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    Wyświetlanie 1-8 z 8
    Tytuł:
    Remarks on five equivalent forms of the fractional – order backward – difference
    Autorzy:
    Ostalczyk, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/202441.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    discrete systems
    fractional order backward difference
    fractional - order backward sum
    Opis:
    In this paper a fractional-order backward-difference/sum (FOBD/S) equivalent formulae are considered. From the Gr¨unwald- Letnikov (GL - FOBD) definition formula and its Horner equivalent form one derives the Riemann-Liouville FOBD (RL - FOBD). Also the Caputo and polynomial-like forms are defined. All forms may be useful in real-time calculations (in the evaluation of digital control strategies) due to the reduction of fractional orders. The investigations are illustrated by a numerical example.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 2; 271-278
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On simplified forms of the fractional-order backward difference and related fractional-order linear discrete-time system description
    Autorzy:
    Ostalczyk, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/200397.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional calculus
    discrete-time system response
    ułamkowy rachunek różniczkowy
    czas reakcji
    system dyskretny
    Opis:
    In this paper three simplified forms of the fractional-order (FO) backward difference (BD) are proposed and analysed. Due to time and frequency characteristics criteria parameters of simplified forms of the FOBDs are chosen. Applications of the simplified forms of the FOBDs diminish a number of multiplications and additions needed to evaluate the FOBD. This is very important in real-time microprocessor calculations. It is proved that in a discrete state-space description of a fractional-order system one should correct the input matrix with simplified forms of the FOBD. Investigations are supported by two numerical examples.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2015, 63, 2; 457-464
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Performance evaluation of the construction products as a research challenge. Small error – big difference in assessment?
    Autorzy:
    Szewczak, E.
    Piekarczuk, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/200289.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    numerical calculation
    uncertainty
    uncertainty influence on product assessment
    niepewność
    obliczenia numeryczne
    wpływ niepewności na ocenę produktu
    Opis:
    The paper refers to the importance of test results uncertainty in the assessment of the construction product performance. Uncertainty understood as dispersion attributed to any value which is result of the tests, calculations or other evaluations, occurs at every level of assessment (material, product, construction). Authors presented the various approaches to uncertainty estimation, especially in situation of small number of tests results which is characteristic for testing of construction products. Effects of uncertainty on final assessment of construction product was analyzed using the example of bearing capacity of thin-walled structure obtained by numerical calculation. Different values of material tests uncertainty resulting from different approaches to its assessment was taken into account. It was demonstrated that the difference in the results of strength tests of a material, which falls within the limits of uncertainty, may result in a very significant difference in the evaluation of a structure.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 4; 675-686
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term
    Autorzy:
    Błasik, Marek
    Powiązania:
    https://bibliotekanauki.pl/articles/2086846.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional derivative
    fractional integral
    integro-differential equations
    numerical method
    finite difference method
    pochodna ułamkowa
    całkowanie ułamkowe
    równanie całkowo-różniczkowe
    metoda numeryczna
    metoda elementów skończonych
    Opis:
    In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 6; e138240, 1--9
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional-order discrete model of an independent wheel electrical drive of the autonomous platform
    Autorzy:
    Bąkała, M.
    Nowakowski, J.
    Ostalczyk, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/200875.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional-order backward difference
    difference equation
    identification
    model dyskretny
    równanie różniczkowe
    identyfikacja
    Opis:
    In the paper the linear time-invariant fractional-order models of the separated wheel closed-loop electrical drive of the autonomous platform are considered. As a reference model one considers the classical model described by the second-order linear difference equation. Two discrete-time fractional-order models are considered: non-commensurate and commensurate. According to the sum of the squared error criterion (SSE) one compares two-parameter integer-order model with the four-parameter non-commensurate and three-parameter commensurate fractional-order ones. Three mathematical models are built and simulated. The computer simulation results are compared with measured velocity of the real autonomous platform separate wheel closed-loop electrical drive.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 433-440
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Parallel computations of the step response of a floor heater with the use of a graphics processing unit. Part 1: models and algorithms
    Autorzy:
    Gołębiowski, J.
    Forenc, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/200428.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    air floor heating
    step response
    implicit finite difference method
    parallel computations
    GPGPU
    Opis:
    The article presents a method of computing the step response of an air floor heater. The method implements parallel algorithms on a graphics processing unit. In the analyzed concrete slab heating ducts are placed. Hot air is transferred through them, thanks to which the heat penetrates into the slab. Heat transfer into the environment takes place on the top surface of the floor by natural convection and radiation. The bottom surface of the slab is thermally insulated. A two-dimensional heat equation was discretized with the use of the implicit finite difference method. In order to solve the obtained system of equations, the conjugate gradient method was used. Moreover, in order to examine the possibility of shortening the computations time, the algorithm of this method was implemented on a graphics processing unit. A computer program, using the CUDA parallel computing platform and linear algebra libraries CUBLAS and CUSPARSE, was developed.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 4; 943-948
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Influence of spatial distribution and the type of material on the occurrence of bandgaps in phononic crystals
    Autorzy:
    Garus, Sebastian
    Sochacki, Wojciech
    Kwiatoń, Paweł
    Nabiałek, Marcin
    Petrů, Jana
    Kubanek, Mariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/27311439.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    finite difference time domain
    band gap
    phononic crystal
    mechanical waves
    propagation
    domena czasowa różnic skończonych
    kryształ fononiczny
    fale mechaniczne
    propagacja
    przerwa energetyczna
    Opis:
    The study investigated the effect of the fill factor, lattice constant, and the shape and type of meta-atom material on the reduction of mechanical wave transmission in quasi-two-dimensional phononic structures. A finite difference algorithm in the time domain was used for the analysis, and the obtained time series were converted into the frequency domain using the discrete Fourier transform. The use of materials with large differences in acoustic impedance allowed to determine the influence of the meta-atom material on the propagation of the mechanical wave.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 3; art. no. e144609
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for the asymptotic stability
    Autorzy:
    Stanisławski, R.
    Latawiec, K. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/200600.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Grünwald-Letnikov fractional difference
    discrete-time fractional order system
    stability conditions
    Cauchy’s argument principle
    Opis:
    This paper presents a series of new results on the asymptotic stability of discrete-time fractional difference (FD) state space systems and their finite-memory approximations called finite FD (FFD) and normalized FFD (NFFD) systems. In Part I, new, general, necessary and sufficient stability conditions are introduced in a unified form for FD/FFD/NFFD-based systems. In Part II, an original, simple, analytical stability criterion is offered for FD-based systems, and the result is used to develop simple, efficient, numerical procedures for testing the asymptotic stability for FFD-based and, in particular, NFFD-based systems. Consequently, the so-called f-poles and f-zeros are introduced for FD-based system and their closed-loop stability implications are discussed.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 2; 353-361
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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