Convolutional Dimension-Reduction with Knowledge Reasoning for Reliability Approximations of Structures under High-Dimensional Spatial Uncertainties

Along with the rapid advancement of additive manufacturing technology, 3D-printed structures and materials have been popularly employed in diverse applications. Computer simulations of these structures and materials are often characterized by a vast number of spatial-varied parameters to predict the structural response of interest. Direct Monte Carlo methods are infeasible for the uncertainty quantification and reliability assessment of such systems as they require a huge number of forward model evaluations in order to obtain convergent statistics. To alleviate this difficulty, this paper presents a convolutional dimension-reduction network with knowledge reasoning-based loss regularization as explainable deep learning framework for surrogate modeling and uncertainty quantification of structures with high-dimensional spatial variations. To manage the inherent high-dimensionality, a deep Convolutional Dimension-Reduction network (ConvDR) is constructed to transform the spatial data into a low-dimensional latent space. In the latent space, domain knowledge is formulated as a form of loss regularization to train the ConvDR network as a surrogate model to predict the response of interest. Then evolutionary algorithms are utilized to train the deep convolutional dimension-reduction network. Two 2D structures with manufacturing-induced spatial-variated material compositions are used to demonstrate the performance of the proposed approach.