Research On Multiple Failures Diagnosability Of Fuzzy Discrete Event Systems

Discrete event systems(DES) are synthetic dynamical systems whose state transition is governed by the abrupt occurrence of discrete event according to certain rules. However, there are a large number of complex systems with uncertainty, fuzziness and subjectivity in real life. Fuzzy discrete event systems(FDES) combines the merits of both DES and fuzzy theory, and it play a significant role in describing and dealing with these systems.The research of multiple failure diagnosis of FDES is based on automata in this thesis. Fuzzy discrete event system with fuzzy events(FEDES) and fuzzy discrete event system with fuzzy events and fuzzy transition function at the same time(FETDES) are mainly analyzed here. Diagnosability, necessary and sufficient condition for diagnosability and online multiple failure diagnostic method are discussed respectively for FEDES and FETDES. After that, these theories are applied in medical diagnosis. The main contributions of this paper are as follows.(1)The degree of observability of events and the membership of each failure occurring on each event is presented in this paper, which takes values in the interval[0,1]. In the framework of fuzzy discrete event systems, Σ-%diagnosability is proposed on the basis of the concept of undistinguishable strings. And PS-(partial-state)fuzzy diagnoser has been constructed to find the collections of the undistinguishable strings. Then, the notion of diagnosability degree set is defined. What’s more, the matrix algorithm of diagnosability degree set of failure is investigated for FEDES. Finally, a necessary and sufficient condition is obtained for multiple failures diagnosability of FEDES based on PS- diagnoser.(2) PS- fuzzy diagnoser only consider the part of state connected with indistinguishable string, so it is unable to diagnose failures online. In order to solve this problem, a new diagnoser based on Σ-%diagnosability is defined in this paper—— FS-(full-state) fuzzy diagnoser. One correspondence between the collections of the undistinguishable strings and the neat circle in the diagnoser is established in terms of certain properties of this diagnoser. Thus, a necessary and sufficient condition is obtained for diagnosability of FEDES based on FS- diagnoser. Finally, it is proposed that online failure diagnosis method is combined with Mlcut matrix and failure membership matrix of state.(3)Besides fuzziness of events, fuzzy transition function is considered in this paper. Degree of state transition caused by event is denoted by Membership function of state transition. Thus, S%- F- diagnosability of FETDES and the approach to construct FS- F- diagnoser has been put forward. Then, calculation of membership transfer vector and matrix algorithm of diagnosability degree set of failure for FETDES are discussed. Thereby, a necessary and sufficient condition for diagnosability of FETDES is obtained based on FS- F- diagnoser. Finally, it is presented that failure diagnosis online method of FETDES combined with ?lcut matrix and failure membership matrix.The methods of failure diagnosis for FDES presented in this thesis are general methods, they can diagnosis various FDES. The diagnoser structured on the basis of system model can not only analysis the diagnosability offline, but also diagnosis failure online. It means that the research have a good practical significance and value.