Wyniki wyszukiwania - Biblioteka Nauki

1

Wpływ korelacji między błędami na współczynnik koherencji w ocenie niepewności za pomocą redukcyjnej arytmetyki interwałowej

100%

Konopka K.

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tom z. 98

335-344

PL

Zagadnienie dotyczy zastosowania redukcyjnej arytmetyki interwałowej do wyznaczania niepewności wyników pomiaru. Stosowany w niej współczynnik koherencji określa wzajemne związki zachodzące między zbiorami wartości błędu. W przypadku, gdy zbiory te nie są skorelowane, wartość współczynnika koherencji związana jest z kształtem rozkładu. Skorelowanie zbiorów powoduje pojawienie się dodatkowego składnika związanego ze współczynnikiem korelacji. W referacie pokazano w jaki sposób zależy wypadkowy współczynnik koherencji dla wybranych typów rozkładów od wartości współczynnika korelacji w zakresie od -1 do 1. W końcowej części przedstawiono wnioski dotyczące sposobu składania współczynnika korelacji i współczynnika koherencji związanego z kształtem rozkładu.

EN

The problem described applies to application of reducing interval arithmetic to determining the uncertainty of measuring results. The coherence factor used there describes mutual relations between error values sets. In case when these sets are not correlated the coherence factor is connected only with the form of distribution. When error sets are correlated, additional component appears. The paper shows how resultant coherence factor changes for different distribution forms and for correlation factor changing in range from -1 to 1.

2

Set arithmetic and the enclosing problem in dynamics

100%

Mrozek M. , Zgliczyński P.

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2000

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tom 74

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nr 1

237-259

EN

We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.

3

New Approach to the Uncertainty Assessment of Acoustic Effects in the Environment

100%

Batko W. , Pawlik P.

Archives of Acoustics

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2012

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tom Vol. 37, No. 1

57-61

EN

The acoustic climate assessment needed for the selection of solutions (technical, legal and organisa- tional), which will help to minimise the acoustic hazards in the analysed areas, is realised on the basis of acoustic maps. The reference computational algorithms, assigned to them, require very thorough prepa- ration of input data for the considered noise source model representing – in the best possible way – the acoustic climate. These input data are burdened with certain uncertainties in this class of computational tasks. The uncertainties are related to the problem of selecting proper argument values (from the inter- val of their possible variability) for the modelled processes. This situation has a direct influence on the uncertainty of acoustic maps. The idea of applying the interval arithmetic for the assessment of acoustic models uncertainty is formulated in this paper. The computational formalism assigned to the interval arithmetic was discussed. The rules of interval estimations for the model solutions determining the sound level distribution around the analysed noise source – caused by possible errors in the input data – were presented. The application of this formalism was illustrated in uncertainty assessments of modelling acoustic influences of the railway noise linear source on the environment.

4

Solving the Generalized Poisson Equation in Proper and Directed Interval Arithmetic

100%

Hoffmann T. , Marciniak A.

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tom Vol. 22, No. 4

225--232

EN

In the paper some interval methods for solving the generalized Poisson equation (GPE) are presented. The main aim of this work is focused on providing such algorithms for solving this type of equation that are able to store information about potentially made numerical errors inside the results. In order to cope with these assumptions the floating-point interval arithmetic is used. We proposed to use interval versions of the central-difference method for two types of interval arithmetic: proper and directed. In the experimental part of this paper both arithmetics for three examples of GPE are compared

5

On probabilistic bounds inspired by interval arithmetic

100%

Zilinskas A. , Zilinskas J.

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tom Vol. 39, no 2

507-525

EN

A randomized method aimed at evaluation of probabilistic bounds for function values is considered. Stochastic intervals tightly covering ranges of function values with probability close to one are modelled by a randomized method inspired by interval arithmetic. Statistical properties of the modelled intervals are investigated experimentally. The experimental results are discussed with respect to application of this method in the construction of a branch and bound type randomized algorithm for global optimization.

6

Interval arithmetic-based fuzzy discrete-time crane control scheme design

88%

Smoczek J.

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tom Vol. 61, nr 4

863--870

EN

In many manufacturing segments, container terminals and shipping yards the automation of material handling systems is an important element of enhancing productivity, safety and efficiency. The fast, precise and safe transfer of goods in crane operations requires a control application solving the problems, including non-collision trajectory planning and limitation of payload oscillations. The paper presents the interval arithmetic-based method of designing a discrete-time closed-loop anti-sway crane control system based on the fuzzy interpolation of linear controller parameters. The interval analysis of a closed-loop control system characteristic polynomial coefficients deviation from their nominal values is proposed to define a minimum number of fuzzy sets on the scheduling variables universe of discourse and to determine the distribution of triangular-shaped membership functions parameters, which satisfy the acceptable range of performances deterioration in the presence of the system’s parameters variation. The effectiveness of this method was proved in experiments conducted using the PAC system on the laboratory scaled overhead crane.

7

Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties

88%

Rauh A. , Minisini J. , Hofer E.

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nr 3

425-439

EN

Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.

8

Solving Systems of Linear Equations under Conditions of Uncertainty on the Example of the Leontief Model

88%

Kacprzak D.

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2018

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tom 5

|

nr 52

EN

The paper presents various methods of solving systems of linear equations under conditions of uncertainty. In a situation when the parameters of such systems cannot be precisely determined with real numbers, they can be represented by interval numbers, fuzzy numbers or ordered fuzzy numbers. Solutions of systems of linear equations with such representations of parameters are shown in the example of Leontief input-output model. It has also been shown that when ordered fuzzy numbers are applied, their additional feature – orientation – can broaden and deepen economic analysis.

9

Analysis of linear mechanical structures with uncertainties by means of interval methods

75%

Kulpa Z. , Pownuk A. , Skalna I.

Computer Assisted Mechanics and Engineering Sciences

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1998

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tom Vol. 5, nr 4

443-477

EN

One of the simplest ways of representation of uncertain or inexact data, as well as inexact computations with them, is based on interval arithmetic. In this approach, an uncertain (real) number is represented by an interval (a continuous bounded subset) of real numbers which presumably contains the unknown exact value of the number in question. Despite its simplicity, it conforms very well to many practical situations, like tolerance handling or managing rounding errors in numerical computations. Also, the so-called alfa-cut method of handling fuzzy sets membership functions is based on replacing a fuzzy set problem with a set of interval problems.

10

RDM interval method for solving quadratic interval equation

75%

Landowski M.

|

tom R. 93, nr 1

65--68

EN

The main task of uncertainty theory is to find the solution with uncertain variable. The ways of uncertainty description are probability density distribution, possibility distribution or interval. To solve the problem with uncertainty variable the calculation on interval is needed. The article presents the usage of RDM interval arithmetic for solving quadratic interval equation. The results obtained from examples are compared with Moore’s standard interval arithmetic solutions.

PL

Głównym zadaniem teorii niepewnos´ci jest znalezienie rozwiazania ze zmienna˛ niepewna˛. Niepewnos´c´ moz˙na zapisac´ w postaci rozkładu ge˛stos´ci prawdopodobien´stwa, rozkładu moz˙liwos´ci lub przedziału. Do rozwia˛zania zadania ze zmienna˛ niepewna˛ potrzebne sa˛ obliczenia na przedziałach. Artykuł przedstawia wykorzystanie arytmetyki interwałowej RDM do rozwia˛zania interwałowych równan´ kwadratowych. Wyniki otrzymane z przykładów porównano z rozwia˛zaniami standardowej arytmetyki interwałowej Moore’a.

11

Validated high precision solution of second order initial value problem with Taylor model

75%

Stręk T.

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tom Vol. 21

357--360

EN

The problem of reliability of computer computations is one of great concern to specialists in many areas of science and engineering. The notion of computing estimates of numerical error in computer simulations is not new. In recent years, considerable progress has been made in determining theoretical and computational techniques that aid to improve the reliability of results of simulations. An important advance in this area has been the recent discovery of methods to determine upper and lower bounds of local approximation error in any given simulation. Different from floating-point computations, interval arithmetic offers a simple mechanism to evaluate an enclosure of a function. Interval arithmetic is the arithmetic defined on sets of intervals, rather than sets of real numbers. The power of the interval arithmetic lay in implementation of interval arithmetic on computers. The fundamental problem in interval methods is computing the ranges of values of real function. The overestimation of the range of a given function by the interval arithmetic expression is strongly dependent on the arithmetic expression of the given function. The reason for this is based on the fact that interval arithmetic does not follow the same rules as the arithmetic for real numbers.

12

Numerical modelling of solidification process using interval boundary element method

63%

Piasecka-Belkhayat A.

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tom Vol. 8, iss. 4

171-176

EN

In this paper an application of the interval boundary element method for solving problems with interval thermal parameters and interval source function in a system casting-mould is presented. The task is treated as a boundary-initial problem in which the crystallization model proposed by Mehl-Johnson-Avrami-Kolmogorov has been applied. The numerical solution of the problem discussed has been obtained on the basis of the interval boundary element method (IBEM). The interval Gauss elimination method with the decomposition procedure has been applied to solve the obtained interval system of equations. In the final part of the paper, results of numerical computations are shown.

13

Nowa metoda oceny niepewności identyfikacji źródeł hałasu

63%

Batko W. , Pawlik P.

|

tom R. 59, nr 6

529--531

PL

W artykule przedstawiono nową metodę oceny niepewności estymacji poziomu dźwięku pochodzącego od identyfikowanych źródeł oraz tła akustycznego. Wykorzystano metodę eliminacji w celu zbadania wpływu poszczególnych źródeł na sumaryczny poziom hałasu. Operacje matematyczne opisujące wykorzystaną metodykę obliczeniową, przeprowadzono w formalizmie redukcyjnej arytmetyki przedziałowej, w celu oceny wpływu niepewności pomiarowej na wyniki obliczeń. W artykule przedstawiono ogólny schemat oceny niepewności, dający możliwość uwzględnienia informacji probabilistycznej związanej z wynikami pomiaru. Zaproponowane rozwiązanie oparto na pomiarach zrealizowanych w warunkach laboratoryjnych.

EN

A new method for uncertainty assessment of the sound level originated from identified noise sources and their acoustic background is presented in the paper. The elimination method [1] was applied in order to investigate influence of individual sources on the cumulative noise level. Mathematical operations describing the used computational method were performed in the reduction interval arithmetic formalism [6] to assess the influence of the measuring uncertainty on the calculation results. The measurement values of the total noise level and the noise levels characteristic for disconnections of successive noise sources were presented in the interval numbers. These numbers contain the measurement values and the uncertainty (Tab. 2). The authors determined the ranges of variation for estimates of the noise levels by individual sources and the background noise using the reductive interval arithmetic (Tab. 3). The general uncertainty estimation scheme presented in the paper provides the possibility of taking into account probabilistic information related to the obtained results. The proposed solution was based on measurements realised under laboratory conditions.

14

Uogólnienie metody TOPSIS w warunkach niepewnosci rozmytej

63%

Tikhonenko-Kedziak A.

|

2014

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tom Nr 1(7)

13--38

PL

Technika obliczania odległości od rozwiązania idealnego (TOPSIS) jest jedną z najbardziej znanych klasycznych metod wielokryterialnego podejmowania decyzji (MCDM). W klasycznej metodzie TOPSIS wartości i wagi kryteriów są zwykłymi liczbami. Czasami jednak rozwiązanie zagadnienia dokładnego wyznaczenia wartości kryteriów jest trudne, dlatego w konsekwencji ich wartości są przedstawione w postaci liczb rozmytych. Istnieje kilka publikacji dotyczących zastosowania metody TOPSIS w ramach niepewności rozmytej, lecz autorzy zazwyczaj wprowadzają rozmaite ograniczenia oraz uproszczenia sformułowanego problemu, które mogą prowadzić do otrzymania niepoprawnych wyników. W niniejszym opracowaniu przedstawiono nowe podejście oparte na matematyce przedziałowej.

EN

The TOPSIS method is a technique for establishing order preference by similarity to the ideal solution and was primarily developed for dealing with real-valued data. This technique is currently one of most popular methods for Multiple Criteria Decision Making (MCDM). In many cases, it is hard to present precisely exact ratings of alternatives with respect to local criteria and as a result these ratings are seen as fuzzy values. A number of papers have been devoted to fuzzy extensions of the TOPSIS method in the literature, but in most of them, a defuzzification of elements of the fuzzy decision matrix is used, that leads inevitably to a loss of important information and may even produce the wrong results. In this paper a new direct approach to the fuzzy extension of the TOPSIS based on interval arithmetic had proposed.

15

Kontrola dokładności numerycznego przetwarzania danych pomiarowych

51%

Górka P.

Pomiary Automatyka Kontrola

|

2008

|

tom R. 54, nr 12

854-856

PL

W artykule przedstawiono wybrane metody automatycznej kontroli dokładności obliczeń w procesie przetwarzania danych pomiarowych. Metody te powinny - w założeniu - uwzględniać dokładność wyników pomiarów, jak i błędy numeryczne. Najwięcej uwagi poświęcono omówieniu możliwości zastosowania arytmetyki przedziałowej jako najbardziej uniwersalnej metody kontroli dokładności obliczeń. Przedstawiono zasady jej stosowania, zalety jak i uwagi dotyczące ominięcia jej mankamentów.

EN

The paper presents some methods of the automatic accuracy check of calculations performed during computer processing of measurement data. The mentioned methods should take into account the measurement data accuracy and numerical errors. The paper discusses mainly the interval arithmetic method which appears as the most universal one. The basis of the method, its advantages and possibility to avoid some problems which can be connected with the use of interval arithmetic are presented as well.