【作者】 王毅兵；

【导师】 刘晓东；

【作者基本信息】 大连海事大学 ， 应用数学， 2005， 硕士

【摘要】 自1965年,美国控制论专家查德(L.A.Zadeh)教授提出模糊集的概念以来,模糊集与系统理论作为一门新的工程数学方法,被人们广泛研究并应用于各个领域.文献[26-31]中提出的AFS(Axiomatic Fuzzy Set)理论是一种新的模糊数学分析方法,在AFS理论框架内,给出了依据原始数据和相关信息确定隶属函数及其模糊逻辑运算的一个新算法,使得隶属函数和模糊逻辑的建立更客观、严密和统一.AFS理论已初步应用于数据挖掘,模式识别,故障诊断等领域. 用AFS理论进行故障诊断时,由于AFS结构的复杂和庞大,增加了在实际应用中分析和诊断的难度,因而如何有效地降低AFS结构的复杂程度成为我们关注的焦点.文献[28]在理论上论证了降低AFS结构的复杂程度的可行性.本文在文献[28]理论研究的基础上,具体提出了AFS结构直和分解算法,实现了把一个复杂的AFS结构划分为若干个相互独立的子AFS结构,使得同一个子AFS结构中的元素是相互关联的,而不同子AFS结构中的元素是相互独立的,即每个子AFS结构均是一个连通系统,从而有效地降低了分析AFS结构的难度.在此基础上应用AFS理论进行故障诊断,引用了船用柴油机故障诊断的实例,应用Matlab编写程序,通过这个例子,进一步检验出该分解算法客观,统一性强,并与专家经验相一致,而且对于非常复杂的系统,应用结构分解算法就更显其优越性.更多还原

【Abstract】 The theory of fuzzy sets and systems has been studied widely and applied in many fields as a new mathematics method since it was proposed by Professor L. A. Zadeh, an American cyberneticist, in 1965. AFS (Axiomatic Fuzzy Set) theory was proposed first in [26-31] as a new analytic method of fuzzy mathematics. In the framework of AFS theory, the membership functions and their logic operations for fuzzy concepts can be impersonally determined according to original data and facts. AFS theory has been applied to data mining, pattern recognition and failure diagnosis.When we study failure diagnosis of system based on AFS theory, the complexity of AFS structure increases the difficulty in calculation and analysis for the real-world applications. Therefore our focus is on how to reduce the complexity of AFS structure effectively. In [28], the author has proved the feasibility in mathematics. In this paper, we propose a direct sum decomposition algorithm of AFS structure based on the research in [28], which decomposes a complex AFS structure into several independent sub-AFS structures, thus the elements in the same sub-AFS structure are dependent on each other, the elements in the different sub-AFS structures are independent. This implies that each sub-AFS structure is a connected system. Then we apply AFS theory to diagnose failures of marine diesel engine. The example shows that the decomposition algorithm is objective, uniform, easy to control and coincidence with experts’ experiences. Especially in more complex systems, this decomposition algorithm will show more superiority.更多还原