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14
Analysis of Linear Mechanical Structures With Uncertainties By Means of Interval Methods
, 1998
"... ... 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 sy ..."
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... 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.
Diagrammatic representation for interval arithmetic
 LINEAR ALGEBRA AND ITS APPLICATIONS
, 2001
"... The paper presents a diagrammatic representation of a standard interval space (the socalled MRdiagram), 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 ISdiagram representation ..."
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The paper presents a diagrammatic representation of a standard interval space (the socalled MRdiagram), 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 ISdiagram representation devised earlier by the author to represent interval relations. First, the MRdiagram is defined together with appropriate graphical notions and constructions for basic interval relations and operations. Second, diagrammatic constructions for all standard arithmetic 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.
Interval Computations as an Important Part of Granular Computing: An Introduction
 in Handbook of Granular Computing, Chapter 1
, 2008
"... This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing. ..."
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This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing.
A study of uncertain state estimation
 IEEE Trans. on Systems Man and Cybernetics, SMCA
, 2003
"... 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 repre ..."
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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 filteredwhiteGaussian 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 reallife system. Index Terms—Confidence limit analysis, state uncertainty set, system modeling, uncertain state estimation. I.
Using Extended Interval Algebra in Discrete Mechanics
"... 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, discretizi ..."
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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 EulerLagrange equation must be modified when working with interval input.
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"... 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 ..."
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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
devant le jury composé de:
, 2010
"... sous le sceau de l’Université Européenne de Bretagne pour le grade de ..."
Function Interval Arithmetic
"... Abstract. We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithm ..."
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Abstract. We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation solving using the AERN library and within the Acumen hybrid system modeling tool. (2) Numerical theorem proving using the PolyPaver prover.
Verification of Floating Point Programs
, 2010
"... 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 ..."
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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
Interval Extensions of Multivalued Inverse Functions The Implementation of Interval Relational Arithmetic in gaol
"... The implementation of inverse functions provided by most interval arithmetic software libraries is restricted to bijective functions and to the principal branch of multivalued functions. On the other hand, some algorithms—most notably, constraint propagation algorithms—require multivalued inverse fu ..."
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The implementation of inverse functions provided by most interval arithmetic software libraries is restricted to bijective functions and to the principal branch of multivalued functions. On the other hand, some algorithms—most notably, constraint propagation algorithms—require multivalued inverse functions as well. We present in details in this paper the algorithms to implement interval arithmetic extensions of the following multivalued inverse functions: the inverse integral power, the inverse cosine, the inverse sine, the inverse tangent, the inverse hyperbolic cosine, and the inverse multiplication. The issues raised by their effective as well as efficient implementation with floatingpoint numbers in the gaol C++ library are carefully addressed.