【作者】 张新锋；

【导师】 徐国华； 施浒立；

【作者基本信息】 西安电子科技大学 ， 机械制造及其自动化， 2007， 博士

【摘要】 工程中广泛地存在着不确定性,随机性和模糊性是两类不同的不确定性,概率论、模糊理论和凸集理论是不确定性度量的有力的数学工具。针对不确定性结构与系统可靠性度量问题,本文从不同角度和层面对其进行了有益的探索和研究。研究主要涉及模糊可靠度与模糊安全系数、能双可靠性度量、非概率可靠性度量、混合不确定性结构系统可靠性度量和系统可靠性的故障树分析等方面的内容,具体如下:1.提出了模糊可靠性意义下的模糊安全系数,以模糊应力-模糊强度和随机应力-模糊强度两种干涉模型为研究对象,分别研究了隶属函数为正态型和非正态型时,模糊安全系数的确定方法,证明了模糊安全系数与模糊可靠度之间存在确定的函数关系,以及模糊可靠度与中心模糊安全系数、模糊强度和(模糊)应力等效变异系数(变异系数)直接相关。2.分析了现有的顶点法存在的缺陷,运用区间分析和最优化理论,提出了改进的顶点法优化模型,并将其用于能双可靠性度量,给出了线性和非线性多模糊变量结构系统可靠度计算方法。3.研究了结构非概率可靠性的度量方法,对比分析了基于区间的非概率可靠性模型和基于凸集合模型的非概率可靠性模型这两种情况下的非概率可靠性指标,证明了它们之间存在着确定的函数关系,揭示两种指标之间的差异是由不确定因子所决定的本质,并对其进行定性的解释。说明基于区间的非概率可靠性指标总是大于基于凸集的非概率可靠性指标,而且随着不确定性因子的增大,区间非概率可靠性指标趋于保守;随着不确定性因子的减小,二者趋于统一。得出了基于凸集的非概率可靠性指标比基于区间非概率可靠性指标更为经济的结论。4.研究了现有的几种模糊随机化方法,提出了用模糊等效随机变换法解决混合变量结构可靠度计算问题。证明了尺度变换式与模糊等效随机变换式是统一的;给出了常用的线性隶属函数和正态型隶属函数经这几种方法变换所得到的等效概率密度函数,及其它们的数字特征;从理论上证明了模糊可靠性与概率可靠性具有相容性,使用概率度量模糊变量和随机变量并存的混合不确定性结构系统可靠性是合理的;并将其应用于这种结构系统的可靠度计算,发现这些模糊随机化方法本质上虽然存在着差异,但都能很好度量结构系统可靠性,数值上具有一致性。5.针对传统故障树分析中存在的不确定性难于量化的问题,在D-S理论的基础上,运用区间分析理论,提出了失效独立情况下的故障树区间分析方法,构造了故障树区间算子。6.把区间概率理论应用到失效相关时的故障树失效概率估算,提出了失效相关时的故障树区间分析法,构造了失效相关时的故障树区间算子,从而推广了传统的故障树分析方法。更多还原

【Abstract】 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.更多还原