UK Nonlinear News, November 2002


Recent thesis


Contributions to the theory of discontinuous dynamical systems

Marius-F. Danca, Spiru Haret College, Cluj-Napoca, Rumania

Supervisors: Professor Josif Kolumban, Faculty of Mathematics, University Babes-Bolyai, Cluj-Napoca, Rumania

The thesis concerns a class of dynamical systems discontinuous with respect the state variable. Generally, the physical laws are expressed by this kind of discontinuity which occur in many real problems as example discontinuous dependence of the friction force on the velocity in the cases of dry friction, oscillating systems with combined dry and viscous damping, electrical circuits, forced vibrations, brake processes with locking phase, convex optimisation, control synthesis, uncertain systems, etc.

Due to the right-hand side discontinuity, the initial value problem need not have any solution and another concept of solution must be used. In this purpose, the initial value problem will be transformed into a differential inclusion via the Filippov regularisation. The set-valued functions on the obtained initial value problem enjoy the upper semicontinuity together with the compactness and convexity, properties which assures the existence and, under a special Lipschitz condition for set-valued functions, even the uniqueness of generalised solutions. Several aspects of this class of dynamical systems are studied. Introducing a generalised derivative for these discontinuous functions, several properties as synchronisation and anticontrol are analysed.

A short version of the thesis are available at:
ftp://ftp.utcluj.ro/pub/users/mdanca/REZUMA~1.PDF.

Source: Marius-Florin Danca ( Marius.Danca@Aut.UTCluj.Ro).


Hierarchical model-based fault diagnosis with application to vehicle systems

Pierluigi Pisu

Ohio State University

Supervisors: V.I. Utkin and G. Rizzoni

Abstract

In the context of complex plants, a fault diagnosis system for on-line applications must provide guaranteed response times completing the diagnosis in a deterministic amount of time, it must be able to reason about time because much information can be deducted from time events, and it must use all the information available for improving and speeding the diagnosis. The fundamental issues of how to model the system and develop a diagnostic procedure arise in this context.

In the case of complex system, the application of model-based FDI algorithms becomes computationally very difficult or even intractable. In this dissertation, we present a new framework for hierarchical model-based fault diagnosis in complex systems that combines qualitative and quantitative methodologies and allows great flexibility, modularity, and fault isolation with a reduced computational effort. The presented framework is structurally divided into a passive and an active components. The model-based passive component represents knowledge about the fault behaviour of the system under analysis, and consists of a Hierarchical Fault Propagation Digraph and a Hierarchical Model-Based FDI scheme. The active component is constituted by a Fault Location and Isolation Process and a Supervisory Process that use the model-based knowledge for diagnosis. The fundamental novelties in the presented method with respect to the past are related to the use of fault propagation digraphs having weighted arcs with fault propagation probabilities and upper/lower bounds on fault propagation times, and nodes corresponding to active/activatable fault detection units. The introduction of these properties and components in the digraph, not only makes the proposed scheme more valuable than approaches as FMEA, event trees and FTA, but also allows the use of model-based FDI to compensate for the absence of system dynamics modelling, making the scheme more simple, attractive and powerful than signed digraphs.

The combination of a quantitative methodology with a qualitative methodology constitutes the innovative idea in this dissertation and contributes to fill one of the biggest gaps in the current literature on fault diagnosis. The methodology is applied to a vehicle brake-by-wire and steer-by-wire systems with simulations and experimental results that shown the validity of the presented approach.

The theses is available at : http://wwwlib.umi.com/dissertations/fullcit/3039515.

Source: Pierluigi Pisu.


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