The granular computing in uncertain identification problems - Orantek, Piotr; Burczyński, Tadeusz (Computer Assisted Methods in Engineering and Science, 2022)
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.