模糊、灰色理论在故障树分析中的应用

Application of fuzzy & grey theories in fault tree analysis

在故障树诊断中,底事件的概率是很难获得的,给分析计算带来了一定的难度。将故障树分析法与模糊理论及灰色理论相结合,由专家对各种故障模式发生的可能性大小进行评估,通过左右模糊排序法将自然评价语言转化为模糊失效概率值,并对故障底事件进行灰关联分析及关联度排序,对各种故障模式发生的可能性大小做出了判断。

The paper describes the application of fuzzy set theory and grey system theory in fault tree analysis. In practice, the indetermi- nacy exists in the occurrence probability of fault tree basic events. Based on the previous research, the main purpose of this study is to provide a scientific basis for fault handling and to improve the relia- bility and security of system. Because of the random disability of fault tree basic event in telling the aecurate possibility, therefi）re this paper adopts subjective expert judgment method to directly estimate the fail- ure probability of the vague event. The basic event occurrence proba- bility is denoted with trapezoidal fuzzy number and the occurrence probability of event is used as linguistic variable. Both of them are integrated into fault tree analysis afterwards. Grey correlation analysis method in the grey system is employed to analyze the fuzzy fault tree. The method has regarded typical modes as primary sequences, the structural importance degrees of basis cases as sub-sequences and the top-difference as the correct transforming method of basis data to esti- mating indexes of minimal cuts. Possibility of fault tree model was judged correctly in fault tree analysis. An example of fault tree is used to demonstrate the procedures. The results indicate that the pro- posed approach is very useful to work out with the uncertainties of FTA. It provides a convenient way for the technician in system＇s weaknesses checking and best inspect sequence finding.