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

The probabilistic crack approach, based on the Monte Carlo method, was rece ntly 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, Youn g modulus, etc.) to vary spatially following a normal distribution. N sampl es of the vector of random variables are generated from a specific probabil ity density function, and the N samples corresponding to a simulation are f unctions of the mean value and of the standard deviation that define the Ga uss 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 usi ng neural networks for the determination of the statistical distribution pa rameters (e.g., for a normal distribution, the mean and the standard deviat ion) 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 a ccessible to direct testing.