... of this paper is to investigate possibilities of and problems with application of interval methods in (qualitative) analysis of linear mechanical systems with parameter uncertainties, in particular truss structures and frames. The paper starts with an introduction to interval arithmetic and systems of linear interval equations, including an overview of basic methods for finding interval estimates for the set of solutions of such systems. The methods are further illustrated by several examples of practical problems, solved by our hybrid system of analysis of mechanical structures. Finally, several general problems with using interval methods for analysis of such linear systems are identified, with promising avenues for further research indicated as a result. The problems discussed include estimation inaccuracy of the algorithms (especially the fundamental problem of matrix coefficient dependence), their computational complexity, as well as inadequate development of methods for analysis of interval systems with singular matrices.

The paper presents a diagrammatic representation of a standard interval space (the so-called MR-diagram), and shows how to represent and perform interval arithmetic and derive its various properties using the diagram. The representation is an extension and refinement of the IS-diagram representation devised earlier by the author to represent interval relations. First, the MR-diagram is defined together with appropriate graphical notions and con-structions for basic interval relations and operations. Second, diagrammatic constructions for all standard arithme-tic operations are presented. Several examples of the use of these constructions to aid reasoning about various simple, though nontrivial, properties of interval arithmetic are included in order to show how the representation facilitates both deeper understanding of the subject matter and reasoning about its properties.

Abstract—In this paper, we present results of uncertain state estimation of systems that are monitored with limited accuracy. For these systems, the representation of state uncertainty as confidence intervals offers significant advantages over the more traditional approaches with probabilistic representation of noise. While the filtered-white-Gaussian noise model can be defined on grounds of mathematical convenience, its use is necessarily coupled with a hope that an estimator with good properties in idealised noise will still perform well in real noise. In this study we propose a more realistic approach of matching the noise representation to the extent of prior knowledge. Both interval and ellipsoidal representation of noise illustrate the principle of keeping the noise model simple while allowing for iterative refinement of the noise as we proceed. We evaluate one nonlinear and three linear state estimation technique both in terms of computational efficiency and the cardinality of the state uncertainty sets. The techniques are illustrated on a synthetic and a real-life system. Index Terms—Confidence limit analysis, state uncertainty set, system modeling, uncertain state estimation. I.

Abstract: Discrete mechanics deals with discrete mechanical systems, such as cellular automata, in which time proceeds in integer steps and the configuration space is discrete. Directly modeling discrete mechanical systems is a well known alternative to starting from a continuous setting, discretizing the model, and finally force the model to the finite alphabet of a computer. The time evolution of discrete dynamical systems, however, can be calculated exactly. In order to take into account imprecision in the input data and the need to accommodate a finite alphabet, extended interval analysis is introduced in the discrete mechanical systems formulation developed by Baez and Gilliam. It is shown how the Euler-Lagrange equation must be modified when working with interval input.

We live in the world of digital technology that surrounds us and without which we can barely function. There are myriads of examples (which we take for granted) in which computers bring a wealth of services. Computers constitute an omnipresent fabric of the society (Vasilakos and Pedrycz, 2006). As once

Abstract not found

This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without proper acknowledgement. Aston University