Training Data Selection for Machine Learning-Enhanced Monte Carlo Simulations in Structural Dynamics

Abstract

The evaluation of structural response constitutes a fundamental task in the design of ground-excited structures. In this context, the Monte Carlo simulation is a powerful tool to estimate the response statistics of nonlinear systems, which cannot be represented analytically. Unfortunately, the number of samples which is required for estimations with high confidence increases disproportionally to obtain a reliable estimation of low-probability events. As a consequence, the Monte Carlo simulation becomes a non-realizable task from a computational perspective. We show that the application of machine learning algorithms significantly lowers the computational burden of the Monte Carlo method. We use artificial neural networks to predict structural response behavior using supervised learning. However, one shortcoming of supervised learning is the inability of a sufficiently accurate prediction when extrapolating to data the neural network has not seen yet. In this paper, neural networks predict the response of structures subjected to non-stationary ground excitations. In doing so, we propose a novel selection process for the training data to provide the required samples to reliably predict rare events. We, finally, prove that the new strategy results in a significant improvement of the prediction of the response statistics in the tail end of the distribution.