Intelligent Optimization Method and Rapid Design of Cross-scale Structure
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摘要: 跨尺度拓扑优化设计极大激发了结构轻量化潜力，在先进装备的开发中具有重要作用。然而基于传统有限元的结构拓扑优化算法难以适应产品快速迭代的需求。为此，本文提出了一种基于耦合深度学习的跨尺度拓扑优化方法，通过集成残差神经网络（Resnet）、U-net架构及SEnet中的注意力机制，建立快速生成双尺度拓扑结构的深度学习模型。模型训练数据利用双向渐进结构优化算法产生，并用一组全新的数据对模型进行测试。数值算例表明，本文提出的深度学习模型可以高效且准确的生成基于各种边界下的宏观材料分布与微观拓扑结构。Abstract: The multiscale topology optimization design has greatly stimulated the lightweight potential of the structure and play an important role in the development of advanced equipment. However, the structural topology optimization algorithm based on traditional finite element is difficult to meet the needs of rapid product iteration. To this end, this paper proposes a coupled deep learning-based cross-scale topology optimization method to establish a deep learning model for fast generation of dual-scale topologies by integrating residual neural networks (Resnet), U-net architecture and attention mechanism in SEnet. The training data are generated using a bidirectional evolutionary structure optimization algorithm, and the model is tested with a completely new set of data. Numerical examples show that the proposed deep learning model can efficiently and accurately generate macroscopic material distribution and microscopic topology based on various boundaries.
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Key words:
- multiscale topology optimization /
- coupled deep learning /
- micro structure /
- light weigh
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图 2 边界约束及相应的多层级结构
Figure 2. Boundary constraints and corresponding multi-layer structures
图 3 X方向力及边界条件，Y方向力及边界条件， 体积约束
Figure 3. X-direction force and boundary conditions, Y-direction force and boundary conditions, volume constraints
图 6 耦合神经网络模型架构 和 Resnet-SE模块
Figure 6. Coupled neural network model architecture and resnet-SE module
图 7 针对宏观构型的训练历史参数的变化
Figure 7. Changes in training history parameters for macroscopic configurations
图 8 针对微观构型的训练历史参数的变化
Figure 8. Changes in training history parameters for micro configurations
表 1 深度学习模型和BESO方法生成的二维多层级拓扑优化结构的比较（从测试集中随机选取的10个样本）
Table 1. Comparison of 2D multi-level topology optimization structures generated by deep learning models and BESO methods (10 samples randomly selected from the test set)
边界条件和负载 BESO生成的
宏观结构神经网络生成的
宏观结构BESO生成的
微观结构神经网络生成的
微观结构Dice $ \begin{gathered} \theta = {105^ \circ } \\ {V_{\text{f}}} = 0.8 \\ \end{gathered} $ 
宏观：0.957
微观：0.933$ \begin{gathered} \theta = {50^ \circ } \\ {V_{\text{f}}} = 0.65 \\ \end{gathered} $ 
宏观：0.974
微观：0.962$ \begin{gathered} \theta = {120^ \circ } \\ {V_{\text{f}}} = 0.55 \\ \end{gathered} $ 
宏观：0.934
微观：0.942$ \begin{gathered} \theta = {135^ \circ } \\ {V_{\text{f}}} = 0.78 \\ \end{gathered} $ 
宏观：0.959
微观：0.942$ \begin{gathered} \theta = {40^ \circ } \\ {V_{\text{f}}} = 0.68 \\ \end{gathered} $ 
宏观：0.956
微观：0.951$ \begin{gathered} \theta = {10^ \circ } \\ {V_{\text{f}}} = 0.80 \\ \end{gathered} $ 
宏观：0.958
微观：0.946$ \begin{gathered} \theta = {20^ \circ } \\ {V_{\text{f}}} = 0.60 \\ \end{gathered} $ 
宏观：0.953
微观：0.936$ \begin{gathered} \theta = {25^ \circ } \\ {V_{\text{f}}} = 0.55 \\ \end{gathered} $ 
宏观：0.961
微观：0.988$ \begin{gathered} \theta = {175^ \circ } \\ {V_{\text{f}}} = 0.65 \\ \end{gathered} $ 
宏观：0.946
微观：0.932$ \begin{gathered} \theta = {75^ \circ } \\ {V_{\text{f}}} = 0.70 \\ \end{gathered} $ 
宏观：0.945
微观：0.931
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表 2 有限元方法与耦合深度学习方法计算时间的比较
Table 2. Comparison of computational time between finite element method and coupled deep learning method
编号 有限元方法的计算时间/s 深度学习的计算时间/s 1 116.76 5.36 2 131.26 5.37 3 216.37 5.32 4 124.70 5.24 5 120.76 5.12 6 116.79 5.38 7 140.07 5.51 8 208.86 5.45 9 153.49 5.42 10 106.51 5.46 平均 143.56 5.37
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[1] 张国锋, 徐雷, 王鑫, 等. 面向连续体结构拓扑优化的分区密度修正敏度过滤方法研究[J]. 机械科学与技术, 2022, 41(11): 1641-1649.ZHANG G F, XU L, WANG X, et al. Partition density modified sensitivity filtering method for topology optimization of continuum structure[J]. Mechanical Science and Technology for Aerospace Engineering, 2022, 41(11): 1641-1649. (in Chinese) [2] CHUANG C H, CHEN S K, YANG R J, et al. Topology optimization with additive manufacturing consideration for vehicle load path development[J]. International Journal for Numerical Methods in Engineering, 2018, 113(8): 1434-1445. doi: 10.1002/nme.5549 [3] 舒定真, 郭伟超, 苏力争, 等. 利用聚类分析的宏细观多尺度并行拓扑优化设计方法研究[J]. 机械科学与技术, 2023, 42(4): 521-529.SHU D Z, GUO W C, SU L Z, et al. Investigation of macro and micro multiscale concurrent topology optimization design with cluster analysis[J]. Mechanical Science and Technology for Aerospace Engineering, 2023, 42(4): 521-529. (in Chinese) [4] SHI G H, GUAN C Q, QUAN D L, et al. An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing[J]. Chinese Journal of Aeronautics, 2020, 33(4): 1252-1259. doi: 10.1016/j.cja.2019.09.006 [5] BENDSØE M P, SIGMUND O. Material interpolation schemes in topology optimization[J]. Archive of Applied Mechanics, 1999, 69(9-10): 635-654. doi: 10.1007/s004190050248 [6] XIE Y M, STEVEN G P. A simple evolutionary procedure for structural optimization[J]. Computers & Structures, 1993, 49(5): 885-896. [7] QUERIN O M, STEVEN G P, XIE Y M. Evolutionary structural optimisation (ESO) using a bidirectional algorithm[J]. Engineering Computations, 1998, 15(8): 1031-1048. doi: 10.1108/02644409810244129 [8] WANG S Y, WANG M Y. Radial basis functions and level set method for structural topology optimization[J]. International Journal for Numerical Methods in Engineering, 2006, 65(12): 2060-2090. doi: 10.1002/nme.1536 [9] HUANG X, RADMAN A, XIE Y M. Topological design of microstructures of cellular materials for maximum bulk or shear modulus[J]. Computational Materials Science, 2011, 50(6): 1861-1870. doi: 10.1016/j.commatsci.2011.01.030 [10] GAO J, LUO Z, LI H, et al. Topology optimization for multiscale design of porous composites with multi-domain microstructures[J]. Computer Methods in Applied Mechanics and Engineering, 2018, 344: 451-476. [11] 付君健, 孙鹏飞, 杜义贤, 等. 基于子结构法的多层级结构拓扑优化[J]. 中国机械工程, 2021, 32(16): 1937-1944. doi: 10.3969/j.issn.1004-132X.2021.16.006FU J J, SUN P F, DU Y X, et al. Hierarchical structure topology optimization based on substructure method[J]. China Mechanical Engineering, 2021, 32(16): 1937-1944. (in Chinese) doi: 10.3969/j.issn.1004-132X.2021.16.006 [12] LI H, LUO Z, XIAO M, et al. A new multiscale topology optimization method for multiphase composite structures of frequency response with level sets[J]. Computer Methods in Applied Mechanics and Engineering, 2019, 356: 116-144. doi: 10.1016/j.cma.2019.07.020 [13] YU Y Y, HUR T, JUNG J, et al. Deep learning for determining a near-optimal topological design without any iteration[J]. Structural and Multidisciplinary Optimization, 2019, 59(3): 787-799. doi: 10.1007/s00158-018-2101-5 [14] WHITE D A, ARRIGHI W J, KUDO J, et al. Multiscale topology optimization using neural network surrogate models[J]. Computer Methods in Applied Mechanics and Engineering, 2019, 346: 1118-1135. doi: 10.1016/j.cma.2018.09.007 [15] 叶红玲, 李继承, 魏南, 等. 基于深度学习的跨分辨率结构拓扑优化设计方法[J]. 计算力学学报, 2021, 38(4): 430-436. doi: 10.7511/jslx20210509403YE H L, LI J C, WEI N, et al. Cross-resolution acceleration design for structural topology optimization based on deep learning[J]. Chinese Journal of Computational Mechanics, 2021, 38(4): 430-436. (in Chinese) doi: 10.7511/jslx20210509403 [16] QIU C, DU S Y, YANG J L. A deep learning approach for efficient topology optimization based on the element removal strategy[J]. Materials & Design, 2021, 212: 110179. -
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