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A topological approach to failure diagnosis of large-scale systems

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3 Author(s)
Yoshiteru Ishida ; Department of Applied Mathematics and Physics, Kyoto University, Yoshidahonmachi, Sakyo-ku, Kyoto-shi, 606 Japan ; Norihiko Adachi ; Hidekatsu Tokumaru

A failure diagnosis model which consists of a set of units that are faulty, a set of measurements to detect a faulty unit, and an incidence matrix representing the binary relation between these two sets is presented. A binary relation is defined by whether or not a fault of one unit is detected by a measurement. Considering this failure diagnosis model as a simplicial complex in topological geometry, the relationship between the diagnostic aspects of the model and the topological properties of the corresponding simplicial complex is studied. The diagnosability of a failure diagnosis model with multiple faults is expressed as a covering property of each simplex in a simplicial complex. The capability of distinguishing a faulty unit by a given number of measurement is determined by examining the global connective structure of the simplicial complex. This analysis of connectivity is done by performing q-analysis on a simplicial complex. It is noted hat all possible combinations of fault patterns are considered under a permissible number of faults. However, in actual systems, only restricted fault patterns are possible in which faulty units are functionally connected with each other, even in multiple fault situations.

Published in:

IEEE Transactions on Systems, Man, and Cybernetics  (Volume:SMC-15 ,  Issue: 3 )