A numerical study of the response function of a sleeper

There are some phenomena and engineering problems whose complexity is very large. The structural response of a railway sleeper is effectively one of these. The complexity is due to different stiffnesses and material involved, with a large spread in the characterization. A lot of data is required and the numerical simulations could generate them. Firstly a selection of which variables are relevant was necessary and a analysis of which of those could be stochastics has been completed. Once the variables are identified, with a mapping procedure simulations have been realized. In the present work a reduction of time consuming related to simulations is an issue. Then, some convergence studies and a tentative of simplification have been necessary. The ODE's relative tolerance and the time step has been analyzed. A certain number of data have been obtained. Due to the established tolerance, a numerical noise in the response occured. In order to simplify, surrogates model could help to build a continue and easier function to be studied. In this thesis work, a polynomial regression was established to obtain a certain smoothness of the response surface.