Machine learning RBF-based surrogate models for uncertainty quantification of age and time-dependent fracture mechanics

Abstract

This paper proposes a machine learning strategy using radial basis function (RBF) as surrogate models for uncertainty quantification of age and time-dependent fracture mechanics problems. The RBF surrogate models are trained to replace the time-consuming evaluations of the mapping integral of the time-dependent energy release rate. The probabilistic problem considers input random variables of geometry, loading, and material parameters for a concrete plate section with the presence of an initial surface crack. The performance of the RBF surrogates was evaluated through cross-validation and Monte Carlo reference solutions that expensively evaluated the integrals. The results of mean square errors and the Kolmogorov-Smirnov goodness-of-fit tests on the predicted probability and cumulative density functions show that, the RBF surrogates reached good accuracy even for a small training set size, rather than second-order polynomial models which could reasonably perform only for bigger training set sizes. The RBF surrogates accurately predict even long-tail distributions for farther prediction times with relatively small training sets. The proposed RBF surrogate models presented the generalization capabilities to predict thousands of unseen data points from Monte Carlo simulations and successfully assess the uncertainty quantification of the time-dependent energy release rate.