Use of neural networks for fitting of FE probabilistic scaling model parameters

The probabilistic crack approach, based on the Monte Carlo method, was recently developed for finite element analysis of concrete cracking and related size effects. In this approach the heterogeneity of the material is taken into account by considering the material properties (tensile strength, Young modulus, etc.) to vary spatially following a normal distribution. N samples of the vector of random variables are generated from a specific probability density function, and the N samples corresponding to a simulation are functions of the mean value and of 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 used in the analysis. The paper proposes an inverse finite element analysis using neural networks for the determination of the statistical distribution parameters (e.g., for a normal distribution, the mean and the standard deviation) from a given response of the structure (for instance, an average load-displacement curve). From FE-analysis of 4-point bending beam tests, it is shown that the backanalysis technique developed in this paper is a powerful tool to determine the probabilistic distribution functions at the material level from structural tests for material volumes which are generally not accessible to direct testing. This revised version was published online in July 2006 with corrections to the Cover Date.