动态系统受模糊干扰的响应分析

Response Analysis of Dynamic Systems Subjected to Fuzzy Excitation

为了使模糊数学的理沦更有效地处理动态模糊问题,在文献[5～7]中,我们定义了动态模糊集和模糊过程,提出了模糊过程的a·f·s微积分理论。在此基础上,本文通过用模糊过程模拟动态模湖干扰,提出了可用微分方程描述的一类动态系统在模糊干扰下响应分析的基本方法;然后通过定义模糊响应的最大、最小值并利用满足测度,提出了动态系统的模糊可靠性分析的方法。

In order to make fuzzy mathematics theory more effective in the treatment of tfe fuzzy dynamic problems,in our previous papers[5—7],the fuzzy dynamic sets and fuzzy processes have been defined and the basic theory of a.f.s calculus for the fuzzy process has been presented.In this paper,by using the fuzzy processes to simulate the fuzzy dynamic excita- tions and based ont he a.f.s solution of a fuzzy differential equation, ananalytical method is presented for the fuzzy responses of the dynamic systems which can be described by differential equations subjected to the fuzzy excitations.Then,by further defining the maximum and minimum values of the fuzzy response and using the satisfactory measure,a method is also presented for the analysis of fuzzy reliability of the dynamic system.