Discrete-time Bayesian Network Analysis Method Based On T-S Dynamic Fault Tree

Traditional fault tree and T-S fault tree analysis methods can only express static logic relationships.Dugan dynamic fault tree analysis method can not express any form of static and dynamic logic relations,but usually needs to use Markov chain and Monte Carlo method to solve dynamic subtrees,so it can not directly perform quantitative analysis.T-S dynamic fault tree analysis method overcomes the shortcomings of the existing methods.The advantages of T-S dynamic fault tree and Bayesian network model in mechanism analysis modeling and inference calculation can be fully utilized.Therefore,the discrete-time Bayesian network analysis method based on T-S dynamic fault tree and its importances and sensitivity are studied.Firstly,the T-S dynamic fault tree analysis method is studied.The construction process of T-S dynamic fault tree and the description rules of T-S dynamic gates are introduced.There are two kinds of description rules: time state rules and event occurrence rules.The algorithms of input and output rules of T-S dynamic gates are given.The method is compared with Dugan dynamic fault tree analysis method solved by Markov chains and Monte Carlo method and also compared with T-S fault tree analysis method.The practicability and simplicity of the proposed method are proved.Secondly,the transformation method of T-S dynamic fault tree to discrete-time Bayesian network is studied.The construction method of directed acyclic graph of discrete-time Bayesian network based on T-S dynamic fault tree is introduced.The conditional probability tables of discrete-time Bayesian network and the fault probability algorithm of leaf node and the posterior probabilities algorithm of root nodes are given.The method is compared with T-S dynamic fault tree analysis method to verify the feasibility.Then,aiming at the importance judgment of components in dynamic systems,the importance measures and sensitivity algorithms of discrete-time Bayesian network are proposed based on traditional fault tree and static Bayesian networks' importance measures and sensitivity,which including risk importance measure,upgrading function,differential importance measure and sensitivity.These algorithms describe the importance of the root nodes with dynamic failure characteristics.By comparing with static Bayesian network algorithms,feasibility and superiority of the proposed algorithms are verified.Finally,the reliability of hydraulic system of concrete pump is analyzed by using the proposed discrete-time Bayesian network method based on T-S dynamic fault tree.The failure probability of the system and the Birnbaum importance measure,criticality importance measure,F-V importance measure,upgrading function,differential importance measure and sensitivity of each component are obtained by the proposed importance measures and sensitivity methods.The results are analyzed to provide methods and theoretical basis for the reliability analysis of the hydraulic system of concrete pump and the identification of the weakness of the system.