The granular computing in uncertain identification problems

  • Piotr Orantek Silesian University of Technology
  • Tadeusz Burczyński Cracow University of Technology

Abstract

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.

Keywords

evolutionary algorithms, granular computing, intervals, fuzzy sets, theory of probability, Identification,

References

[1] J. Arabas. Wykłady z Algorytmów 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'Ol, Sydney, Australia, 2001.
Published
Aug 17, 2022
How to Cite
ORANTEK, Piotr; BURCZYŃSKI, Tadeusz. The granular computing in uncertain identification problems. Computer Assisted Methods in Engineering and Science, [S.l.], v. 14, n. 4, p. 695-704, aug. 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/804>. Date accessed: 23 dec. 2024.
Section
Articles