Evidential Reasoning(ER)rule,which can combine multiple pieces of independent evidence conjunctively,is widely applied in multiple attribute decision analysis.However,the assumption of independence among evidence is o...Evidential Reasoning(ER)rule,which can combine multiple pieces of independent evidence conjunctively,is widely applied in multiple attribute decision analysis.However,the assumption of independence among evidence is often not satisfied,resulting in ER rule inapplicable.In this paper,an Evidential Reasoning rule for Dependent Evidence combination(ERr-DE)is developed.Firstly,the aggregation sequence of multiple pieces of evidence is determined according to evidence reliability.On this basis,a calculation method of evidence Relative Total Dependence Coefficient(RTDC)is proposed using the distance correlation method.Secondly,as a discounting factor,RTDC is introduced into the ER rule framework,and the ERr-DE model is formulated.The aggregation process of two pieces of dependent evidence by ERr-DE is investigated,which is then generalized to aggregate multiple pieces of non-independent evidence.Thirdly,sensitivity analysis is carried out to investigate the relationship between the model output and the RTDC.The properties of sensitivity coefficient are explored and mathematically proofed.The conjunctive probabilistic reasoning process of ERr-DE and the properties of sensitivity coefficient are verified by two numerical examples respectively.Finally,the practical application of the ERr-DE is validated by a case study on the performance assessment of satellite turntable system.展开更多
Due to the excellent performance in complex systems modeling under small samples and uncertainty,Belief Rule Base(BRB)expert system has been widely applied in fault diagnosis.However,the fault diagnosis process for co...Due to the excellent performance in complex systems modeling under small samples and uncertainty,Belief Rule Base(BRB)expert system has been widely applied in fault diagnosis.However,the fault diagnosis process for complex mechanical equipment normally needs multiple attributes,which can lead to the rule number explosion problem in BRB,and limit the efficiency and accuracy.To solve this problem,a novel Combination Belief Rule Base(C-BRB)model based on Directed Acyclic Graph(DAG)structure is proposed in this paper.By dispersing numerous attributes into the parallel structure composed of different sub-BRBs,C-BRB can effectively reduce the amount of calculation with acceptable result.At the same time,a path selection strategy considering the accuracy of child nodes is designed in C-BRB to obtain the most suitable submodels.Finally,a fusion method based on Evidential Reasoning(ER)rule is used to combine the belief rules of C-BRB and generate the final results.To illustrate the effectiveness and reliability of the proposed method,a case study of fault diagnosis of rolling bearing is conducted,and the result is compared with other methods.展开更多
基金co-supported by the National Natural Science Foundation of China (No. 61833016)the Shaanxi Outstanding Youth Science Foundation,China (No. 2020JC-34)the Shaanxi Science and Technology Innovation Team,China(No. 2022TD-24)
文摘Evidential Reasoning(ER)rule,which can combine multiple pieces of independent evidence conjunctively,is widely applied in multiple attribute decision analysis.However,the assumption of independence among evidence is often not satisfied,resulting in ER rule inapplicable.In this paper,an Evidential Reasoning rule for Dependent Evidence combination(ERr-DE)is developed.Firstly,the aggregation sequence of multiple pieces of evidence is determined according to evidence reliability.On this basis,a calculation method of evidence Relative Total Dependence Coefficient(RTDC)is proposed using the distance correlation method.Secondly,as a discounting factor,RTDC is introduced into the ER rule framework,and the ERr-DE model is formulated.The aggregation process of two pieces of dependent evidence by ERr-DE is investigated,which is then generalized to aggregate multiple pieces of non-independent evidence.Thirdly,sensitivity analysis is carried out to investigate the relationship between the model output and the RTDC.The properties of sensitivity coefficient are explored and mathematically proofed.The conjunctive probabilistic reasoning process of ERr-DE and the properties of sensitivity coefficient are verified by two numerical examples respectively.Finally,the practical application of the ERr-DE is validated by a case study on the performance assessment of satellite turntable system.
基金supported by the Natural Science Foundation of China(Nos.61773388,61751304,61833016,61702142,U1811264 and 61966009)the Shaanxi Outstanding Youth Science Foundation,China(No.2020JC-34)+2 种基金the Key Research and Development Plan of Hainan,China(No.ZDYF2019007)China Postdoctoral Science Foundation(No.2020M673668)Guangxi Key Laboratory of Trusted Software,China(No.KX202050)。
文摘Due to the excellent performance in complex systems modeling under small samples and uncertainty,Belief Rule Base(BRB)expert system has been widely applied in fault diagnosis.However,the fault diagnosis process for complex mechanical equipment normally needs multiple attributes,which can lead to the rule number explosion problem in BRB,and limit the efficiency and accuracy.To solve this problem,a novel Combination Belief Rule Base(C-BRB)model based on Directed Acyclic Graph(DAG)structure is proposed in this paper.By dispersing numerous attributes into the parallel structure composed of different sub-BRBs,C-BRB can effectively reduce the amount of calculation with acceptable result.At the same time,a path selection strategy considering the accuracy of child nodes is designed in C-BRB to obtain the most suitable submodels.Finally,a fusion method based on Evidential Reasoning(ER)rule is used to combine the belief rules of C-BRB and generate the final results.To illustrate the effectiveness and reliability of the proposed method,a case study of fault diagnosis of rolling bearing is conducted,and the result is compared with other methods.
