Quantification of Uncertainties Distributed in Network-Like Systems

Network-like engineering systems, such as transport networks and lattice metamaterials, are featured by high dimensional, complex topological characteristics, which pose a great challenge for uncertainty quantification (UQ). Existing UQ approaches are only applicable to parametric uncertainties, or high dimensional random quantities distributed in a simply connected space (e.g., line section, rectangular area, etc.). The topological characteristics of the input space cannot be captured by existing UQ models. To resolve this issue, a network-based Gaussian random process UQ approach is proposed in this work. By representing the topological input space as a node-edge network, network distance is employed to replace the Euclidean distance in characterizing the spatial correlations. Furthermore, a conditional simulation-based approach is proposed for sampling. Realizations of random quantities on each edge of the network is sampled conditionally on the node values, which are modeled by a multivariable Gaussian distribution. The effectiveness of the proposed approach is demonstrated with two engineering case studies: stochastic thermal conduction analysis of a 3D lattice structure, and characterization of the distortion pattern of an additively manufactured cellular structure.