Algebraic Binary Decision Diagram For Analysis Of Dynamic Fault Tree

A fault tree is a special tree-like logical causality diagram that uses event symbols,logic gate symbols,and transition symbols to describe the causal relationship between various events in the system.The input event of the logic gate is the "cause" of the output event,and the output event of the logic gate is the "result" of the input event.The traditional static fault tree uses Boolean logic to model the events that occur in the system,regardless of the sequence in which the events occur.The dynamic fault tree is an extension of the traditional static fault tree.The dynamic logic gate is introduced to represent the sequential logic relationship between fault events,in order to analyze the reliability of the system with dynamic characteristics such as fault recovery and sequential correlation.Nowadays,there are many analysis algorithms to establish a dynamic fault tree model of the system,and then transform the large and complex fault tree model into the existing known mathematical model,so that the dynamic system can be analyzed to solve the random problem and systematic problem with sexual failure and correlation that the traditional static fault tree is not applicable.For the quantitative analysis of dynamic fault tree,a method for sequential binary decision diagram has been proposed by adding sequential nodes to traditional binary decision diagram.However,sequential binary decision diagram can only be used to analyze dynamic fault trees where dynamic gates only include basic events or certain event inputs.In addition to sequential binary decision diagram,there is also an algebraic analysis method based on dynamic fault tree sequential structure functions,but this method will encounter exponential complexity problems when quantitatively analyzing the dynamic fault tree through the canonical form.In this thesis,the above two dynamic fault tree analysis methods are further studied.Based on this,a dynamic fault tree analysis method based on algebraic binary decision diagram is proposed.This method can reduce the complexity of the analysis and can be applied to the dynamic fault tree of any structure.The main work and contributions of this thesis are as follows:1)In the algebraic binary decision diagram,an algebraic representation of MDDE(Minimum Decision Diagram Expression)is proposed to construct an algebraic binary decision diagram model.Among the existing algebra methods,there is an algebraic representation similar to the disjunction paradigm called CSSs(Cut Sequence Sets),which is used to solve the failure rate of the dynamic fault tree.CSSs are not suitable as input to decision diagram to construct algebraic binary decision diagram because the number of product terms may increase exponentially,and the construction(combination)of decision diagram does not support sequential operators.For the original dynamic fault tree logic expression,we designed a set of simplification rules to generate MDDE for constructing algebraic binary decision diagram.Compared to CSSs,the number of product terms in MDDE is small,and the specified sequential operator can only connect two basic events,and can be treated as nodes in the decision diagram like other single basic events.2)In the algebraic binary decision diagram,in order to solve the problem of constructing an algebraic binary decision graph model,it is assumed that all the input events are independent of each other and the dependencies between the input events are not considered.The simplification rule simplifies the path leading to the "1" terminal node in the algebraic binary decision graph model.In addition,based on the original algebra framework,a new logical relationship formula containing non-event AND,OR and sequential operator BEFORE is added to rigorously prove this new set of simplification rules.3)By observing the formal characteristics of the SDP(Sum of the Disjoint Products)after simplification,an algorithm is proposed to generate all the cut sequences by simplified SDP.After all the cut sequences are generated based on the method,the probability calculations can be performed for each cut sequence by using multiple integrals,and the sum of the obtained probabilities is the failure rate of the entire dynamic fault tree.