Research On Several Key Problems Based On Fault Tree Analysis

Fault Tree Analysis (FTA) has become an effective tool in field of reliability analysis and fault diagnosis, and it has important reference value in course of analyzing failure modes, looking for weaknesses and guiding failure repairing.In this dissertation, several key problems and their implementations of FTA theory have been researched. The purposes of researching key details include two sides: One is expanding FTA tool and optimizing fault tree structure to improve analysis efficiency, and the other is expanding ways of analyzing bottom event and looking for new estimation methods and evaluation strategies to improve means of analyzing bottom event. Dissertation expands around the following clues: to make FTA→to research fault tree optimization→to research how to get failure distribution of bottom event. For research methodology, it mainly involves theoretical analysis, algorithm implementation and verification. For research content, it mainly relates to making modular decomposition to fault tree, analyzing and expanding key technologies of Binary Decision Diagram (BDD), making Prime Implicant Set (PIS) and"Minimal Cut Set"("MCS") from Non-Coherent Fault Tree (NCFT), improving determining method about failure distribution of bottom event and making parameter estimation, making failure analysis of bottom event based on fuzzy theory.Aiming at the disadvantages of low efficiency to directly analyze large-scale fault tree, the modular decomposition technology applied to fault tree has been researched. Taken as a key technology, the method of Depth-First Searching (DFS) has been used to search steps of all nodes, and the key point is distinguishing searching mode to intermediate nodes (logic gates) and bottom events. Getting node steps is an important foundation for forming modules, for, any node whether a module or not can be determined only by means of judging inclusion relations between time interval of common ancestor and maximum time interval of its child nodes.Due to inherent drawbacks of complexity and time-consuming character in method of traditional FTA, the principle and method of BDD technology used for FTA have been researched. The main contents are shown as follow: Connection rules and their recursive implementation between two sub-BDDs have been researched; A sort of technique called"inheritance"to make non-intersection cut set has been put forward (The key technology is that all nodes directly"inherit"node's information his father-node has inherited, but"inherit"its father-node's information with different ways); On the basis of analyzing principle of the best index order, the core technology to form theory optimal BDD structure has been achieved (to get index order of nodes with minimum cost based on principle of constant index cost), and at the same time, the disadvantage that storing truth table of target node will waste time and space has been stated, and the drawback that original method can only get one optimal solution has been analyzed too. The implementation of optimal index order has been improved (i.e. the truth table used for storing target node's Boolean value has been deleted, and the setting of getting optimal solution of original method has been changed to obtain all the optimal solutions); As an integral part of optimal BDD, the implementation method of formal optimal BDD has been researched. Its main task is to remove father-node whose two child-nodes are equivalent, and the recursive method with DFS technology has been used for searching BDD structure. In this key technology, the states of three elements in BDD structure have been judged (mainly to get the length of the second and third element respectively, and to judge whether the values of the two elements are equal or not) to determine whether making branch searching, deleting and restructuring BDD or not; In order to improve the efficiency of FTA, the implementation of optimal path BDD has been researched, which is based on analyzing the principle of the simplest cut set BDD, and the essential differences between the optimal BDD (the least number of nodes) and the simplest cut set BDD (the least number of paths) have been illustrated.Getting"MCS"is the premise to obtain PIS of NCFT. On the basis of analyzing the method of recursive structure function, the drawback that"irregular"BDD structure may cover up the function of"non-monotonic"bottom event has been analyzed (Searching can not distinguish whether one bottom event is"monotonous"and need not consider it a member of failure mode or is"non-monotonous"and must be considered as a member of failure mode). A strategy by means of coding all bottom events with unified method has been proposed, and then the"regular"BDD technology has been used to obtain"MCS"of NCFT.Because intuitively judging leaf-figure has drawback with roughness in determining failure distribution of bottom event, a method of correlation coefficient has been put forward to improve the intuitive judgment, which make determining failure distribution has basis of amount. Taken as a core technology, wavelet transform is applied to original experimental data to extract low frequency contour, so that the difference between true distribution and other distributions is strengthened (i.e. to make correlation coefficient correspond to true distribution be significantly larger than others), which can increase the correctness of judgment. Because the figure estimation or linear regression estimation has drawback with roughness (The former has subjective and arbitrary factor, and the latter has"average"component), the Weibull distribution parameters have been estimated with the method of linear regression-Maximum Likelihood Estimation (MLE) by means of intelligent optimization algorithm. In this method, the Particle Swarm Optimization (PSO) algorithm is taken as a key tool to jointly estimate parameters (The linear regression estimation offers initial solution for PSO algorithm, and the PSO algorithm is used for getting digital solutions of MLE).The Fuzzy numbers based on expert judgments may overcome the difficulties that the bottom events have no failure data. To quantify the experts'credibility, the method of Analytical Hierarchy Process (AHP) has been used to determine experts'weights to replace strategy of average weight. In course of pooling fuzzy judgments, theα-cut set has been used to form Fuzzy numbers, which is based on multiple extension principle.