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 successfully employed in various 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 uncertainty quantification and reliability assessment of such systems as they require a large number of forward model evaluations to obtain convergent statistics. To alleviate this difficulty, this paper presents a convolutional dimension-reduction method with knowledge reasoning-based loss regularization for surrogate modeling and uncertainty quantification of structures with high-dimensional spatial uncertainties. 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, knowledge reasoning is formulated as a form of loss regularization, and evolutionary algorithms are employed to train both the ConvDR network and a linear regression model as surrogate models for predicting the response of interest. 2D structures with spatial-variated material compositions are used to demonstrate the performance of the proposed approach.