SAT-Based Approximate Computation And Quantitative Analysis Of Fault Tree

Fault tree analysis(FTA)is a prominent reliability analysis technology widely used in important technical fields such as aerospace,nuclear power and medical technology.Using FTA technology,the reliability of the system can be qualitatively and quantitatively analyzed,that is,the combination of all failure modes of the system,namely all the minimum cut sets(MCSs)of the fault tree can be obtained,and then the probability of system failure can be determined.As the complexity of the system increases,more and more components are included in the system.It is difficult to analyze large-scale fault trees,which may cause exponential explosion problems.However,in practical engineering,it is not necessary to solve all MCSs,so it is of great engineering practical value to study the approximate solution method of minimum cut set of fault tree(referred to as approximate caculation of fault tree).Aiming at the limitations of the existing fault tree approximate caculation and quantitative caculation method in the analysis of complex or large-scale fault trees,this thesis proposes a novel fault tree analysis method.The detail work is as below:Firstly,in the qualitative analysis of fault tree,we propose a basic algorithm of SAT-based Computation of approximate Minimal Cut Sets—T-SATMCS.T-SATMCS is an improvement over the existing SATMCS algorithm of SAT-based Computation of all the Minimal Cut Sets.The algorithm truncates the MCS from three aspects: order,probability and unavailability.By using the efficient SAT solver,T-SATMCS searches MCSs of the fault tree by continuously iterate that meets the truncation requirements.T-SATMCS can increasingly learn the basic information generated in the process of cut set search,which speeds up the pruning search space,and effectively solves the problem of large-scale fault tree analysis.Secondly,according to the results of qualitative analysis of fault tree,we carry out quantitative analysis and focus on the calculation method of probability of occurrence of fault tree top event.In quantitative analysis,we mainly propose two methods:(1)accurate probability solution method;(2)approximate probability solution method.In the accurate solution method,we propose a disjoint quantitative analysis method based on Boolean Vector,which reduces the memory utilization by encoding the MCS into a Boolean vector.At the same time,we propose two kinds of operations COMpare and ABSorb to simplify the existing quantitative analysis formula.The simplified result contains fewer terms and is easier to solve.However,the accurate solution method has some limitations when the number of MCS is very large.Furthermore,we propose a fault tree quantitative analysis approximate solution method.The probability of the top event is determined within a certain range by the upper and lower bounds.Finally,based on the proposed fault tree analysis method,we build an automated fault tree analysis tool—FTAS.By inputting the basic information of the fault tree,FTAS can automatically output the qualitative and quantitative analysis result,and show fault tree graphically.At the same time,we apply our fault tree analysis method on the existing real life fault tree data sets to show the effectiveness of the method.