Spectral representation-based neural network assisted stochastic structural mechanics

This paper explores the applicability of artificial neural networks (ANN) for predicting the spread of structural response under the presence of uncertain parameters described as random fields. The use of ANN is carried out in combination with Monte Carlo simulation (MCS) for calculating response statistics in stochastic analysis of structural systems using finite elements. To this extent, the ANNs are trained with a few samples, following a conventional MCS procedure and used henceforth to predict the stochastic response for the rest of samples. The basic idea is to achieve a dimensionality reduction of the input ANN training space by using as input vector the random phase angles of the spectral representation method instead of the random variables describing the uncertain input parameters. A further improvement of the efficiency of the proposed approach is achieved by exploiting the uniform distribution of the random phase angles, in order to span efficiently the training space using a latin hypercube sampling (LHS) technique. The advantage of this approach over conventional computation of stochastic response via a standard stochastic finite element-based MCS is the fast and reliable prediction of the required response sample space which can be accomplished at a fraction of computing time and is independent of the size of the finite element model. Numerical results are presented, demonstrating the efficiency and the applicability of the proposed methodology as well as its distinct advantages over existing ANN-based stochastic finite element methodologies (SFEM).