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中文核心期刊

基于人工神经网络的声子晶体逆向设计

INVERSE DESIGN OF PHONONIC CRYSTALS BY ARTIFICIAL NEURAL NETWORKS

  • 摘要: 声子晶体是一种人工周期性复合材料, 其带隙特性使其在减振、隔声、滤波和声学功能器件等领域具有潜在的应用价值. 如何准确操纵声波和机械波是声子晶体设计的主要挑战. 现有设计方法是基于对结构几何参数与材料参数的分析调整使其匹配特定的应用特性, 设计效率不高且无法达到最佳性能. 为此, 本文以一维层状声子晶体为例, 提出了一种基于Softmax逻辑回归和多任务学习的人工神经网络声子晶体逆向设计方法, 其中, Softmax逻辑回归实现分层结构各区域材料种类的选择, 通过多任务学习确定各区域材料的分布, 从而, 将声子晶体逆向设计问题转化为对单位胞元拓扑结构多组分材料的分类问题. 首先, 随机生成大量声子晶体拓扑结构样本; 然后, 采用有限元法进行并行计算得到所有样本的带隙分布; 接着, 通过神经网络建立带隙分布和拓扑结构之间的映射关系; 最后, 利用训练好的神经网络设计具有目标带隙特性的声子晶体, 即以目标带隙作为神经网络的输入, 网络将直接输出对应的声子晶体单元胞元拓扑结构. 算例表明本方法可根据应用需求快速高效地得到具有目标带隙的一维声子晶体. 该方法为声子晶体的逆向设计提供了一种新颖思路.

     

    Abstract: Phononic crystals represent a special kind of artificial periodic composite materials. The peculiar band-gap characteristics provide potential applications in the vibration reduction, wave filtering, sound insulation and acoustic functional devices. However, how to accurately manipulate acoustic and elastic waves is a major challenge for designing phononic crystals. The conventional design method is based on matching the specific application requirements by analyzing and adjusting the geometrical and material parameters of the phononic crystal structures. This method has a low efficiency and can hardly achieve the optimal performance. An artificial neural networks inverse design method for muti-layered phononic crystals based on the Softmax logistic regression and the multi-task learing is proposed in this study. In the proposed method, the Softmax logistic regression is used to choose the material type and the multi-task learing is used to determine the material distribution for each area of the multi-layered structure, so the phononic crystal reverse design problem is transformed into the classification problem of multi-component materials for the unit cell by the proposed method. First, a large number of the samples for the topological structures are randomly generated. Second, the band-gap structures of the samples are obtained by parallel finite element calculation. After that, the relationship between the topological structures and the band-gaps are established by the neural networks. Finally, the trained neural network is ultimately employed to design a phononic crystal structure with the targeted band-gaps, that is, the targeted band gap is used as the input of the neural network, and the trained neural network will output the corresponding cell topology of the phononic crystal unit cell directly. The example shows that the proposed method can obtain one-dimensional (1D) phononic crystals with the targeted band-gaps for the specified application requirements quickly and efficiently. This method provides a new way for the inverse design of phononic crystals.

     

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