Fourier-Motzkin methods for fault diagnosis in discrete event systems

Al-Ajeli, Ahmed Khelfa Obeid (2017). Fourier-Motzkin methods for fault diagnosis in discrete event systems. University of Birmingham. Ph.D.

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Abstract

The problem of fault diagnosis under partial observation is a complex problem; and the challenge to solve this problem is to find a compromise between the space complexity and time complexity. The classic method to solve the problem is by constructing an automaton called a diagnoser. This method suffers from the state explosion problem which limits its application to large systems. In this thesis, the problem of fault diagnosis in partially observed discrete event systems is addressed. We assume that the system is modelled by Petri nets having no cycle of unobservable transitions. The class of labelled Petri nets is also considered with both bounded and unbounded cases. We propose a novel approach for fault diagnosis using the Integer Fourier-Motzkin Elimination method. The main idea is to reduce the problem of constructing the diagnoser to a problem of projecting between two spaces. In other words, we first obtain a set of inequalities derived from the state equation of Petri nets. Then, the elimination method is used to drop the variables corresponding to the unobservable transitions and we design two sets of inequalities in variables representing the observable transitions. One set ensures that the fault has occurred, whereas the other ensures that fault has not occurred. Given these two sets, we have proved that the occurrences of faults can be decided as any other diagnoser can do. The obtained result are extended to diagnose violations of constraints such as service level agreement and Quality of Service, which is of particular interested in telecommunication companies. We implement our approach and demonstrate gains in performance with respect to existing approaches on a benchmark example.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

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