The granular computing in uncertain identification problems

• Autorzy: Orantek P. , Burczyński T.
• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to applications of evolutionary algorithms in identification of structures being under the uncertain conditions. Uncertainties can occur in boundary conditions, in material parameters or in geometrical parameters of structures and are modelled by three kinds of granularity: interval mathematics, fuzzy sets and theory of probability. In order to formulate the optimization problem for such a class of problems by means of evolutionary algorithms the chromosomes are considered as interval, fuzzy and random vectors whose genes are represented by: (i) interval numbers, (ii) fuzzy numbers and (iii) random variables, respectively. Description of evolutionary algorithms with granular representation of data is presented in this paper. Various concepts of evolutionary operator such as a crossover and a mutation and methods of selections are described. In order to evaluate the fitness functions the interval, fuzzy and stochastic finite element methods are applied. Several numerical tests and examples of identification of uncertain parameters are presented.

Słowa kluczowe

EN

evolutionary algorithm; granular computing; intervals; fuzzy sets; theory of probability; identification

PL

algorytm genetyczny; identyfikacja

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2007
• Tom: Vol. 14, No. 4
• Strony: 695--704
• Opis fizyczny: Bibliogr. 21 poz., rys., tab., wykr.

Twórcy

autor

Orantek P.

autor

Burczyński T.

• Silesian University of Technology, Department for Strength of Materials and Computational Mechanics, ul. Konarskiego 18 A, 44-100 Gliwice

Bibliografia

• [1] J. Arabas. Wyklady z Algorytmow Ewolucyjnych. WNT, 2001.
• [2] A. Arslan, M. Kaya. Determination of fuzzy logic membership functions using genetic algorithms. Fuzzy Sets and Systems, 118, Elsevier, 2001.
• [3] A. Bargiela, W. Pedrycz. Granular Computing: An Introduction. Kluwer Academic Publishers, Boston-Dordrecht-London, 2002.
• [4] H.D. Bui. Inverse Problems in the Mechanics of Materials: An Introduction. CRC Press, Boca Raton, 1994.
• [5] T. Burczyński, P. Orantek. Application of neural networks in controlling of evolutionary algorithms. First Asian-Pacific Congress on Computational Mechanics APCOM'01, Sydney, Australia, 2001.
• [6] T. Burczyński, J. Skrzypczyk. Fuzzy aspects of the boundary element method. Engineering Analysis with Boundary Elements, 19: 209-216, 1997.
• [7] L. Chen, S.S. Rao. Fuzzy finite element approach for vibrating analysis of imprecisely defined systems. Finite Elements in Analysis and Design, 27: 69-83, 1977.
• [8] O. Cordon, F. Gomide, F. Herrera, F. Homann, L. Magdalena. Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets and Systems, 141: 5-31, 2004.
• [9] E. Czogala, W. Pedrycz. Elementy i Metody Teorii Zbiorów Rozmytych. PWN, Warszawa, 1985.
• [10] J. Kacprzyk. Zbiory Rozmyte w Analizie Systemowej. PWN, Warszawa, 1986.
• [11] Design of an adaptive fuzzy logic controller using a genetic algorithm. Proc. 4th Int. Conf. on Genetic Algorithms, San Diego, July 13-16, 1991, pp. 450-457.
• [12] M. Kleiber, ed. Handbook of Computational Solid Mechanics. Springer-Verlag, Berlin, 1998
• [13] P. Orantek. The optimization and identification problems of structures with fuzzy parameters. Proc. of 3rd European Conference on Computational Mechanics ECCM-2006, Lisbon, Portugal, 2006.
• [14] A. Papoulis. Probability, Random Variables, and Stochastic Processes. McGraw-Hill, New York, 1991
• [15] W. Pedrycz. Fuzzy Evolutionary Computing. Soft Computing, 2, Springer-Verlag, 1998.
• [16] A. Piegat. Modelowanie i Sterowanie Rozmyte. Akademicka Oficyna Wydawnicza EXIT, Warszawa, 2003.
• [17] D. Rutkowska, M. Piliński, L. Rutkowski. Sieci Neuronowe, Algorytmy Genetyczne i Systemy Rozmyte. PWN Warszawa-Łódź, 1997.
• [18] R. Schaefer. Podstawy Genetycznej Optymalizacji Globalnej. Wydawnictwo Uniwersytetu Jagiellońskiego, Kraków, 2002.
• [19] I. Skalna. Zastosowanie Metod Algebry Przedziałowej w Jakościowej Analizie Układów Mechanicznych. Praca doktorska. Politechnika Śląska, Gliwice, 2002.
• [20] J. Skrzypczyk, T. Burczyński. Theoretical and computational aspects of the fuzzy boundary element methods. In: T. Burczyński, ed., Advanced Mathematical and Computational Mechanics Aspects of Boundary Element Method, pp. 351-364, Kluwer, 2001.
• [21] L.A. Zadeh. Fuzzy sets. Information and Control: 8, 1965.