Research On Reliability Measure Of Uncertainty Structures And Systems

Uncertainty exists extensively in engineering. Uncertainty is classified into random uncertainty and fuzzy uncertainty. Those theories, such as probability theory, fuzzy theory and convex theory, are the powerful tools of uncertainty measure. The exploring research is made in order to solve the reliability measure of uncertainty structures and systems. The research includes fuzzy reliability and fuzzy safety factor, posbist reliability measure, non-probability reliability measure, structural reliability measure in hybrid uncertainty and faulty tree analysis of system reliability and so on. The detail contents are followed as:1.The theory of information entropy provides the possibility and method to transform fuzzy variables into random variables. Relying on the fundamental concept of equivalent transformations, namely the entropy based transformation or the scaling of fuzzy membership function, fuzzy safety factor is proposed. Two interferential models of fuzzy-fuzzy and random-fuzzy structure reliability are described, and their respective fuzzy safety factors are determined in the case of normal and non-normal membership functions. The functions of fuzzy safety factor and fuzzy reliability are also deduced. The result shows that fuzzy reliability is directly related to central fuzzy safety factor and the equivalent variant factors of stress and strength. And an example is given for clearer illustration.2. When the structure is defined with fuzzy input parameters, every fuzzy variable is described by fuzzy membership function. An optimization model based on improved vertex method is developed, by which fuzzy joint membership function of structure is solved. Relying on the fundamental concept of equivalent transformations, namely the scaling of fuzzy membership function, the formulas of structure fuzzy reliability are given. The reliability computation under fuzzy uncertainty is elucidated numerically with examples for comparative study.3.In the case of scarce data or insufficient information available, a non-probabilistic set model is a valid alternative to structural reliability analysis. In analysis of structural non-probabilistic reliability, structure reliability is measured by non-probabilistic reliability index. Two non-probabilistic reliability indices based on interval model and convex model are compared. With optimization theory, function of those two non-probabilistic reliability indices is deduced, which shows that the difference between two indices arises from the factor of uncertainty. The result proves: (1) non-probabilistic reliability index based on interval model is more conservative than that based on convex model, and (2) with the decrease of the factor of uncertainty, those indices tend to be equal. And the causes are analyzed.4. Hybrid uncertainty reliability analysis is one of the important parts in structural reliability analysis. The comparisons of several various transformations of the fuzzy variables into equivalent random variables are drawn. The formula of the transformation of fuzzy variables into random variables is proposed and applied to the computation of structural reliability with hybrid uncertainty. Specific formulas of the equivalent Probability Disrubution Functions (PDFs) and their numerical chrematisties are obtained, such as the linear membership function and the normal membership function. The compatibility of fuzzy reliability and random reliability is proved by means of the transformations. And probabilistic measurement of hybrid uncertain structure is reasonable. The reliability computation with hybrid uncertainty is illustrated with an example for comparative study on the consistency of the transformations. The results show that those methods are all effective and consistent.5. To formulate the uncertainties of conventional fault tree analysis (FTA), the method of fault tree interval analysis based on D-S theory is proposed, and the interval operators of FTA are described by interval analysis theory. The likelihood function and belief function in the D-S theory are used to calculate separately the upper bound and lower bound of fault interval probability of elementary events in FTA. Then, the AND operator, OR operator and Voting operator based on interval analysis theory are proposed to compute interval probability of FTA. The example shows the validity of the proposed method.6. The premises in Fault tree analysis (FTA) is independence between basic events. It simplifies the calculation of failure greatly, but it is satisfied hardly in practical systems. Based on that, the application of interval probability theory to the estimation of failure probability with failure dependence is proposed and traditional FTA is extended. The operation of estimation of failure probability is based on interval analysis. The example shows the method is efficient.