Optimal design of acoustic metamaterial cloaks under uncertainty
Optimal design of acoustic metamaterial cloaks under uncertainty
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DOI：
10.1016/j.jcp.2021.110114
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发表时间：
2021-02-03
影响因子：
4.1
通讯作者：
Ghattas, Omar
中科院分区：
文献类型：
--
作者：
Chen, Peng;Haberman, Michael R.;Ghattas, Omar
在这项工作中，我们考虑了不确定性下声学斗篷的优化设计问题，并开发了可扩展的近似和优化方法来解决该问题。设计变量被视为代表材料属性的无限维空间变化场，而附加的无限维随机场代表例如材料属性的可变性或制造误差。该优化设计问题的离散化导致高维设计变量和不确定参数。为了解决这个问题，我们开发了一种基于泰勒近似和近似牛顿优化方法的计算方法，该方法基于随机场均值导出的 Hessian 矩阵。我们证明了我们的方法在设计变量和不确定参数的维度上是可扩展的，从某种意义上说，对于多达一百万个设计变量和五十万个不确定参数的数值实验，声波传播的必要数量基本上与这些维度无关。我们证明，使用我们的计算方法，可以以易于处理的方式实现对材料不确定性具有鲁棒性的声学斗篷的优化设计。针对环形隐身区域包围的经典圆形障碍物，同时受到单向单频入射波和多向多频入射波的影响，提出并求解了不确定性问题下的优化设计。最后，我们将该方法应用于具有复杂几何形状的确定性大规模最优隐形问题，以证明近似牛顿法的 Hessian 计算对于大型复杂问题是可行的。 (C) 2021 Elsevier Inc. 保留所有权利。
In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents, e.g., the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. We demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method's Hessian computation is viable for large, complex problems. (C) 2021 Elsevier Inc. All rights reserved.