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    Wyświetlanie 1-8 z 8
    Tytuł:
    Non integer order, state space model of heat transfer process using Atangana-Baleanu operator
    Autorzy:
    Oprzędkiewicz, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/202078.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non integer order systems
    heat transfer equation
    infinite dimensional systems
    fractional order state equation
    Riesz operator
    Caputo operator
    Atangana-Baleanu operator
    Opis:
    In the paper a new, state space, non integer order model of an one-dimensional heat transfer process is proposed. The model uses a new operator with Mittag-Leffler kernel, proposed by Atangana and Beleanu. The non integer order spatial derivative is expressed by Riesz operator. Analytical formula of the step response is given, the convergence of the model is discussed too. Theoretical results are verified by experiments.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 1; 43-50
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Unified summation equations and their applications in tribology wear process
    Autorzy:
    Wierzcholski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/200950.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    unified operator of summation
    summation equation
    micro-bearing wear
    Opis:
    This paper presents some applications of summation equations with regard to the calculation prognosis of micro-bearing wear parameters. Summation equations are presented in a new form of difference and recurrence equations where the unknown micro-bearing wear function occurs as the argument of the reciprocal unified operator of summation (UOS). In this paper the properties of the UOS and reciprocal UOS as well as the unitary translation operator (UTO) are defined and applied to a micro-bearing wear determination. The approach of both dual and interaction between summation and recurrence equations and micro-bearing wear determination, makes this paper unique.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 2; 405-417
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non integer order, state space model of heat transfer process using Caputo-Fabrizio operator
    Autorzy:
    Oprzędkiewicz, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/201464.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non-integer order systems
    heat transfer equation
    infinite dimensional systems
    fractional order state equation
    Riesz operator
    Caputo operator
    Caputo-Fabrizio operator
    systemy niecałkowitego rzędu
    układ niecałkowitego rzędu
    twierdzenie Riesza
    pochodna Caputo
    Opis:
    The paper is intended to show a new state space, non integer order model of an one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space semigroup model. The fractional order derivative with respect to time is by a new operator proposed by Caputo and Fabrizio, the non integer order spatial derivative is expressed by Riesz operator. The Caputo-Fabrizio operator can be directly implementated using MATLAB, because it does not require us to apply any approximation. Analytical formulae of step response are given, the system decomposition was discussed also. Main results from the paper show that the use of Caputo Fabrizio operator allows us to obtain the simple in implementation and analysis model of the considered heat transfer process. The accuracy of the proposed model in the sense of a MSE cost function is satisfying.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 3; 249-255
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The positivity of the fractional order model of a two-dimensional temperature field
    Autorzy:
    Oprzędkiewicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/27311454.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    heat transfer equation
    fractional order state equation
    Caputo operator
    positivity
    thermal camera
    non-integer order systems
    równanie wymiany ciepła
    równanie stanu rzędu ułamkowego
    operator Caputo
    kamera termowizyjna
    systemy niecałkowitego rzędu
    dodatniość
    Opis:
    The paper presents analysis of the positivity for a two-dimensional temperature field. The process under consideration is described by the linear, infinite-dimensional, noninteger order state equation. It is derived from a two-dimensional parabolic equation with homogenous Neumann boundary conditions along all borders and homogenous initial condition. The form of control and observation operators is determined by the construction of a real system. The internal and external positivity of the model are associated to the localization of heater and measurement. It has been proven that the internal positivity of the considered system can be achieved by the proper selection of attachment of a heater and place of a measurement as well as the dimension of the finite-dimensional approximation of the considered model. Conditions of the internal positivity associated with construction of real experimental system are proposed. The postivity is analysed separately for control and output of the system. This allows one to analyse the positivity of thermal systems without explicit control. Theoretical considerations are numerically verified with the use of experimental data. The proposed results can be applied i.e. to point suitable places for measuring of a temperature using a thermal imaging camera.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e145675
    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 heat transfer process using time and spatial Grünwald-Letnikov operator
    Autorzy:
    Oprzędkiewicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2173561.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order systems
    heat transfer equation
    fractional order state equation
    fractional order backward difference
    Grünwald-Letnikov operator
    practical stability
    systemy ułamkowego rzędu
    równanie wymiany ciepła
    równanie stanu rzędu ułamkowego
    różnica wsteczna rzędu ułamkowego
    operator Grünwalda-Letnikowa
    stabilność praktyczna
    Opis:
    In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; art. no. e135843
    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 heat transfer process using time and spatial Grünwald-Letnikov operator
    Autorzy:
    Oprzędkiewicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2090693.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order systems
    heat transfer equation
    fractional order state equation
    fractional order backward difference
    Grünwald-Letnikov operator
    practical stability
    systemy ułamkowego rzędu
    równanie wymiany ciepła
    równanie stanu rzędu ułamkowego
    różnica wsteczna rzędu ułamkowego
    operator Grünwalda-Letnikowa
    stabilność praktyczna
    Opis:
    In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; e135843, 1--10
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator
    Autorzy:
    Oprzędkiewicz, K.
    Dziedzic, K.
    Więckowski, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/200257.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non integer order systems
    heat transfer
    fractional order state equation
    fractional order backward difference
    Grünwald-Letnikov operator
    convergence
    Opis:
    The paper is intented to show a new, state space, discrete, non integer order model of a one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space model and it uses the discrete Grünwald-Letnikov operator to express the fractional order difference with respect to time. Stability and spectrum decomposition for the proposed model are recalled, the accuracy and convergence are analyzed too. The convergence of the proposed model does not depend on parameters of heater and measuring sensors. The dimension of the model assuring stability and predefined rate of convergence and stability is estimated. Analytical results are confirmed by experiments.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 5; 905-914
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new algorithm for a CFE-approximated solution of a discrete-time noninteger-order state equation
    Autorzy:
    Oprzędkiewicz, K.
    Stanisławski, R.
    Gawin, E.
    Mitkowski, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/199796.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order calculus
    discrete-time noninteger-order state equation
    continuous fraction expansion
    Al-Alaoui operator
    równanie dyskretne
    aproksymacja Al-Alaoui
    CFE
    Opis:
    In the paper, a new method for solution of linear discrete-time fractional-order state equation is presented. The proposed method is simpler than other methods using directly discrete-time version of the Grünwald-Letnikov operator. The method is dedicated to use with any approximator to the operator expressed by a discrete transfer function, e.g. CFE-based Al-Alaoui approximation. A simulation example confirms the usefulness of the method.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 4; 429-437
    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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