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  1. 5 International Journal of Applied Mathematics and Computer Science
  2. 4 Przegląd Elektrotechniczny
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  1. 2 Dyvak M.
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1
Content available An interval Kalman filter enhanced by lowering the covariance matrix upper bound
Tran Tuan Anh, Jauberthie Carine, Trave-Massuyés Louise, Lu Quoc Hung
International Journal of Applied Mathematics and Computer Science
|
2021
|
Vol. 31, no. 2
259--269
EN
This paper proposes a variance upper bound based interval Kalman filter that enhances the interval Kalman filter based on the same principle proposed by Tran et al. (2017) for uncertain discrete time linear models. The systems under consideration are subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of the Gaussian noises. By using the spectral decomposition of a symmetric matrix and by optimizing the gain matrix of the proposed filter, we lower the minimal upper bound on the state estimation error covariance for all admissible uncertainties. This paper contributes with an improved algorithm that provides a less conservative error covariance upper bound than the approach proposed by Tran et al. (2017). The state estimates are determined using interval analysis in order to enclose the set of all possible solutions of the classical Kalman filter consistent with the uncertainties.
2
Content available remote Approaches to the determination of the working area of parallel robots and the analysis of their geometric characteristics
Malyshev Dmitry, Rybak Larisa, Posypkin Mikhail, Usov Alexander
Engineering Transactions
|
2019
|
Vol. 67, iss. 3
333--345
EN
The article presents and experimentally confirms two approaches to the problem of determining the working area of parallel robots using the example of a planar robot DexTAR with two degrees of freedom. The proposed approaches are based on the use of constraint equations of coordinates. In the first approach, the original kinematic equations of coordinates in the six-dimensional space (two coordinates describing the position of the output link and four coordinates – the rotation angles of the rods) followed by projecting the solution onto the two-dimensional plane is used. In the second approach, the system of constraint equations is reduced to a system of inequalities describing the coordinates of the output link of the robot, which are solved in a two-dimensional Euclidean space. The results of the computational experiments are given. As an algorithmic basis of the proposed approaches, the method of non-uniform coverings is used, which obtains the external and internal approximation of the solution set of equality/inequality systems with a given accuracy. The approximation is a set of boxes. It is shown that in the first approach, it is more efficient to apply interval estimates that coincide with the extremes of the function on the box, and in the second approach, grid approximation performs better due to multiple occurrences of variables in inequalities.
3
Content available remote Mathematical model in task of recurrent laryngeal nerve identification by electrophysiological method
Dyvak M., Pukas A., Melnyk A., Kłos-Witkowska A., Karpiński M.
Przegląd Elektrotechniczny
|
2017
|
R. 93, nr 12
266--270
EN
The method of constructing the mathematical model for visualization the recurrent laryngeal nerve positioning during neck surgery is described in this paper. Proposed model shows the dependence between the amplitude of information signal as response on stimulation the recurrent laryngeal nerve and the coordinates of stimulation point based on interval data analysis.
PL
Poniższy artykuł opisuje metodę konstrukcji modelu matematycznego do wizualizacji, podczas operacji, położenia nerwu krtaniowego wstecznego. Proponowany model pokazuje zależność między amplitudą sygnału informacyjnego, jako odpowiedzią na symulacje nerwu krtaniowego wstecznego a współrzędną punktu symulacji bazującego na interwałowej analizie danych.
4
Content available remote A Sign Function Approach to Solve Algebraically Interval System of Linear Equations for Nonnegative Solutions
Chakraverty S., Hladík M., Mahato N. R.
Fundamenta Informaticae
|
2017
|
Vol. 152, nr 1
13--31
EN
This paper deals with solving interval system of linear equations. The problem is to find a nonnegative algebraic solution. Based on sign function approach and using interval center and radius arithmetic operations, we propose an algorithm for computation of an algebraic interval solution vector. We also discuss fundamental properties of this solution vector, such as existence and uniqueness. Further, the nonnegative solution algorithm has been extended to other signrestricted approach. Numerical examples of interval system of linear equations show efficiency of the algorithms presented.
5
Content available remote True Concurrent Equivalences in Time Petri Nets
Virbitskaite I., Bushin D., Best E.
Fundamenta Informaticae
|
2016
|
Vol. 149, nr 4
401--418
EN
The intention of the paper is towards a framework for developing, studying and comparing observational equivalences in the setting of a real-time true concurrent model. In particular, we introduce a family of trace and bisimulation equivalences in interleaving, step, partial order and causal net semantics in the setting of time Petri nets (elementary net systems whose transitions are labeled with time firing intervals, can fire only if their lower time bounds are attained, and are forced to fire when their upper time bounds are reached) [3]. We deal with the relationships between the equivalences showing the discriminating power of the approaches of the linear-time - branching-time and interleaving - partial order spectra and construct a hierarchy of equivalent classes of time Petri nets. This allows studying in complete detail the timing behaviour in addition to the degrees of relative concurrency and nondeterminism of processes.
6
Content available remote Analiza dynamiczna konstrukcji z tłumikami z niedokładnie określonymi parametrami projektowymi
Łasecka-Plura M., Lewandowski R.
Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture
|
2016
|
z. 63, nr 1/I
439--446
PL
W pracy został omówiony sposób obliczania charakterystyk dynamicznych ram z niedokładnie określonymi parametrami projektowymi. Analizowano konstrukcje z wbudowanymi pasywnymi tłumikami drgań. Zakłada się, że parametry projektowe mogą się zmieniać, jednak zakres ich zmienności jest znany. Zastosowany rachunek interwałowy pozwala wyrazić parametry projektowe jako tzw. liczby przedziałowe. Przyjęto, że dolna i górna granica szukanych charakterystyk dynamicznych jest przedstawiona jako rozwinięcie w szereg Taylora pierwszego rzędu. W pracy został zamieszczony przykład numeryczny, w którym analizowano ośmiokondygnacyjną, trójprzęsłową ramę z tłumikami. Prezentowana metoda może mieć zastosowanie w praktyce w celu określenia zakresu zmienności charakterystyk dynamicznych przy niedokładnie określonych parametrach projektowych.
EN
In the paper a method for determining dynamic characteristics of frame with uncertain design parameters is described. The structures with built-in passive dampers are considered. The proposed method could be used when the parameters of structures or parameters of dampers are uncertain. The main idea is that values of design parameters could change with respect to values adopted in the design process but the range of their variation is known. The design parameters are expressed as interval values what makes possible calculation of dynamic characteristics of structures by use of interval analysis. In this paper the lower and upper bounds of dynamic characteristics are obtained by use of Taylor series expansion. At the end of the paper a simple numerical example is presented. The eight-storey frame with three bays and three dampers mounted on it is considered. This structure was designed according to EC8 Part 1. The dampers parameters are uncertain. The obtained results are compared with ones determined with a help of the vertex method. This method assumes that it is necessary to calculate end-point combination of uncertain design parameters. The presented method may be applicable in practice in order to predict the limit values of chosen dynamic characteristics of structures with uncertain design parameters.
7
Content available Towards robust predictive fault-tolerant control for a battery assembly system
Seybold L., Witczak M., Majdzik P., Stetter R.
International Journal of Applied Mathematics and Computer Science
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2015
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Vol. 25, no. 4
849--862
EN
The paper deals with the modeling and fault-tolerant control of a real battery assembly system which is under implementation at the RAFI GmbH company (one of the leading electronic manufacturing service providers in Germany). To model and control the battery assembly system, a unified max-plus algebra and model predictive control framework is introduced. Subsequently, the control strategy is enhanced with fault-tolerance features that increase the overall performance of the production system being considered. In particular, it enables tolerating (up to some degree) mobile robot, processing and transportation faults. The paper discusses also robustness issues, which are inevitable in real production systems. As a result, a novel robust predictive fault-tolerant strategy is developed that is applied to the battery assembly system. The last part of the paper shows illustrative examples, which clearly exhibit the performance of the proposed approach.
8
Content available remote Interwałowe oszacowania wskaźników niezawodności strukturalnej systemów elektroenergetycznych
Grishkevich A., Grishkevich M.
Przegląd Elektrotechniczny
|
2014
|
R. 90, nr 6
249--252
PL
Otrzymano interwałowe oszacowania wypadkowych wskaźników niezawodności strukturalnej systemów elektroenergetycznych na podstawie rozwiązań układów równań liniowych na krańcach interwałów danych początkowych. Uwzględniono interwałowe wartości udziałów stanów awaryjnych w wypadkowych wskaźnikach niezawodności dla testowych wartości danych początkowych.
EN
Generation of interval estimations of resultant indices of electric power systems’ structural reliability on the basis of solutions of linear equations systems on border intervals of initial data is considered. Interval values for the contribution of the failure states of the resulting reliability for the test values of the original data are given.
9
Content available P1-TS fuzzy scheduling control system design using local pole placement and interval analysis
Smoczek J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2014
|
Vol. 62, nr 3
455--464
EN
The linear parameter-varying (LPV) discrete-time model based design of a fuzzy scheduling control scheme is developed through incorporating the advantages of P1-TS theory, and applying the local pole placement method and interval analysis of closed-loop system polynomial coefficients. The synthesis of fuzzy scheduling control scheme is proposed in the form of iterative procedure, which enables to find the appropriate number of intervals of a fuzzy interpolator ensuring that a family of local linear controllers places closed-loop polynomial coefficients within a desired range. The computational complexity of multidimensional fuzzy scheduling control scheme synthesis is reduced using a fundamental matrix method and recursive procedure for fuzzy rule-based interpretation. The usability of the proposed method is illustrated by an implementation example and experimental results obtained on a laboratory scaled overhead crane.
10
Content available remote Modelowanie statystyczne oszacowań interwałowych wskaźników niezawodności strukturalnej układów elektrycznych
Grishkevich A., Burmutaew A.
Przegląd Elektrotechniczny
|
2012
|
R. 88, nr 8
77-79
PL
Rozpatrzono sposób otrzymania interwałowych oszacowań wypadkowych wskaźników niezawodności strukturalnej układów elektrycznych na podstawie interwałowych rozwiązań układów równań liniowych. Zbadano dokładność i złożoność modelowania statystycznego interwałów prawdopodobieństwa stanów modeli, opisujacych funkcjonowanie jednego i dwóch elementów.
EN
Generation of interval estimations of resultant indices of structural reliability of electric systems on the basis of interval solutions of systems of the linear equations is considered. Precision and complexity of statistical modeling of intervals of states' probabilities for the models describing functioning of one and two elements are investigated.
11
Is the conventional interval arithmetic correct?
Piegat A., Landowski M.
Journal of Theoretical and Applied Computer Science
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2012
|
Vol. 6, nr 2
27-44
EN
Interval arithmetic as part of interval mathematics and Granular Computing is unusually important for development of science and engineering in connection with necessity of taking into account uncertainty and approximativeness of data occurring in almost all calculations. Interval arithmetic also conditions development of Artificial Intelligence and especially of automatic thinking, Computing with Words, grey systems, fuzzy arithmetic and probabilistic arithmetic. However, the mostly used conventional Moore-arithmetic has evident weak-points. These weak-points are well known, but nonetheless it is further on frequently used. The paper presents basic operations of RDM-arithmetic that does not possess faults of Moore-arithmetic. The RDM-arithmetic is based on multi-dimensional approach, the Moore-arithmetic on one-dimensional approach to interval calculations. The paper also presents a testing method, which allows for clear checking whether results of any interval arithmetic are correct or not. The paper contains many examples and illustrations for better understanding of the RDM-arithmetic. In the paper, because of volume limitations only operations of addition and subtraction are discussed. Operations of multiplication and division of intervals will be presented in next publication. Author of the RDM-arithmetic concept is Andrzej Piegat.
12
Content available remote Interval analysis of navigational problems
Banachowicz A., Wolski A.
Journal of KONBiN
|
2012
|
No. 2 (22)
89--96
EN
Algorithms of solutions to navigational problems usually comprise elements for numerical calculations. Apart from random errors, numerical errors of varying nature can be found in them. These errors are due to the level of precision of input data, the approximability of computing methods and errors generated by the computing very process itself in a computer. The latter category includes numerical precision (floating point of a numerical notation) and rounding off of numbers. These errors are analyzed as absolute and relative errors, rounding off errors and are regarded as random errors with a triangular distribution. Over the last decade or more the interval analysis of rounding off errors has been dynamically developing. Despite increased computing effort (costs), in some cases such analysis is necessary, particularly when we want to get a result of specific precision. It can be extended as an analysis of random errors with uniform distribution.
PL
Algorytmy rozwiązania zagadnień nawigacyjnych zazwyczaj zawierają elementy o obliczeń numerycznych. Występują więc w nich, oprócz błędów losowych, również błędy numeryczne o różnym charakterze. Błędy te wywołane są poziomem precyzji danych wejściowych, przybliżonością metod obliczeniowych oraz błędami generowanymi samym procesem obliczeniowym w komputerze. Do tych ostatnich należą precyzja numeryczna (reprezentacja zmiennopozycyjna) oraz zaokrąglenia. Błędy te analizujemy jako błędy bezwzględne, błędy względne, błędy zaokrągleń oraz traktuje się je jako błędy losowe o rozkładzie trójkątnym. W ostatnich kilkunastu latach dynamicznie rozwija się analiza przedziałowa błędów zaokrągleń. Pomimo zwiększone nakładu obliczeń (kosztów) jest ona w niektórych przypadkach niezbędna, szczególnie gdy chcemy otrzymać wynik o odpowiedniej precyzji. Można ją również rozszerzyć na analizę błędów losowych o rozkładzie jednostajnym.
13
Content available Zastosowanie analizy przedziałowej do szacowania zasobów węglowodorów przy słabym rozpoznaniu własności złoża
Wojnarowski P.
Wiertnictwo, Nafta, Gaz
|
2010
|
T. 27, z. 4
781-787
PL
W trakcie prac mających na celu zagospodarowanie nowo odkrytego złoża bardzo istotne jest właściwe oszacowanie jego zasobów. Niestety we wczesnej fazie rozpoznania informacja złożowa jest bardzo uboga. Uniemożliwia to zastosowanie wielu klasycznych narzędzi służących do określania potencjalnych zasobów złoża. W pracy przedstawiono zastosowanie algebry przedziałowej do szacowania zasobów gazu ziemnego metodą objętościową. Podejście to pozwala na określenie zakresu możliwych zasobów złoża nawet w przypadku niewielkiej ilości danych wejściowych. Wyniki analizy porównano z rezultatami uzyskanymi za pomocą symulacji Monte Carlo.
EN
Reliable prediction of the hydrocarbon reserves is essential for the optimization of development plans for oil and gas reservoirs. The uncertainty of the in-place volumes determination may have a direct impact on important economical decisions. In the early exploration phase, when 1 to 2 exploration wells have been drilled, we have usually limited information about reservoir's properties and main difficulty in reservoir description is use of classical tools for reservoir analysis. In this work application of interval analysis for reserves estimation with volumetric method is presented. This method allows to estimate reserves also in case of lack of data. Results obtained from presented methodology were compared with Monte Carlo simulation results. Advantages and limitations of those two methods were discussed.
14
Content available remote Verified solution method for population epidemiology models with uncertainty
Enszer J. A., Stadtherr M. A.
International Journal of Applied Mathematics and Computer Science
|
2009
|
Vol. 19, no 3
501-512
EN
Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.
15
Content available remote Reliable robust path planning with application to mobile robots
Pepy R., Kieffer M., Walter E.
International Journal of Applied Mathematics and Computer Science
|
2009
|
Vol. 19, no 3
413-424
EN
This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.
16
Content available remote Interval analysis for certified numerical solution of problems in robotics
Merlet J. P.
International Journal of Applied Mathematics and Computer Science
|
2009
|
Vol. 19, no 3
399-412
EN
Interval analysis is a relatively new mathematical tool that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization, but numerous other problems may be addressed as well. This approach has the following general advantages: (a) it allows to find solutions of a problem only within some finite domain which make sense as soon as the unknowns in the problem are physical parameters; (b) numerical computer round-off errors are taken into account so that the solutions are guaranteed; (c) it allows one to take into account the uncertainties that are inherent to a physical system. Properties (a) and (c) are of special interest in robotics problems, in which many of the variables are parameters that are measured (i.e., known only up to some bounded errors) while the modeling of the robot is based on parameters that are submitted to uncertainties (e.g., because of manufacturing tolerances). Taking into account these uncertainties is essential for many robotics applications such as medical or space robotics for which safety is a crucial issue. A further inherent property of interval analysis that is of interest for robotics problems is that this approach allows one to deal with the uncertainties that are unavoidable in robotics. Although the basic principles of interval analysis are easy to understand and to implement, this approach will be efficient only if the right heuristics are used and if the problem at hand is formulated appropriately. In this paper we will emphasize various robotics problems that have been solved with interval analysis, many of which are currently beyond the reach of other mathematical approaches.
17
Analiza interwałowa i rozmyta ludzkiej kości biodrowej
John A., Orantek P., Miarka M.
Modelowanie Inżynierskie
|
2007
|
T. 3, nr 34
55-60
PL
Modelowanie numeryczne ludzkiej kości biodrowej jest złożonym procesem, w którym należy wziąć pod uwagę wiele ważnych czynników. Jednym z nich są własności materiału. Obliczenia numeryczne wymagają wprowadzenia parametrów materiałowych, które zależą od wieku, zdrowia, płci, środowiska oraz wielu innych. Aby dobrać prawidłowo parametry materiałowe, należy wziąć pod uwagę różnorodne dane dotyczące pacjentów. Autorzy artykułu założyli wartości przedziałowe wybranych parametrów materiałowych. Zaproponowano interwałową i rozmytą analizę kości biodrowej.
EN
Numerical modeling of the human pelvic bone is a complex process in which many important factors are taken into account. One of them concerns material properties. Numerical calculations require the characteristics of the material properties and the material parameters from the beginning. The material properties of the living body depend on age, health, gender, environment and many others factors. To determine correct material parameters, health details of a group of patients need to be taken into consideration. In this paper authors assumed interval values of the selected material parameters and proposed interval and fuzzy analysis of the pelvic bone.
18
Content available remote Identification of "input-output" dynamic model of the electrical circuits on the basis of interval data
Dyvak M., Stakchiv P., Calishchuc I.
Przegląd Elektrotechniczny
|
2005
|
R. 81, nr 2
60-62
EN
The problem of identification of "input-output" dynamic model of electrical circuit on the basis of interval data is considered. The method of interval parameter's identification of dynamic system is proposed. The results of proposed method used for modeling of electrical circuit ol transformer are shown.
PL
W pracy przedstawiono problem identyfikacji dynamicznego modelu obwodu elektrycznego na podstawie danych interwałowych. Zaproponowano metodę identyfikacji interwałowych parametrów systemu dynamicznego. Zaprezentowano wyniki zastosowania przedstawionej metody do modelowania obwodu elektrycznego transformatora.
19
Content available remote Applying the Interval Multistep Methods of Adams Type to Solution Simple Pendulum Problem
Jankowska M.
Vibrations in Physical Systems
|
2004
|
Vol. 21
167--170
20
Content available remote Interval-analysis-based methods of calculation of building structures reliability
Kinash Roman I.
Górnictwo i Geoinżynieria
|
2003
|
R. 27, z. 3--4
359-364
EN
Results of the research connected with an elaboration basic, simple and easy in the use technical methods to estimate the reliability of building structures using the interval analysis have been presented in the paper. The preprocessor proposed permits to create interval programs with histogram values, using the standard - programming language Pascal. The possibility of the use in the logical expressions, containing this type data, is an important special attribute of the preprocessor.
PL
W pracy omówiono rezultaty badań związanych z opracowaniem podstawowych, prostych i łatwych w użyciu metod technicznych do oceny niezawodności konstrukcji budowlanych z wykorzystaniem analizy interwałowej. Zaproponowany preprocesor pozwala tworzyć programy interwałowe z wartościami histogramowymi, wykorzystując w tym celu standardowy język programowania Pascal. Ważną cechą szczególną preprocesora jest możliwość jego wykorzystania w wyrażeniach logicznych, zawierających dane tego typu.
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