【作者】 高亮；

【导师】 董玉革；

【作者基本信息】 合肥工业大学 ， 机械设计及理论， 2006， 硕士

【摘要】 模糊可靠性设计诞生20多年来,在理论和应用上都获得了长足的发展,但是,目前在模糊可靠性领域中,人们对一些基本概念的含义尚有争议,这妨碍了研究者之间的交流和模糊可靠性理论的发展。针对这样的现状,本文首先从表述模糊可靠性设计理论的若干基本概念入手,对模糊可靠性设计中常见的几种不确定性进行了综合比较分析,并对模糊数学应用中的几个重要概念的实际应用含义进行了阐述。其次,以此为基础,建立了在不同情况下,用隶属函数描述模糊经验信息的决策模型,对分类不确定现象和模糊现象作了区分。然后,从模糊变量向随机变量的变换和基于隶属函数的决策模型出发,讨论了如何用基于隶属函数的方法和基于随机集的方法从专家对随机变量分布状况的语言描述中获取概率分布密度函数。采用基于隶属函数的方法,可以根据专家对随机变量分布状况的语言描述的隶属函数,用从模糊变量向随机变量的变换,获得随机变量的概率分布密度函数。而采用基于随机集的方法,可以通过全概率公式对专家给出的对随机变量的语言描述的清晰边界进行综合,获得随机变量的概率分布密度函数。最后,把从专家对随机变量分布状况的语言描述中获取概率分布密度函数的方法运用于处理强度与应力未确知时的模糊可靠性问题,给出了使用转化法计算产品可靠度的公式,以及计算主观可靠度与客观可靠度误差的方法。更多还原

【Abstract】 Some quite great progresses in fuzzy reliability theory and its application have been made recent twenty years, but the meanings of some important concepts in fuzzy reliability theory are not accepted by all of people. In order to develop and utilize fuzzy reliability theory, some concepts of fuzzy reliability theory must be studied deep. Firstly, in this paper several well-known uncertainties are compared, the meanings of some important concepts in the Fuzzy Sets Theory are described. How to utilize the concepts in engineering and to make them understandable easily by engineers are discussed. Secondly, three decision-making models based on membership functions are given, and they also can be used to distinguish uncertainty between commonly fuzzy uncertainty and complicated uncertainty in classification. Thirdly, based on the decision-making models mentioned above and the transformation which can be used to transform the fuzzy variable to the random variable, two methods which can be used to obtain the probability density functions from the expertise about the distributions of random variables are discussed. In the above two methods, the method based on membership functions can obtain the probability density functions by transforming the fuzzy variable to the random variable, and the method based on random sets can obtain the probability density functions by synthesizing the random sets which are given to explain the language description of random variable by experts. Finally, the two methods are used to analyses the fuzzy reliability when the probability density functions of intension and stress are unknown. The error between subject reliability and object reliability is discussed in the paper.更多还原