基于可能性理论的模糊可靠性设计

【作者】 佟欣；

【导师】 黄洪钟；

【作者基本信息】 大连理工大学 ， 机械设计及理论， 2004， 硕士

【摘要】 本论文研究的内容为模糊可靠性理论中的一个重要分支——基于可能性理论的模糊可靠性(可能可靠性)理论。 可能性理论是由美国著名控制论专家L．A．Zadeh于1978年提出的。它的理论意义在于为模糊集理论建立了一个实际应用上的理论框架。可能性分布和可能性测度是可能性理论中的两个重要概念。它们在可能性理论中的作用如同概率分布和概率测度在概率论中的作用一样。概率测度是一种经典测度；可能性测度是似然性测度，是一种特殊的模糊测度。 基于可能性理论的模糊可靠性就是用可能性测度来代替常规可靠性中的概率测度，试图解决概率可靠性很难解决或无法解决的问题，诸如某些大型复杂系统、新开发的产品、失效概率非常小的零部件的必要统计数据缺乏问题，语言概率问题，人的因素等等。 在国家自然科学基金(50175010)、教育部优秀青年教师资助计划(1766)、高等学校全国100篇优秀博士学位论文作者专项基金(200232)、加拿大国家科学技术研究基金的资助下，本论文对基于可能性理论的模糊可靠性(可能可靠性)理论进行了系统深入的研究，其主要研究内容分为两部分。第一部分主要基于Cai的系统Posbist可靠性理论，研究内容如下： (1)研究了可能可靠性理论中的关键问题——可能性分布的构造。提出凡是构造隶属函数的方法原则上都可直接用来生成相应的可能性分布的观点，总结了构造可能性分布的原则和方法。并结合零件的疲劳强度可能可靠性分析，提出了一种构造各种L-R型可能性分布的新方法。 (2)基于可能性理论对典型系统的Posbist可靠性进行了更为深入的研究。将系统寿命的论域从(0，+∞)拓广到(-∞，+∞)，简化了典型系统Posbist可靠性模型的推导，并推导出了典型系统Posbist可靠度的计算公式。推广了Cai的工作。 (3)用可能性测度来刻划基本事件的失效行为，建立了与Posbist可靠性理论相应的单调关联系统的Posbist故障树模型。为应用Posbist可靠性理论提供了一条切实可行的途径。 第二部分讨论了一种结构可能可靠性分析方法。该方法用新的拓扑空间来代替欧氏空间作为变量的状态空间，用可能性测度代替概率测度来刻划结构的失效行为。 可能可靠性理论的发展只有10多年的时间，目前的工作主要是理论框架的完善。本论文的主要工作在第一部分。可能可靠性理论的发展和完善尚需更多学者的不断努力。更多还原

【Abstract】 Fuzzy reliability theory based on possibility theory （i.e., possibilistic reliability theory）, one of the important domains of fuzzy reliability theory, is studied in the present dissertation.Possibility theory is initiated in 1978 by L. A. Zadeh, a famous American cybernetics expert. The foundation of possibility theory provides a theoretical framework for practical applications of fuzzy set theory. Fuzzy reliability theory based on possibility theory is that: possibility measure instead of probability measure in probability reliability theory is used to attempt to solve some problems that are difficult, or impossible to solve with probability reliability theory, e.g., some complex systems or new products of which necessary statistical data are scarce, some components of which failure probabilities are very small, linguistic information and human error, etc.The main research content consists of two parts. The first part is mostly based on posbist reliability theory by Cai, as follows:（1） The construction of possibility distribution, which is the first fundamental issue associated with applications of the possibilistic reliability theory, is studied. It is presented that all methods developed for generating membership functions can be used to construct relevant possibility distributions. At the same time, the principles and the methods for constructing possibility distributions are summarized. Finally, A method used to generate the L - R type possibility distribution is provided combined with the possibilistic reliability analysis of fatigue of mechanical parts.（2） A detailed analysis of the posbist reliability of typical system structures is provided.The universe of discourse is expanded from（0,+∞） to （-∞,+∞）, thus, the models of posbistreliability of typical systems are simplified. On the basis of this, expressions of the posbist reliability of typical system structures including series, parallel, series-parallel, parallel-series. and cold standby systems are developed and Cai’s important work in this field is extended.（3） Event failure behavior is characterized in the context of possibility measures and a model of posbist fault tree analysis of coherent systems is presented. The model provides a new feasible approach for the practical application of posbist reliability theory.In the second part, a method of structural possibilistic reliability is discussed. A newtopology |U|_∞ = sup|U₁| as the new state space or variaoies, is introaucea toEuclidean space, and the failure behavior of structures is characterized in the context of possibility measures rather than probability measures.更多还原