Research On Static Analysis Method Of Dynamic Fault Tree

Fault tree is a graphical modeling of system failure and can be used to analyze the way of occurrence of accidents in the system.The traditional static fault tree models the failure events of the system with static Boolean logic,which does not consider the sequence relation of the failure events,and it relies on the minimal cut set in the qualitative analysis(the minimal set of basic events that causes the system failure).Compare to static fault tree,temporal logic is added to dynamic fault tree,it can easily model some sequential dependent failure events,but in qualitative analysis,it is necessary to rely on the minimal cut sequence(the minimal sequence of basic events that causes the failure of the system)rather than the minimal cut set in the static fault tree.The calculation of minimal cut sequence is a problem of factorial complexity,and in fault diagnosis,in addition to the current state of all system components,the history of component failure must be recorded and matched with the minimal cut sequence,which increases the cost of system maintenance and fault diagnosis.In addition,the quantitative analysis of dynamic fault tree can be divided into two methods: exact and approximate solution.The exact solution often depends on the equivalent Markov chain,which is prone to the state space explosion problem.The approximate solutions include the discrete-time Bayesian network and Monte Carlo simulation,but the execution time increases rapidly with the increase of number of time interval and the number of simulation.According to the factorial complexity problem of solving minimal cut sequence and historical related problems of fault diagnosis in the qualitative analysis of dynamic fault tree,and the time complexity in the approximate quantitative analysis,the static qualitative and quantitative analysis method of the dynamic fault tree is studied in this thesis on the basis of the existing static transformation work of the partial dynamic logic gates,details are as follows:(1)The static transformation method for all dynamic gates of dynamic fault tree is extended and improved.Firstly,based on the existing static transformation method of partial dynamic gates,such as the priority and gates,two cold standby gates sharing a spare event et al.,the static transformation of the cold gates with multiple inputs and sharing multiple spare events is expanded.And the static transformation method for various warm standby gates and hot standby gates is proposed,thus provide a complete solution for the static transformation of all dynamic gates of the dynamic fault tree.(2)The minimal cut sequence generation algorithm of dynamic fault tree is designed,and the real time and space complexity of the minimal cut sequence of dynamic fault tree and the minimal cut set of static fault tree generated by the transformation are compared and analyzed through examples.In the first step,the CSSs(Cut Sequence Sets)of dynamic fault tree and the minimal cut sets of the equivalent static fault tree are obtained using Maude formalization tool,and a contrast analysis is made between them.Then,the algorithm of generating minimal cut sequences by CSSs is designed,which improves efficiency to a certain extent than exhaustive search.Finally,the time of the execution time of CSSs and the time of generating the minimal cut sequences by CSSs are accumulated to obtain the total time of solving minimal cut sequences.And the comparison between the minimal cut set and the minimal cut sequences is performed by analyzing the time complexity and space complexity,which further demonstrates the practical significance of the static transformation from dynamic fault tree to static fault tree.(3)An algebraic approximation method based on the minimal canonical form of dynamic fault tree is proposed,and the effectiveness and efficiency of the method are verified by comparison with discrete-time Bayesian network and Monte Carlo simulation method.In static fault trees equivalent to dynamic fault trees,temporal semantics of conditioning events are similar to temporal operators in CSSs.On this basis,this thesis proposes an algebraic approximation method based on the minimal canonical form of dynamic fault tree to make a fault prediction for the dynamic system,using the quantitative relationship between the minimal cut sequence and the whole sequence.The effectiveness of the results in engineering application and the advantage of the method in time efficiency are verified by comparison with discrete-time Bayesian network method and Monte Carlo simulation method.The research work of this thesis theoretically improves the static transformation,qualitative and quantitative analysis method of dynamic fault tree.In the practical engineering application,the problem of factorial complexity of the minimal sequence can be avoided,and the historical correlation in system maintenance and fault diagnosis can be solved using the method of this thesis,and it provide a new method for rapid approximation of system reliability with a certain practical value.