Determination of probabilistic parameters of concrete: solving the inverse problem by using artificial neural networks

The probabilistic approach, based on the Monte Carlo method, has been recently introduced to simulate cracking of concrete in the framework of a finite element analysis [Rossi P, Wu X, le Maou F, Belloc A. Mater Struct 1994;27(172):437–44; Rossi P, Ulm F-J, Hachi F. J Engng Mech ASCE 1996;122(11):1038–43; Rossi P, Richer S. Mater Struct 1987;20(119):334–7; Rossi P, Ulm F-J. Mater Struct 1997;30(198):210–6; Fairbairn EMR, Paz CNM, Alves JLD, Silva RCC. Proceedings of XVIII CILAMCE-Iberian Latin American Congress on Computational Methods in Engineering, Brası́lia, vol. 2, 1997;709–15]. If the uncertainties of the material parameters are assumed to vary spatially following a normal distribution, the samples corresponding to a simulation are function of the mean and the standard deviation that define the Gauss density function. The problem is that these statistical moments are not known, a priori, for the characteristic volume of the finite elements. In this paper, neural networks are used to evaluate the parameters characterizing the statistical distribution for a given response of the structure following an inverse analysis procedure. It is shown that this procedure improves a recently proposed algorithm [Fairbairn EMR, Guedes QM, Ulm F-J. Mater Struct 1999;32(215):9–13], which is able to solve the problem, but is very hard to operate. Finally, the procedure presented in this paper is used to identify the probabilistic parameters of a beam tested at TU-Delft.