Quantification of Uncertainties Distributed in Network-Like Systems

Zihan Wang, Hongyi Xu
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Abstract

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.
类网络系统中分布的不确定性的量化
运输网络和晶格超材料等类网络工程系统具有高维、复杂的拓扑特征,这对不确定性量化(UQ)提出了很大的挑战。现有的UQ方法仅适用于参数不确定性,或分布在单连通空间(如线段、矩形区域等)中的高维随机量。现有的UQ模型无法捕获输入空间的拓扑特征。为了解决这一问题,本文提出了一种基于网络的高斯随机过程UQ方法。通过将拓扑输入空间表示为节点边缘网络,利用网络距离代替欧几里得距离来表征空间相关性。此外,提出了一种基于条件模拟的采样方法。在节点值上有条件地采样网络每边上的随机数的实现,节点值由多变量高斯分布建模。通过两个工程实例研究证明了该方法的有效性:三维晶格结构的随机热传导分析,以及增材制造细胞结构的畸变模式表征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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