Dual order-reduced Gaussian process emulators (DORGP) for quantifying high-dimensional uncertain crack growth using limited and noisy data

Abstract

This paper proposes a novel data driven scheme, called dual order-reduced Gaussian Process emulators (DORGP), for efficiently quantifying the high-dimensional uncertain crack growth using limited and noisy data. Firstly, we freshly construct the dual order-reduced spaces that decouple and draw the features among the high-dimensional raw inputs (i.e., material/load uncertainties) and raw outputs (i.e., stress intensity factor and cracks) obtained by isogeometric boundary element simulator, respectively. Secondly, Gaussian Process emulators are built to map the features of the input to the features of the output in the constructed dual order-reduced spaces. Consequently, given new uncertain parameters, the proposed scheme can accurately predict the features with limited and noisy data, and project them back to the high-dimensional space quantifying the complex fatigue crack growth, including the mean value and confidence interval. Numerical examples are provided to validate the efficacy of the proposed approach, including both material and load uncertainties having or without noise. The results demonstrate that the DORGP are highly efficient, with time consumption ranging from 1/4000 to 1/10000 of that required for numerical simulations, and accurate, with relative errors of less than 1%. Furthermore, the approach delivers probabilistic predictions using only a small dataset of samples (e.g., 25), significantly reducing the burden of collecting expensive fatigue data.