Enhancing deep neural networks for multivariate uncertainty analysis of cracked structures by POD-RBF

Abstract

An efficient Monte Carlo (MC) simulation method is proposed to address multivariate uncertainties in the dynamic fracture analysis of cracked structures. Deep neural networks (DNN) based on model order reduction are special surrogate models for enhancing the sampling efficiency of MC simulation. Proper orthogonal decomposition-radial basis functions (POD-RBF) bridge the original full model and the DNN, enabling the training datasets of the neural network to be evaluated rapidly from a reduced-order model. The full-order model snapshot of the cracked structure is obtained using the scaled boundary finite element method (SBFEM). We innovatively tackle multidimensional uncertainties, including individual crack lengths, material parameters, and their combinations. Numerical examples show that the POD-RBF-DNN-MC surrogate model benefits from the uncertainty analysis of large scale and multidimensional random input variables. The method is simpler than full-order sampling and eliminates the scale problem of POD-RBF. In addition, the POD-RBF-DNN-MC surrogate model is more efficient than full-order MC, POD-RBF-MC only, and DNN-MC only, with respect to accelerating the stochastic response analysis based on MC. Finally, we validate the proposed algorithm and show that it significantly improves the efficiency of uncertainty analysis.