Keywords: genetic algorithm, differential evolution, microplane model, parameter estimation, optimization, parallel computing.

Solution of different technical or scientific tasks typically leads to problems described by partial differential equations. Through the last few decades, hand in hand with the growth of computer performance, the so-called artificial intelligence or soft-computing methods were developed as alternatives to traditional solutions of problems which are difficult to be defined, described or resolved using traditional ones. Genetic algorithms [1] are modern optimization methods which are based on an analogy with the evolution processes of living creatures during ages. The main emphasis during our previous work on optimization algorithms was put on the ability to solve multidimensional tasks and identification of local extremes. The algorithm called SADE [2] is the result of this development. It is based on the traditional genetic algorithm scheme and the operations of mutation, crossover and selection, are extended by the so-called local mutation and differential crossover.

This optimization tool is further used to find a set of parameters of a constitutive model for concrete called the microplane model [3]. It is a fully three-dimensional model, which includes tension and compressive softening, damage of the material, different combinations of loading, unloading and cyclic loading and incorporates the development of anisotropy within the material as well. The principal idea of this model is the projection of a macroscopic tensor onto a set of planes with different spatial orientations. Constitutive relations are applied for these orientations and accompanying microstrains. The macroscopic stress tensor is obtained from microstresses using principle of virtual work. The main disadvantage of this model is the numerical demand, which is manifold in comparison with classical approaches. For the microplane model, a particular type of concrete is described using 8 parameters: Young s modulus, Poisson ratio and other six phenomenological parameters, which even do not have a simple physical interpretation, so it is difficult to determine their values from an experiment. A usual scenario is that an experimenter is trying to fit stress-strain diagrams varying the model parameters by the trial and error method. As one of the most up-to-date approaches to estimation of material parameters, stochastic optimization methods could be employed. The preliminary results of our computations show that the SADE algorithm has the ability to find the microplane model parameters with a satisfactory precision.

The disadvantage of parameter finding are the computational demands related to the structural FEM analysis. Our solution to this obstacle is the parallelization of proposed method. So-called "Global parallel model" proposed in [4] is used. More specifically, the program is divided into an optimization and an analysis part and in this way it is implemented in the cluster of PCs.

Results of this project show that, in the engineering practice, an application of automated optimization procedure could save a huge amount of an experimenter's time needed for searching parameters of the microplane material law, or even more sophisticated model, by the trial and error method. In addition, the obtained numerical results show that the computational demand of this task ensures the nearly-linear speedup even for relatively high number of processors.

1

Z. Michalewicz, "Genetic Algorithms + Data Structures = Evolution Programs". Springer-Verlag, 3rd ed., 1999

2

O. Hrstka, A. Kucerová, M. Leps and J. Zeman, "A competitive comparison of different types of evolutionary algorithms". In Proceedings of the Sixth International Conference of Artificial Intelligence to Civil and Structural Engineering, Civil-Comp Press, 2001. doi:10.4203/ccp.74.37

3

J. Nemecek, "Modelling of compressive softening of concrete"", CTU Reports, 4(6), 2000. Ph.D. Thesis.

4

E. Cantú-Paz, "Efficient and Accurate Parallel Genetic Algorithms"", Kluwer Academic Publishers, 2001.

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