A topological approach to failure diagnosis of large-scale systems

Abstract

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.