High-Dimensional Uncertainty Quantification in a Hybrid Data + Model-Based Submodeling Method for Refined Response Estimation at Critical Locations

Abstract

This study presents frameworks to build nonintrusive polynomial chaos expansion (PCE) models with regression and Smolyak sparse-grid quadrature to perform high-dimensional uncertainty propagation and uncertainty quantification (UQ) for response estimated with the hybrid data + model-based submodeling (HDMS) method. The HDMS method drives the finite-element submodel containing a critical location of a structure using the measured response of the real structure at the preselected submodel boundaries to estimate a refined response distribution around the critical location. The proposed UQ frameworks are implemented on an experimental case study of a plate with holes as critical locations under tensile loading. The UQ results at the critical locations from regression-based PCE models built using different sampling methods and the Smolyak sparse-grid quadrature-based PCE models are compared with the UQ results from the traditional Monte Carlo simulation (MCS) method. The regression-based PCE model with Smolyak sparse-grid sampling demonstrated significantly higher accuracy in distribution parameters and probability density functions (pdf) compared to the other regression-based PCE models. While the Smolyak quadrature-based PCE model with a considerably small experimental design showed slightly lower accuracy, it still outperforms regression-based PCE models with MC-based sampling.