基于超椭球模型的T-S模糊因果图的故障分析
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摘要
研究了用区间数对T-S模糊因果图的故障诊断问题,同时考虑了基于超椭球模型对因果图的故障区间加以约束;首先,建立T-S模糊门,通过D-S理论建立适当的超椭球模型处理因果图中不确定性参量的取值范围和解决复杂系统的故障机理和多态性;其次,将超椭球模型转化成单位超椭球模型,在超椭球内产生均匀分布的随机数,对其进行均匀采样,从而得到了更加符合实际T-S规则的故障可能性区间概率;最后,利用Matlab进行数值模拟,证实了由超椭球模型所得结论的有效性;结果显示:超椭球模型能有效减缓因果图获取精确数据的难度,比区间模型下的范围对因果图更加具有可靠性和实际意义。
The fault diagnosis problem of the T-S fuzzy Causality Graph with the interval number is studied,and the fault interval based on the hyper-ellipsoid model is considered to be constrained. First,the T-S fuzzy gate is set up,and a Hyper-ellipsoid model is established by D-S theory to deal with the range of uncertainty parameters in the Causality Graph,and to solve the fault mechanism and polymorphism of the complex system. Secondly,the Hyperellipsoid model is transformed into a unit Hyper-ellipsoid model,and the random number of the uniform distribution is produced in Hyper-ellipsoid model,and it is uniformly sampled,thus the probability of fault possibility interval which is more in line with the actual T-S rule is obtained. Finally,Matlab is used to carry out numerical simulation,which confirms the validity of the conclusion from the Hyper-ellipsoid model. Therefore,the Hyper-ellipsoid model can effectively slow down the difficulty of obtaining accurate data in the Causality Graph,which is more reliable and practical than the range model in the Causal Graph.
The fault diagnosis problem of the T-S fuzzy Causality Graph with the interval number is studied,and the fault interval based on the hyper-ellipsoid model is considered to be constrained. First,the T-S fuzzy gate is set up,and a Hyper-ellipsoid model is established by D-S theory to deal with the range of uncertainty parameters in the Causality Graph,and to solve the fault mechanism and polymorphism of the complex system. Secondly,the Hyperellipsoid model is transformed into a unit Hyper-ellipsoid model,and the random number of the uniform distribution is produced in Hyper-ellipsoid model,and it is uniformly sampled,thus the probability of fault possibility interval which is more in line with the actual T-S rule is obtained. Finally,Matlab is used to carry out numerical simulation,which confirms the validity of the conclusion from the Hyper-ellipsoid model. Therefore,the Hyper-ellipsoid model can effectively slow down the difficulty of obtaining accurate data in the Causality Graph,which is more reliable and practical than the range model in the Causal Graph.
引文
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[2] PEARL J. Evidential Reasoning Using Stochastic Simulation of Causal Models[M]. Elsevier Science Publishers Ltd.,1987
[3]金星,洪延姬,武江涛,等.基于故障树的智能型故障诊断系统[J].宇航学报,2001,22(3):111-113,118JIN X,HONG Y J,WU J T,et al. A Kind of Intelligent Fault Diagnosis System Based on the Fault Tree Analysis[J]. Journal of Astronautics,2001,22(3):111-113,118
[4]宋华,张洪钺,王行仁. T-S模糊故障树分析方法[J].控制与决策,2005,20(8):854-859SONG H,ZHANG H Y,WANG X R. Fuzzy Fault Tree Analysis Based on T-S Model[J]. Control and Decision,2005,20(8):854-859
[5]梁新元,王洪春,石庆喜,等.因果图向故障树转换的研究[J].计算机仿真,2005,22(12):67-70LIANG X Y,WANG H C,SHI Q X,et al. Study on the Conversion of Causality Diagram to Fault Tree[J].Computer Simulation,2005,22(12):67-70
[6]梁新元,张勤.故障树向因果图转换的研究[J].计算机仿真,2005,22(10):144-146LIANG X Y,ZHANG Q. Study on Conversion of Fault Tree to Causality Diagram[J]. Computer Simulation,2005,22(12):67-70
[7]樊兴华,张勤,孙茂松,等.多值因果图的推理算法研究[J].计算机学报,2003,26(3):310-322FAN X H,ZHANG Q,SUN M S,et al. Reasoning Algorithm of Multi Value Causality Diagram[J]. Computer Journal,2003,26(3):310-322
[8]王洪春.基于因果图的不确定性推理理论及算法研究[D].重庆:重庆大学,2005WANG H C. Research on the Theory and Algorithm of Uncertainty Reasoning Based on Causality Diagram[D].Chongqing:Chongqing University,2005
[9]沈文武.因果图推理算法及专家系统应用研究[D].重庆:重庆大学,2005SHENG W W. Causality Graph Reasoning Algorithm and Application Research of Expert System[D]. Chongqing:Chongqing University,2005
[10] SONG H,ZHANG H Y,CHAN C W. Fuzzy Fault Tree Analysis Based on T-S Model With Application to INS/GPS Navigation System[J]. Soft Computing,2009,13(1):31-34
[11]王洪春.基于因果图的一种知识获取方法[J].计算机仿真,2006,23(3):126-128WANG H C. A Method of Knowledge Acquisition Based on Causality Diagram[J]. Computer Simulation,2006,23(3):126-128
[12] WU W Z. Upper and Lower Probabilities of Fuzzy Events Induced by a Fuzzy Set-Valued Mapping[C]∥International Conference on Rough Sets,Fuzzy Sets,Data Mining,and Granular Computing. Springer-Verlag,2005:345-353
[13] JAMESINGLIS. A Mathematical Theory of Evidence[J].Technometrics,1976,20(1):106-106
[14]罗阳军.基于多椭球凸模型的结构非概率可靠性优化设计[D].大连:大连理工大学,2009LUO Y J, Structural Non Probabilistic Reliability Optimization Design Based on Multi Ellipsoidal Convex Model[D]. Dalian:Dalian University of Technology,2009
[15]曹鸿钧,段宝岩.基于凸集合模型的非概率可靠性研究[J].计算力学学报,2005,22(5):546-550CAO H J,DUAN B Y. An Approach on the Nonprobabilistic Reliability of Strctures Based on Uncertainty Convex Models[J]. Chinese Journal of Computational Mechanics,2005,22(5):546-550