基于深度学习和梯度优化的弹性超材料设计

doi:10.3785/j.issn.1008-973X.2024.09.014

浙江大学学报(工学版)

2024, Vol. 58

Issue (9): 1892-1901 DOI: 10.3785/j.issn.1008-973X.2024.09.014

土木与建筑工程

基于深度学习和梯度优化的弹性超材料设计

肖力1,2(

),曹志刚1,3,*(

),卢浩冉1,黄志坚1,蔡袁强1

1. 浙江大学滨海和城市岩土工程研究中心，浙江杭州 310058
2. 浙江大学平衡建筑研究中心，浙江杭州 310028
3. 浙江大学建筑设计研究院有限公司，浙江杭州 310028

Elastic metamaterial design based on deep learning and gradient optimization

Li XIAO1,2(

),Zhigang CAO1,3,*(

),Haoran LU1,Zhijian HUANG1,Yuanqiang CAI1

1. Coastal and Urban Geotechnical Engineering Research Center, Zhejiang University, Hangzhou 310058, China
2. Center for Balance Architecture, Zhejiang University, Hangzhou 310028, China
3. The Architectural Design and Research Institute of Zhejiang University Co. Ltd, Hangzhou 310028, China

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摘要：

为了建立灵活通用的弹性超材料快速迭代设计框架，并实现考虑材料离散性的拓扑结构和材料参数同步优化，提出基于深度学习和梯度优化的设计方法. 以变分自动编码器和带隙神经网络组成的设计网络作为框架，采用自动微分技术和梯度优化算法，利用梯度信息迭代调整设计变量；提出协同优化策略以考虑材料离散性，使结构优化的同时在材料库中选择最佳材料. 基于所提方法分别进行约束条件下带隙宽度最大化和指定带隙区间设计，并探讨同步优化和拓扑构型的影响. 结果表明，与材料和拓扑结构的单独优化相比，同步优化具有更优越的性能；在相同带隙目标和材料组成下，多层构型可以设计出更小尺寸的元胞. 频域和时域分析的数值模拟结果表明，所设计的超材料结构在目标带隙范围内表现出明显的减振性能.

关键词： 弹性超材料; 带隙; 深度学习; 梯度优化; 材料选择

Abstract:

A novel design method based on deep learning and gradient optimization was proposed to establish a flexible and general framework for fast iterative design of elastic metamaterials and achieve simultaneous optimization of topology structure and material considering material discretization. The design network composed of variational autoencoders and band gap neural network was developed as the framework, and auto-differentiation techniques and gradient optimization algorithms were employed to iteratively tune the design variables with the gradient information. Furthermore, a co-optimization strategy was further proposed to consider the material discretization, so that the structure was optimized while the optimal material was selected from the material depot. Band gap width maximization under constraints and on-demand design were carried out respectively, and the effects of simultaneous optimization and topological configuration were explored. Results showed that the simultaneous optimization provided superior performance compared to separate optimization of materials and topology structures. Additionally, the multilayer configuration can achieve basic units with smaller sizes under the same objectives and material composition. Furthermore, the numerical simulation results of frequency and time domain analyses showed that the designed elastic metamaterials exhibited significant vibration damping performance in the target band gap range.

Key words: elastic metamaterial band gap deep learning gradient optimization material selection

收稿日期: 2023-08-05 出版日期: 2024-08-30

CLC:

TB 34

基金资助: 国家自然科学基金资助项目（51978611）；浙江省杰出青年科学基金资助项目（LR21E080004）.

通讯作者: 曹志刚 E-mail: xiaoli1104@zju.edu.cn;caozhigang2011@zju.edu.cn

作者简介: 肖力（1999—），男，硕士生，从事工程超材料优化设计研究. orcid.org/0000-0002-0044-6497. E-mail：xiaoli1104@zju.edu.cn

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引用本文:

肖力,曹志刚,卢浩冉,黄志坚,蔡袁强. 基于深度学习和梯度优化的弹性超材料设计[J]. 浙江大学学报(工学版), 2024, 58(9): 1892-1901.

Li XIAO,Zhigang CAO,Haoran LU,Zhijian HUANG,Yuanqiang CAI. Elastic metamaterial design based on deep learning and gradient optimization. Journal of ZheJiang University (Engineering Science), 2024, 58(9): 1892-1901.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2024.09.014 或 https://www.zjujournals.com/eng/CN/Y2024/V58/I9/1892

图 1 一维弹性超材料示意图

表 1 材料库中的部分材料参数

图 2 变分自动编码器示意图

图 3 生成器训练收敛图

图 4 带隙神经网络示意图

表 2 土层参数的范围

图 5 预测带隙宽度和实际值之间的对比图

图 6 前向计算和反向传播过程

图 7 协同优化策略流程图

表 3 约束条件带隙宽度最大化的设计结果及与遗传算法设计的对比

图 8 工况3迭代收敛图及最优材料选择

图 9 不同场地条件下指定带隙区间设计的结果

表 4 场地土层参数（条件变量）

图 10 超材料-土二维有限元分析结果

1	KUSHWAHA M S, HALEVI P, DOBRZYNSKI L, et al Acoustic band structure of periodic elastic composites[J]. Physical Review Letters, 1993, 71 (13): 2022- 2025 doi: 10.1103/PhysRevLett.71.2022
2	LIU Z, ZHANG X, MAO Y, et al Locally resonant sonic materials[J]. Science, 2000, 289 (5485): 1734- 1736 doi: 10.1126/science.289.5485.1734
3	唐豪, 陈晓斌, 唐孟雄, 等基于复频散曲线特征的周期结构高铁路基减振研究[J]. 岩土工程学报, 2021, 43 (12): 2169- 2179 TANG Hao, CHENG Xiaobing, TANG Mengxiong, et al Vibration reduction of high-speed railway subgrade with periodic structures based on complex dispersion curves[J]. Chinese Journal of Geotechnical Engineering, 2021, 43 (12): 2169- 2179 doi: 10.11779/CJGE202112003
4	CHENG Z, SHI Z, MO Y Complex dispersion relations and evanescent waves in periodic beams via the extended differential quadrature method[J]. Composite Structures, 2018, 187: 122- 136 doi: 10.1016/j.compstruct.2017.12.037
5	DEASI R, GUHA A, SESHU P Modelling and simulation of active and passive seat suspensions for vibration attenuation of vehicle occupants[J]. International Journal of Dynamics and Control, 2021, 9 (4): 1423- 1443 doi: 10.1007/s40435-021-00788-2
6	LI X, CHENG S, YANG H, et al Optimization of vibration characteristics and directional propagation of plane waves in branching ligament structures of wind models[J]. Results in Physics, 2023, 47: 106345 doi: 10.1016/j.rinp.2023.106345
7	LI X, CHENG S, YANG H, et al Bandgap tuning and in-plane wave propagation of chiral and anti-chiral hybrid metamaterials with assembled six oscillators[J]. Physica A, 2023, 615: 128600 doi: 10.1016/j.physa.2023.128600
8	XIAO L, CAO Z, LU H, et al Controllable and scalable gradient-driven optimization design for two-dimensional metamaterials based on deep learning[J]. Composite Structures, 2024, 337: 118072 doi: 10.1016/j.compstruct.2024.118072
9	葛倩倩, 于桂兰有覆层土体中部分埋入式表面波屏障[J]. 工程力学, 2020, 37 (Suppl.1): 249- 253 GE Qianqian, YU Guilan A partially embedded periodic barriers for surface waves in soil with a covered layer[J]. Engineering Mechanics, 2020, 37 (Suppl.1): 249- 253 doi: 10.6052/j.issn.1000-4750.2019.04.S046
10	YI G, YOUN B A comprehensive survey on topology optimization of phononic crystals[J]. Structural and Multidisciplinary Optimization, 2016, 54 (5): 1315- 1344 doi: 10.1007/s00158-016-1520-4
11	熊远皓, 李凤明, 张传增周期结构振动带隙特性优化研究进展[J]. 哈尔滨工程大学学报, 2022, 43 (9): 1229- 1240 XIONG Yuanhao, LI Fengming, ZHANG Chuanzeng Research progress on the optimization of vibration band-gap characteristics for periodic structures[J]. Journal of Harbin Engineering University, 2022, 43 (9): 1229- 1240
12	WANG X, WAN S, ZHOU P, et al Topology optimization of periodic pile barriers and its application in vibration reduction for plane waves[J]. Soil Dynamics and Earthquake Engineering, 2022, 153: 107119 doi: 10.1016/j.soildyn.2021.107119
13	ZHOU P, WAN S, WANG X, et al Topology optimization of the periodic pile barrier with initial stresses arranged in rectangular and equilateral triangular lattices[J]. Structures, 2023, 51: 628- 639 doi: 10.1016/j.istruc.2023.03.013
14	LIU Z, ZHU D, RODRIGUES S P, et al Generative model for the inverse design of metasurfaces[J]. Nano Letters, 2018, 18 (10): 6570- 6576 doi: 10.1021/acs.nanolett.8b03171
15	贾宇翔, 王甲富, 陈维, 等基于智能算法的超材料快速优化设计方法研究进展[J]. 雷达学报, 2021, 10 (2): 220- 239 JIA Yuxiang, WANG Jiafu, CHEN Wei, et al Research progress on rapid optimization design methods of metamaterials based on intelligent algorithms[J]. Journal of Radars, 2021, 10 (2): 220- 239 doi: 10.12000/JR21027
16	JIN Y, HE L, WEN Z, et al Intelligent on-demand design of phononic metamaterials[J]. Nanophotonics, 2022, 11 (3): 439- 460 doi: 10.1515/nanoph-2021-0639
17	LI X, NING S, LIU Z, et al Designing phononic crystal with anticipated band gap through a deep learning based data-driven method[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 361: 112737 doi: 10.1016/j.cma.2019.112737
18	GURBUZ C, KRONOWETTER F, DIETZ C, et al Generative adversarial networks for the design of acoustic metamaterials[J]. The Journal of the Acoustical Society of America, 2021, 149 (2): 1162- 1174 doi: 10.1121/10.0003501
19	曹蕾蕾, 朱旺, 武建华, 等基于人工神经网络的声子晶体逆向设计[J]. 力学学报, 2021, 53 (7): 1992- 1998 CAO Leilei, ZHU Wang, WU Jianhua, et al Inverse design of phononic crystals by artificial neural networks[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53 (7): 1992- 1998 doi: 10.6052/0459-1879-21-142
20	LIU C, YU G Intelligent design of engineered metabarrier based on deep learning[J]. Composite Structures, 2022, 280: 114911 doi: 10.1016/j.compstruct.2021.114911
21	LIU C, YU G Inverse design of locally resonant metabarrier by deep learning with a rule-based topology dataset[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 394: 114925 doi: 10.1016/j.cma.2022.114925
22	LIU C, YU G Deep learning-based topology design of periodic barrier for full-mode waves[J]. Construction and Building Materials, 2022, 314: 125579 doi: 10.1016/j.conbuildmat.2021.125579
23	LIU D, TAN Y, KHORAM E, et al Training deep neural networks for the inverse design of nanophotonic structures[J]. ACS Photonics, 2018, 5 (4): 1365- 1369 doi: 10.1021/acsphotonics.7b01377
24	ABUEIDDA D W, ALMASRI M, AMMOURAH R, et al Prediction and optimization of mechanical properties of composites using convolutional neural networks[J]. Composite Structures, 2019, 227: 111264 doi: 10.1016/j.compstruct.2019.111264
25	CUI X, WANG S, HU S A method for optimal design of automotive body assembly using multi-material construction[J]. Materials and Design, 2008, 29 (2): 381- 387 doi: 10.1016/j.matdes.2007.01.024
26	XIAO L, CAO Z, LU H, et al Optimal design of one-dimensional elastic metamaterials through deep convolutional neural network and genetic algorithm[J]. Structures, 2023, 57: 105349 doi: 10.1016/j.istruc.2023.105349
27	石志飞, 程志宝, 向宏军. 周期结构理论及其在隔震减振中的应用[M]. 北京: 科学出版社, 2017: 270−276.
28	CAMLEY R, DJAFARIROUHANI B, DOBRZYNSKI L, et al Transverse elastic-waves in periodically layered infinite, semi-infinite, and slab media[J]. Journal of Vacuum Science and Technology B, Woodbury: Amer Inst Physics, 1983, 1 (2): 371- 375 doi: 10.1116/1.582559
29	LUO C, NING S, LIU Z, et al Interactive inverse design of layered phononic crystals based on reinforcement learning[J]. Extreme Mechanics Letters, 2020, 36: 100651 doi: 10.1016/j.eml.2020.100651
30	KINGMA D P, WELLING M. Auto-encoding variational bayes [EB/OL]. (2013-12-20) [2023-9-13]. https://doi.org/10.48550/arXiv.1312.6114.
31	KINGMA D P, BA J. Adam: a method for stochastic optimization [EB/OL]. (2014-12-22) [2023-9-13]. https://doi.org/10.48550/arXiv.1412.6980.
32	BAYDIN A G, PEARLMUTTER B A, RADUL A A. Automatic differentiation in machine learning: a survey [EB/OL]. (2015-2-20) [2023-9-13]. https://doi.org/10.48550/arXiv.1502.05767.
33	ABADI M, BARHAM P, CHEN J, et al. TensorFlow: a system for large-scale machine learning [EB/OL]. (2016-5-24) [2023-9-13]. https://doi.org/10.48550/arXiv.1605.08695.
34	GUO T, LIU Y, HAN C An overview of stochastic quasi-newton methods for large-scale machine learning[J]. Journal of the Operations Research Society of China, 2023, 10: 245- 275

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