Quantification and propagation of Aleatoric uncertainties in topological structures
Quantification and propagation of Aleatoric uncertainties in topological structures
复制标题
DOI：
10.1016/j.ress.2023.109122
复制
发表时间：
2023-01
期刊：
影响因子：
--
通讯作者：
Zihan Wang;Mohamad Daeipour;Hongyi Xu
中科院分区：
文献类型：
--
作者：
Zihan Wang;Mohamad Daeipour;Hongyi Xu
分布在复杂拓扑结构中的任意不确定性的量化和传播仍然是一个挑战。现有的不确定性量化和传播方法只能处理分布在单连通空间域中的参数不确定性或高维随机量。在不确定性分析中，缺乏一种系统的方法来捕捉结构域的拓扑特征。因此，本文提出了一种新的方法来量化和传播任意的不确定性，例如分布在拓扑空间域中的局部材料性质和缺陷的空间变化。我们提出了一种新的基于随机场的不确定性表示方法，该方法利用最短内部路径距离来捕捉拓扑特征。采用PPCA和β变分自动编码器(βVAE)等参数化方法将不确定性的随机场表示转化为一小部分独立的随机变量。然后利用多项式混沌展开和单变量降维等非侵入式不确定性传播方法将参数不确定性传播到问题的输出。通过工程实例验证了该方法的有效性。通过与蒙特卡罗模拟在足够大样本下的参考值的比较，证实了该方法的准确性和计算效率。
Quantification and propagation of aleatoric uncertainties distributed in complex topological structures remain a challenge. Existing uncertainty quantification and propagation approaches can only handle parametric uncertainties or high dimensional random quantities distributed in a simply connected spatial domain. There lacks a systematic method that captures the topological characteristics of the structural domain in uncertainty analysis. Therefore, this paper presents a new methodology that quantifies and propagates aleatoric uncertainties, such as the spatially varying local material properties and defects, distributed in a topological spatial domain. We propose a new random field-based uncertainty representation approach that captures the topological characteristics using the shortest interior path distance. Parameterization methods like PPCA andβ-Variational Autoencoder (βVAE) are employed to convert the random field representation of uncertainty to a small set of independent random variables. Then non-intrusive uncertainties propagation methods such as polynomial chaos expansion and univariate dimension reduction are employed to propagate the parametric uncertainties to the output of the problem. The effectiveness of the proposed methodology is demonstrated by engineering case studies. The accuracy and computational efficiency of the proposed method is confirmed by comparing with the reference values of Monte Carlo simulations with a sufficiently large number of samples.