Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries
Stochastic modeling of geometrical uncertainties on complex domains, with application to additive manufacturing and brain interface geometries
复制标题
复杂领域几何不确定性的随机建模，应用于增材制造和大脑接口几何
DOI：
10.1016/j.cma.2021.114014
复制
发表时间：
2021
影响因子：
7.2
通讯作者：
Gomez, Luis J.
中科院分区：
文献类型：
--
作者：
Zhang, Hao;Guilleminot, Johann;Gomez, Luis J.
我们提出了一个随机建模框架来表示和模拟复杂几何形状的空间相关的几何不确定性。虽然考虑随机几何扰动一直是计算工程中感兴趣的主题，但迄今为止提出的大多数研究都涉及规则几何形状（如圆柱体和板）的情况。在这里，标准的随机场表示，如Karhunen-Loève展开，可以很容易地使用，特别是由于相对简单的构造规则形状的协方差算子。相反，将这种技术应用于任意的非凸域通常仍然很困难。在这项工作中，我们制定了一个新的表示空间相关的几何不确定性，允许复杂的域被有效地处理。建立在作者以前的贡献，该方法依赖于一个随机偏微分方程方法的组合，引入捕获显着特征的基础几何形状，如局部曲率和奇点的飞行，和信息理论模型，旨在执行非高斯。更具体地说，我们提出了一种方法，感兴趣的接口浸入到一个虚构的域，并定义算法程序，直接采样随机扰动的流形上。一个简单的策略，统计条件的基础上也提出了更新实现和防止自相交的扰动有限元网格。最后，我们提供了具有挑战性的例子来证明框架的鲁棒性，包括由增材制造和患者特定几何形状的大脑接口产生的螺旋结构的情况。在这两个应用程序中，我们讨论了合适的参数化的滤波算子和量化的不确定性，通过向前传播的影响。
We present a stochastic modeling framework to represent and simulate spatially-dependent geometrical uncertainties on complex geometries. While the consideration of random geometrical perturbations has long been a subject of interest in computational engineering, most studies proposed so far have addressed the case of regular geometries such as cylinders and plates. Here, standard random field representations, such as Karhunen–Loève expansions, can readily be used owing, in particular, to the relative simplicity to construct covariance operators on regular shapes. On the contrary, applying such techniques on arbitrary, non-convex domains remains difficult in general. In this work, we formulate a new representation for spatially-correlated geometrical uncertainties that allows complex domains to be efficiently handled. Building on previous contributions by the authors, the approach relies on the combination of a stochastic partial differential equation approach, introduced to capture salient features of the underlying geometry such as local curvature and singularities on the fly, and an information-theoretic model, aimed to enforce non-Gaussianity. More specifically, we propose a methodology where the interface of interest is immersed into a fictitious domain, and define algorithmic procedures to directly sample random perturbations on the manifold. A simple strategy based on statistical conditioning is also presented to update realizations and prevent self-intersections in the perturbed finite element mesh. We finally provide challenging examples to demonstrate the robustness of the framework, including the case of a gyroid structure produced by additive manufacturing and brain interfaces in patient-specific geometries. In both applications, we discuss suitable parameterization for the filtering operator and quantify the impact of the uncertainties through forward propagation.