Estimation of spatial uncertainty in material property distributions within heterogeneous structures using optimized convolutional neural networks

Variations in material behaviors within structures built with heterogeneous materials lead to damage initiation and evolution in locally weak regions. Quantifying the property variability within the structure and forward propagation of the impact of the material property uncertainty on the structural response is critical for reliability analysis and structural performance maximization. Commonly, quantification of the variability requires either computationally expensive high-fidelity models of the underlying microstructure or extensive experimental testing. In this paper, we model the uncertainty with spatially correlated random fields and calibrate the model parameters from limited strain field observations using Neural Networks (NNs). The calibration is performed by trained NNs, which outputs best-fit parameters for the spatial correlation model by accepting filtered Digital Image Correlation (DIC) strain distributions as the input. We demonstrate that by training the NNs using simulated data, the resulting networks are able to calibrate the spatial distribution uncertainty models effectively for a set of Fused Filament Fabrication (FFF) printed structures. The methodology requires a limited number of experimental datasets and produces fast estimations of the best-fit parameters of the uncertainty model compared to optimization or inverse fitting methods. This method allows experimentalists to use the same DIC information routinely obtained during modulus or strength testing to calibrate a spatial property distribution uncertainty model for the underlying microstructure.