Chosen possibilities of ɛ-fuzzy boundary elements method application in the analysis of conductivity problems with uncertainties

• Autorzy: Witek Halina , Witek Bernard

Identyfikatory

DOI

10.24423/cames.565

• Języki publikacji: EN

Abstrakty

EN

The paper presents a methodology of solving boundary problems with uncertainty parameters based on the use of interval perturbation numbers. This methodology allows for the analysis of very complex problems with different uncertain parameters. Fuzzy Boundary Element Method (FBEM) using ɛ-number will be called ɛ-Fuzzy Boundary Element Method (ɛ-FBEM). Detailed discussion of the problems of computing and applications will be presented on the example of the fuzzy boundary integral equation arising from the boundary problem for the potential problems with heterogeneous, fuzzy boundary conditions of Dirichlet and Neumann type, fuzzy internal sources, fuzzy boundary and fuzzy fundamental solution. The presented methodology can be used to solve various engineering problems (e.g. in civil engineering, power engineering and others) – e.g. to analyze the temperature distribution in structural elements or elements located in the vicinity of objects or devices. In the latter case the increased temperature may be a symptom of a severe failure (e.g. power transformer overload, overexcitation or a fault) which cannot be tolerated due to the threat to the object and to the entire power system. Proposed method maybe used for electrical equipment diagnosis and in consequence as a power system failure prevention. In this paper calculation methodology is illustrated on the example of an area bounded by a square, on the left boundary of which a certain temperature is set, while on the rest of the boundaries the conditions are equal to zero. A dedicated computer program allows for the calculation of both temperature and temperature derivative for any number of boundary elements using ɛ-FBEM.

Słowa kluczowe

EN

ɛ-fuzzy boundary element method; ɛ-number; fuzzy boundary element method; heat conduction; temperature distribution; object diagnosis

PL

ɛ-metoda rozmytych elementów brzegowych; metoda rozmytych elementów brzegowych; przewodnictwo cieplne; rozkład temperatury; diagnoza obiektu

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2023
• Tom: Vol. 30, no. 4
• Strony: 407--426
• Opis fizyczny: Bibliogr. 15 poz., rys., wykr.

Twórcy

autor

Witek Halina

• Faculty of Civil Engineering, Silesian University of Technology, Akademicka 5,44-100 Gliwice, Poland

autor

Witek Bernard

• Electrical Faculty, Silesian University of Technology, Krzywoustego 2, 44-100 Gliwice,Poland

Bibliografia

• 1. T. Burczynski, J. Skrzypczyk, The fuzzy boundary element method: A new methodology, Zeszyty Naukowe Politechniki Slaskiej, seria Budownictwo, 83: 25–42, 1995.
• 2. T. Burczynski, J. Skrzypczyk, The boundary element method for fuzzy systems, [in:] IASTED International Conference on Modelling, Simulation and Optimization, pp. 24–27, Singapore, August 11–14, 1997.
• 3. L.M. Campos, J.F. Huete, Independence concepts in possibility theory: Part I, Fuzzy Sets and Systems, 103: 127–152, 1999.
• 4. D. Dubois, H. Prade, Bayesian conditioning in possibility theory, Fuzzy Sets and Systems, 92: 223–240, 1997.
• 5. Y. Hase, Handbook of Power System Engineering, John Wiley and Sons, Chichester, 2007.
• 6. D.J. Glover, M.S. Sarma, T.J. Overbaye, Power System Analysis and Design (SI Edition), Cengage Learning, Stamford, 2017.
• 7. K. Rönberg, Heat-transfer Simulations Applied to Electrical Machines, KTH Royal Institute of Technology, Stockholm, Sweden, 2020.
• 8. J. Skrzypczyk, On fuzzy singular integration, Zeszyty Naukowe Politechniki Śląskiej, seria Budownictwo, 83: 121–130, 1995.
• 9. J. Skrzypczyk, Fuzzy methods in the analysis of uncertain systems, Zeszyty Naukowe Politechniki Śląskiej, seria Budownictwo, 86: 183–196, 1999.
• 10. J. Skrzypczyk, Perturbation methods – A new arithmetic [in Polish: Metody perturbacyjne – nowa arytmetyka], [in:] Zeszyty Naukowe Politechniki Śląskiej, seria Budownictwo, Księga jubileuszowa z okazji 70. lecia Prof. dra hab. inż. W. Starosolskiego, pp. 391–398, Gliwice, 2003.
• 11. J. Skrzypczyk, T. Burczynski, Theoretical and computational aspects of the fuzzy boundary element methods, [in:] IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method, Cracow, May 31 – June 3, 1999, pp. 351–364, Kluwer Academic Publishers, Dordrecht/Boston/London, 2001.
• 12. J. Skrzypczyk, H. Witek, Estimation of the solutions approximation accuracy of the linear equations systems with uncertain parameters [in Polish: Oszacowanie dokładności aproksymacji rozwiazań układów równań liniowych o niepewnych parametrach], [in:] Zeszyty Naukowe Politechniki Śląskiej, seria Budownictwo, Księga jubileuszowa z okazji 70-lecia Prof. dra hab. inż. W. Starosolskiego, pp. 399–406, Gliwice, 2003.
• 13. J. Skrzypczyk, H. Witek, Fuzzy boundary element methods: A new perturbation approach for systems with fuzzy parameters, [in:] Proceedings of International Conference New Trends in Statics and Dynamics of Buildings, Faculty of Civil Engineering SUT, Bratislava, Slovakia, 2005.
• 14. H. Ungrad, W. Winkler, A. Wiszniewski, Protection Techniques in Electrical Energy Systems, Marcel Dekker, New York, 1995.
• 15. Y. Yang et al., Thermal management of electric machines, IET Electrical Systems in Transportation, 8(2): 104–116, 2017.