,对顺序离散事件机电系统建立了模糊Petri网模型,推导了库所中托肯的模糊隶属度函数计算方法,提出了基于模糊推理的故障预测方法。
在微钻检测设备上的实验结果表明,所提故障诊断和预测方法是可行的,具有较高的故障诊断准确率,本文所研究的相关内容可以为其他具有离散特征的工业故障诊断应用提供借鉴。
The function of automation equipment becomes more powerful, the structure becomes more complicated and the frequency of fault becomes higher with the quick development of modern science and technology, at the same time, there are a lot of discrete event mechatronic system with the character of instantaneousness, asynchronies, sequence, in many large and complicated mechatronic systems. The sequential discrete event mechatronic system is special, but it lacks of related research methods. In order to adapt to the requirement of reliability and stability, it is necessary to research the fault diagnosis methods of the sequential discrete event mechatronic system.
The typical styles and characters of sequential discrete event mechatronic system were studied in this article, including serial sequence, select sequence and parallel sequence. The characteristics and principle of the fault of sequential discrete event mechatronic system and the related modeling were analyzed. Analyze the foundation of the Petri net modeling the system and establish the basic Petri net models for the three typical types based on the action characters of sequential discrete event mechatronic system. At the same time, consider the time as statistical information pulled in Petri net, and establish timed Petri net modeling for the sequential discrete event mechatronic system. The fault diagnosis arithmetic based on Bayes test method and the significance-test of time statistics of the transition was put forward. Under the guidance of modular fault diagnosis idea, stratify and locate the fault source combined with prior probability and posterior probability of the system. Analyzing the two types fault in this arithmetic, discussed and deduced the threshold probability when the misdiagnosis probability was least. The work characteristics of micro-drill’s detection equipment were studied in this paper, and the feasibility of considering it as the test platform of the sequential discrete event mechatronic system was analyzed. Fault forecast methods based on fuzzy reasoning were studied and put forward, and establish the fuzzy Petri net model for the sequential discrete event mechatronic system, and deduce the fuzzy membership functions calculation method of tokens of the places, based on fault diagnosis.
The test result of micro-drill’s detection equipment shows that the fault diagnosis and forecast methods are feasible, and the accuracy rate of fault diagnosis is high, and the research result in this dissertation provides technical reference for the other industrial fault diagnosis with the characters of discretization.
研究归纳了顺序离散事件机电系统的主要类型,分析了顺序离散事件机电系统的故障特点,研究了其相应的建模方法。基于顺序离散事件机电系统的行为特点,分析了Petri网作为系统建模工具的依据,并在此基础上对三种主要类型建立基本Petri网模型,同时将时间统计信息引入Petri网,对顺序离散事件机电系统建立赋时Petri网模型。提出了基于Bayes试验方法的故障诊断算法,对变迁的时间统计量进行显著性检验,结合系统的先验和后验概率,在模块化故障诊断思想的指导下,分层定位至故障源。分析了在该算法下两类错误的概率,探讨了在最小误诊率的情况下,阈值概率的最优化问题,并推导了其计算方法。研究了微钻检测机的工作特点,分析了其作为顺序离散事件机电系统故障诊断实验平台的可行性。在故障诊断的基础上,研究了故障预测的方法,对顺序离散事件机电系统建立了模糊Petri网模型,推导了库所中托肯的模糊隶属度函数计算方法,提出了基于模糊推理的故障预测方法。
在微钻检测设备上的实验结果表明,所提故障诊断和预测方法是可行的,具有较高的故障诊断准确率,本文所研究的相关内容可以为其他具有离散特征的工业故障诊断应用提供借鉴。
The function of automation equipment becomes more powerful, the structure becomes more complicated and the frequency of fault becomes higher with the quick development of modern science and technology, at the same time, there are a lot of discrete event mechatronic system with the character of instantaneousness, asynchronies, sequence, in many large and complicated mechatronic systems. The sequential discrete event mechatronic system is special, but it lacks of related research methods. In order to adapt to the requirement of reliability and stability, it is necessary to research the fault diagnosis methods of the sequential discrete event mechatronic system.
The typical styles and characters of sequential discrete event mechatronic system were studied in this article, including serial sequence, select sequence and parallel sequence. The characteristics and principle of the fault of sequential discrete event mechatronic system and the related modeling were analyzed. Analyze the foundation of the Petri net modeling the system and establish the basic Petri net models for the three typical types based on the action characters of sequential discrete event mechatronic system. At the same time, consider the time as statistical information pulled in Petri net, and establish timed Petri net modeling for the sequential discrete event mechatronic system. The fault diagnosis arithmetic based on Bayes test method and the significance-test of time statistics of the transition was put forward. Under the guidance of modular fault diagnosis idea, stratify and locate the fault source combined with prior probability and posterior probability of the system. Analyzing the two types fault in this arithmetic, discussed and deduced the threshold probability when the misdiagnosis probability was least. The work characteristics of micro-drill’s detection equipment were studied in this paper, and the feasibility of considering it as the test platform of the sequential discrete event mechatronic system was analyzed. Fault forecast methods based on fuzzy reasoning were studied and put forward, and establish the fuzzy Petri net model for the sequential discrete event mechatronic system, and deduce the fuzzy membership functions calculation method of tokens of the places, based on fault diagnosis.
The test result of micro-drill’s detection equipment shows that the fault diagnosis and forecast methods are feasible, and the accuracy rate of fault diagnosis is high, and the research result in this dissertation provides technical reference for the other industrial fault diagnosis with the characters of discretization.
引文
[1] Andrew K.S. Jardine, Daming Lin, Dragan Banjevic. A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mechanical Systems and Signal Processing 20(2006) 1483-1510
[2]杨士元.数字系统的故障诊断与可靠性设计[M].北京:清华大学出版社,2000.
[3] Dong Shang Chang, Shwu-Tzy Jiang. Assessing quality performance based on the on-line sensor measurements using neural networks. Computers & Industrial Engineering, 2002, (42): 417-424
[4] I. Inasaki. Sensor fusion for monitoring and controlling grinding processes, Int J Adv Manuf Technol (1999)15: 730-736
[5] Jay Lee. Smart machines and e- manufacturing Systems for e-business transformation.中国机械工程,12(2005):526-530
[6] P.-J. Vlok, M. Wnek, M. Zygmunt, Utilising statistical residual life estimates of bearings to quantify the influence of preventive maintenance actions, Mechanical Systems and Signal Processing 18 (2004) 833-847.
[7] Araiza M L. Kent R Espinosa R, Real-time Embedded Diagnostics and Prognostics in Advanced Artillery Systems[J]. Autotestcon Proceedings,2002,IEEE,2002:818-841
[8] D. Djurdjanovic, J. Lee, J. Ni. Watchdog Agent– an infortronics-based prognostics approach for product performance degradation assessment and prediction. Advanced Engineering Informatics, 2003, 17: 109-125
[9]劭长桥,杜晓辉,李光芹.信号交叉口排队离散车头时距统计分析.公路交通科技.2003,20(4):76-79
[10]董昭,李翔.离散时间序列的网络模体分析.物理学报.2010,59(3):1600-1607
[11]曾鹏等,多变量时间序列的主成分分析及估计.南京邮电学院学报,4(1996):112-116
[12]林春方,郭立.动态独立分量分析算法及其应用研究,核电子学与探测技术,6(2006):726-730
[13] Lee J M, et al. Vanrollegheghem Perer A, Lee In-Beum. Nonlinear process monitoring using principal component analysis [J]. Chemical Engineering Science,2004,59: 223-234
[14] He Q B,Kong F R,Yan R Q. Subspaced-based gearbox monitoring by kernel principal component analysis[J]. Mechanical Systems and Signal Processing,2007,21: 1755-1772
[15] M.L. Fugate, H. Sohn, C.R. Farrar, Vibration-based damage detection using statistical process control, Mechanical Systems and Signal Processing 15 (2001) :707-721
[16] M. Guo, L. Xie, S.-Q. Wang, J.-M. Zhang, Research on an integrated ICA-SVM basedframework for fault diagnosis, in: Proceedings of the 2003 IEEE International Conference on Systems, Man and Cybernetics, vol. 3, Washington, DC, USA, 2003, pp. 2710-2715
[17] L.R. Rabiner, Tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE 77 (1989) 257-286.
[18]符文星,朱苏朋,阎杰,陈士橹.参数估计法在运载火箭动力系统故障诊断中的应用.弹箭与制导学报,2007,27(1):181-183
[19]齐俊桐,韩建达.基于MIT规则的自适应Unscented卡尔曼滤波及其在旋翼飞行机器人容错控制的应用.2009,45(4):115-124
[20]夏天,王新晴,肖云魁,梁升.基于离散粒子群优化算法的汽车发动机故障特征选取.中国工程机械学报.2010,8(2):219-223
[21]马晓旭,张传利,夏明超,黄益庄.基于离散隐马尔科夫模型的变压器励磁涌流鉴别新算法.电力系统自动化.2000,3:23-28.
[22]吕冬梅,于飞,颜秉勇,刘喜梅.LMI方法的不确定离散时滞系统故障诊断.哈尔滨工业大学学报.2009.41(12):270-272
[23]陈玉东,翁正新,施颂椒.基于最小二乘估计的非线性离散系统鲁棒故障诊断.应用科学学报.2003,21(1):77-83
[24] Trunov A B,Polycarpou M M. Automated fault diagnosis in nonlinear multivariable systems using a learning methodology[J]. IEEE Trans Neural network,2000,11(1):91-101
[25]朱大奇,于盛林.电子电路故障诊断的神经网络数据融合算法[J].东南大学学报,2001(12):87-91
[26]郭文鑫等.计及警报信息时序特性的电网故障诊断解析模型.电力系统自动化,2008(22):26-31
[27]陈小异.基于噪声信号处理的机电一体化设备故障诊断.机床与液压,2005(12):183-185
[28] J. Yan, M. Koc, J. Lee, A prognostic algorithm for machine performance assessment and its application, Production Planning and Control 15 (2004) 796–801.
[29] C. Kwan, X. Zhang, R. Xu, L. Haynes, A novel approach to fault diagnostics and prognostics, in: Proceedings of the 2003 IEEE International Conference on Robotics and Automation, vols. 1–3, New York, 2003, pp. 604–609.
[30] W.Q. Wang, M.F. Golnaraghi, F. Ismail, Prognosis of machine health condition using neuro-fuzzy systems, Mechanical Systems and Signal Processing 18 (2004) 813–831.
[31] R.C.M. Yam, P.W. Tse, L. Li, P. Tu, Intelligent predictive decision support system for condition-based maintenance, International Journal of Advanced Manufacturing Technology 17 (2001) 383–391.
[32]屈梁生,张海军.机械诊断中的几个基本问题,中国机械工程,2002(2):211-217
[33]梁远华,苑秉成.基于BP算法的模糊Petri网鱼雷故障诊断方法.武汉理工大学学报,2010,34(5):895-899
[34]马敏,黄建国,夏侯士戟.基于自适应模糊Petri网的雷达故障诊断方法研究.仪器仪表学报.2008,29(2):261-265
[35]唐达,杨元生.基于层次细化Petri网的工作流参与者机制与动态特性研究.计算机研究与发展.2004,41(9):1545-1553
[36]李慧芳,李人厚,陈浩勋.受控赋时Petri网在批处理系统建模中的应用.西安交通大学学报.2000,34(4):55-59
[37] L Wells. Performance Analysis Using Colored Petri Nets[C]//Proceeding of the IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems.2002
[38]刘剑刚,高洁,王明哲.模糊Petri网及其在模糊推理中的应用.计算机仿真.2004,11:152-154
[39]胡松立等.微钻刃面图像边缘角点自适应提取方法.上海交通大学学报.2009,43(5):825-833
[40]吴丁云,许黎明,胡松立,陈明.微型钻针内芯倒锥度测量新方法的研究.工艺与检测.2009(1):95-98
[41] Martinez M A T, Moreno E G. Fault Diagnosis and Modeling of The Liquids Packaging Process. A Research Based on Petri Nets. 2008 10th Intl. Conf. on Control, Automation, Robotics and Vision. Hanoi, Vietnam, 2008:1620-1624.
[42] XUE Fei, ZHENG Da-zhong. Fault diagnosis of timed event graph. Control Theory and Applications,2005, 22(4):609-614.
[43] Wang xiaoli, Chen guangju, Xie yue, et al. Fault Detection and Diagnosis Based on Time Petri Net. The Eighth International Conference on Electronic Measurement and Instruments, 2007, 3259-3263.
[44]张金槐,刘琦,冯静. Bayes试验分析方法.长沙:国防科技大学出版社,2007.
[45]张金槐.再入飞行器落点散布鉴定中验前概率的确定.飞行器测控技术,1991(2):1-7.
[46]张金槐,唐雪梅.验前分布的确定及导弹落点精度鉴定.飞行器测控技术,1990(2):1-9.
[47] Chen M Z, Zhou D H, Liu G P. A new particle predictor for fault prediction of nonlinear time-varying systems[J]. Developments in Chemical Engineering and Mineral Processing, 2005, 13(3):379-388.
[48]贾占强等,基于综合环境加速寿命试验的电子装备故障预测研究[J].电子学报,2009,36(6):1277-1282.
[49] Cao Y, Chen G.A fuzzy Petri-Nets model for computing with words[J].IEEE Transactions on Fuzzy Systems,2010,18(3):486-499.
[50] Wai R J, Liu C M. Design of dynamic petri recurrent fuzzy neural network and its applicationto path-tracking control of nonholonomic mobile robot[J]. IEEE Transactions on Industrial Electronics,2009,56(7):2667-2683.
[51] Aziz A M. Effects of fuzzy membership function shapes on clustering performance in multisensory-multitarget data fusion systems[J]. IEEE International Conference on Fuzzy Systems,2009,1839-1844.
[52] Xin M T, Shi S Z. Metal model based fuzzy Petri nets back propagation learning algorithm[J].IMACS Multiconference on“Computational Engineering in Systems Applications”,CESA,2006,1853-1857.
[53] Tinos R, Terra M H, Bergerman M. A fault tolerance framework for cooperative robotic manipulators[J].Journal of Intelligent Manufacturing,2007,18(3):433-448.
[54] Y Ting, W B Lu, C H Chen, et al. A fuzzy reasoning design for fault detection and diagnosis of a computer-controlled system[J].Engineering Applications of Artificial Intelligence,2008,21(2):157-170.
[55] X Li, F Lara-Rosano. Adaptive fuzzy petri nets for dynamic knowledge representation and inference[J]. Expert Systems with Applications, 2000, 19(3):235-241.
[2]杨士元.数字系统的故障诊断与可靠性设计[M].北京:清华大学出版社,2000.
[3] Dong Shang Chang, Shwu-Tzy Jiang. Assessing quality performance based on the on-line sensor measurements using neural networks. Computers & Industrial Engineering, 2002, (42): 417-424
[4] I. Inasaki. Sensor fusion for monitoring and controlling grinding processes, Int J Adv Manuf Technol (1999)15: 730-736
[5] Jay Lee. Smart machines and e- manufacturing Systems for e-business transformation.中国机械工程,12(2005):526-530
[6] P.-J. Vlok, M. Wnek, M. Zygmunt, Utilising statistical residual life estimates of bearings to quantify the influence of preventive maintenance actions, Mechanical Systems and Signal Processing 18 (2004) 833-847.
[7] Araiza M L. Kent R Espinosa R, Real-time Embedded Diagnostics and Prognostics in Advanced Artillery Systems[J]. Autotestcon Proceedings,2002,IEEE,2002:818-841
[8] D. Djurdjanovic, J. Lee, J. Ni. Watchdog Agent– an infortronics-based prognostics approach for product performance degradation assessment and prediction. Advanced Engineering Informatics, 2003, 17: 109-125
[9]劭长桥,杜晓辉,李光芹.信号交叉口排队离散车头时距统计分析.公路交通科技.2003,20(4):76-79
[10]董昭,李翔.离散时间序列的网络模体分析.物理学报.2010,59(3):1600-1607
[11]曾鹏等,多变量时间序列的主成分分析及估计.南京邮电学院学报,4(1996):112-116
[12]林春方,郭立.动态独立分量分析算法及其应用研究,核电子学与探测技术,6(2006):726-730
[13] Lee J M, et al. Vanrollegheghem Perer A, Lee In-Beum. Nonlinear process monitoring using principal component analysis [J]. Chemical Engineering Science,2004,59: 223-234
[14] He Q B,Kong F R,Yan R Q. Subspaced-based gearbox monitoring by kernel principal component analysis[J]. Mechanical Systems and Signal Processing,2007,21: 1755-1772
[15] M.L. Fugate, H. Sohn, C.R. Farrar, Vibration-based damage detection using statistical process control, Mechanical Systems and Signal Processing 15 (2001) :707-721
[16] M. Guo, L. Xie, S.-Q. Wang, J.-M. Zhang, Research on an integrated ICA-SVM basedframework for fault diagnosis, in: Proceedings of the 2003 IEEE International Conference on Systems, Man and Cybernetics, vol. 3, Washington, DC, USA, 2003, pp. 2710-2715
[17] L.R. Rabiner, Tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE 77 (1989) 257-286.
[18]符文星,朱苏朋,阎杰,陈士橹.参数估计法在运载火箭动力系统故障诊断中的应用.弹箭与制导学报,2007,27(1):181-183
[19]齐俊桐,韩建达.基于MIT规则的自适应Unscented卡尔曼滤波及其在旋翼飞行机器人容错控制的应用.2009,45(4):115-124
[20]夏天,王新晴,肖云魁,梁升.基于离散粒子群优化算法的汽车发动机故障特征选取.中国工程机械学报.2010,8(2):219-223
[21]马晓旭,张传利,夏明超,黄益庄.基于离散隐马尔科夫模型的变压器励磁涌流鉴别新算法.电力系统自动化.2000,3:23-28.
[22]吕冬梅,于飞,颜秉勇,刘喜梅.LMI方法的不确定离散时滞系统故障诊断.哈尔滨工业大学学报.2009.41(12):270-272
[23]陈玉东,翁正新,施颂椒.基于最小二乘估计的非线性离散系统鲁棒故障诊断.应用科学学报.2003,21(1):77-83
[24] Trunov A B,Polycarpou M M. Automated fault diagnosis in nonlinear multivariable systems using a learning methodology[J]. IEEE Trans Neural network,2000,11(1):91-101
[25]朱大奇,于盛林.电子电路故障诊断的神经网络数据融合算法[J].东南大学学报,2001(12):87-91
[26]郭文鑫等.计及警报信息时序特性的电网故障诊断解析模型.电力系统自动化,2008(22):26-31
[27]陈小异.基于噪声信号处理的机电一体化设备故障诊断.机床与液压,2005(12):183-185
[28] J. Yan, M. Koc, J. Lee, A prognostic algorithm for machine performance assessment and its application, Production Planning and Control 15 (2004) 796–801.
[29] C. Kwan, X. Zhang, R. Xu, L. Haynes, A novel approach to fault diagnostics and prognostics, in: Proceedings of the 2003 IEEE International Conference on Robotics and Automation, vols. 1–3, New York, 2003, pp. 604–609.
[30] W.Q. Wang, M.F. Golnaraghi, F. Ismail, Prognosis of machine health condition using neuro-fuzzy systems, Mechanical Systems and Signal Processing 18 (2004) 813–831.
[31] R.C.M. Yam, P.W. Tse, L. Li, P. Tu, Intelligent predictive decision support system for condition-based maintenance, International Journal of Advanced Manufacturing Technology 17 (2001) 383–391.
[32]屈梁生,张海军.机械诊断中的几个基本问题,中国机械工程,2002(2):211-217
[33]梁远华,苑秉成.基于BP算法的模糊Petri网鱼雷故障诊断方法.武汉理工大学学报,2010,34(5):895-899
[34]马敏,黄建国,夏侯士戟.基于自适应模糊Petri网的雷达故障诊断方法研究.仪器仪表学报.2008,29(2):261-265
[35]唐达,杨元生.基于层次细化Petri网的工作流参与者机制与动态特性研究.计算机研究与发展.2004,41(9):1545-1553
[36]李慧芳,李人厚,陈浩勋.受控赋时Petri网在批处理系统建模中的应用.西安交通大学学报.2000,34(4):55-59
[37] L Wells. Performance Analysis Using Colored Petri Nets[C]//Proceeding of the IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems.2002
[38]刘剑刚,高洁,王明哲.模糊Petri网及其在模糊推理中的应用.计算机仿真.2004,11:152-154
[39]胡松立等.微钻刃面图像边缘角点自适应提取方法.上海交通大学学报.2009,43(5):825-833
[40]吴丁云,许黎明,胡松立,陈明.微型钻针内芯倒锥度测量新方法的研究.工艺与检测.2009(1):95-98
[41] Martinez M A T, Moreno E G. Fault Diagnosis and Modeling of The Liquids Packaging Process. A Research Based on Petri Nets. 2008 10th Intl. Conf. on Control, Automation, Robotics and Vision. Hanoi, Vietnam, 2008:1620-1624.
[42] XUE Fei, ZHENG Da-zhong. Fault diagnosis of timed event graph. Control Theory and Applications,2005, 22(4):609-614.
[43] Wang xiaoli, Chen guangju, Xie yue, et al. Fault Detection and Diagnosis Based on Time Petri Net. The Eighth International Conference on Electronic Measurement and Instruments, 2007, 3259-3263.
[44]张金槐,刘琦,冯静. Bayes试验分析方法.长沙:国防科技大学出版社,2007.
[45]张金槐.再入飞行器落点散布鉴定中验前概率的确定.飞行器测控技术,1991(2):1-7.
[46]张金槐,唐雪梅.验前分布的确定及导弹落点精度鉴定.飞行器测控技术,1990(2):1-9.
[47] Chen M Z, Zhou D H, Liu G P. A new particle predictor for fault prediction of nonlinear time-varying systems[J]. Developments in Chemical Engineering and Mineral Processing, 2005, 13(3):379-388.
[48]贾占强等,基于综合环境加速寿命试验的电子装备故障预测研究[J].电子学报,2009,36(6):1277-1282.
[49] Cao Y, Chen G.A fuzzy Petri-Nets model for computing with words[J].IEEE Transactions on Fuzzy Systems,2010,18(3):486-499.
[50] Wai R J, Liu C M. Design of dynamic petri recurrent fuzzy neural network and its applicationto path-tracking control of nonholonomic mobile robot[J]. IEEE Transactions on Industrial Electronics,2009,56(7):2667-2683.
[51] Aziz A M. Effects of fuzzy membership function shapes on clustering performance in multisensory-multitarget data fusion systems[J]. IEEE International Conference on Fuzzy Systems,2009,1839-1844.
[52] Xin M T, Shi S Z. Metal model based fuzzy Petri nets back propagation learning algorithm[J].IMACS Multiconference on“Computational Engineering in Systems Applications”,CESA,2006,1853-1857.
[53] Tinos R, Terra M H, Bergerman M. A fault tolerance framework for cooperative robotic manipulators[J].Journal of Intelligent Manufacturing,2007,18(3):433-448.
[54] Y Ting, W B Lu, C H Chen, et al. A fuzzy reasoning design for fault detection and diagnosis of a computer-controlled system[J].Engineering Applications of Artificial Intelligence,2008,21(2):157-170.
[55] X Li, F Lara-Rosano. Adaptive fuzzy petri nets for dynamic knowledge representation and inference[J]. Expert Systems with Applications, 2000, 19(3):235-241.