Research on structure topology optimization design empowered by deep learning method
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摘要:本文综合论述了近年来结构拓扑优化领域与深度学习技术交叉融合发展的相关研究进展. 围绕结构拓扑优化设计的核心方法与关键环节, 以深度学习赋能的角度系统性梳理了两大类赋能方法. 研究指出, 基于深度学习技术的结构优化设计全局代理模型构建方法作为一种直接映射式结构设计方法, 因其简单而典型的设计思想目前已被广泛研究, 然而全局代理模型在计算性和泛化性上的局限与不足也尤为明显; 融合深度学习技术的结构优化设计局部子环节加速与替代方法是一种更加灵活与多样的局部赋能形式, 具有较好的普适性和独特的优越性. 文章对智能赋能结构优化未来的发展进行了展望, 研究重点在于深度学习与结构设计的有机结合方式, 以及数据和知识的混合驱动设计范式.Abstract:This article comprehensively discusses the relevant research progress in the field of structural topology optimization and the cross-integration development of deep learning technology in recent years. Focusing on the core methods and key modules of structural topology optimization design, two major types of empowerment methods are systematically sorted out from the perspective of deep learning empowerment. The study points out that the global surrogate model construction method for structural optimization design based on deep learning technology, as a direct mapping structural design method, has been widely studied because of its simple and typical design ideas. However, the global surrogate model has limitations in computation and generalization. The limitations and deficiencies in performance are also particularly obvious. The structural optimization design method with local sub-link acceleration and replacement integrated with deep learning technology is a more flexible and diverse form of local empowerment, with good universality and unique advantages. The article looks forward to the future development of intelligently empowered structural optimization. Further research work would focus on the organic combination of deep learning and structural design, as well as the co-driven design paradigm of data and knowledge.
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图 1结构优化的三个基本方式: 拓扑优化、形状优化、尺寸优化. 其中, 拓扑优化以优化材料空间布局 (结构内部孔洞的有无、连通性) 为目标, 具有最高的设计自由度, 是提升结构性能最显著的优化设计手段.
图 2结构拓扑优化在航空航天、汽车、建筑设计等领域中的典型工程应用. (a) 星敏相机支架设计(Orme et al. 2017), (b) 机翼设计(Aage et al. 2017), (c) 轮毂设计(Zhang et al. 2021b), (d) 机舱铰链支架设计(Tomlin and Meyer 2011), (e) 机舱结构保形设计(Zhu et al. 2016), (f) 斗拱结构设计(Duan et al. 2023), (g) 喷气发动机支架设计(Senhora et al. 2022b).
图 4主流传统拓扑优化方法. (a)变密度法, 以各向同性实体材料惩罚模型法 (solid isotropic material with penalization, SIMP) 为代表, (b)水平集法 (the level-set methods, LSM), (c)双向渐进结构优化方法 (bi-directional evolutionary structural optimization, BESO), (d)移动可变形组件/空腔法 (moving morphable components/void method , MMC/MMV).
图 8典型基于回归式模型构建的拓扑优化代理模型(Nakamura & Suzuki 2020). 以无迭代拓扑优化为例, 代理模型输入通常包含设计域信息、边界条件和载荷条件, 输出为优化后的结构拓扑. 通常回归式模型基于经典CNN网络——U-Net(Ronneberger et al. 2015)构建.
图 9典型基于生成式模型构建的拓扑优化代模型(Nie et al. 2021). 生成器G用于生成多样式的结构拓扑, 判别器D用于判断该结构拓扑“真”与“假”. 训练完成后生成器能够生成与真实拓扑高度相似的拓扑结构.
图 10深度学习技术与拓扑优化物理响应分析结合的三类形式. (a)基于多分辨率思想的大规模结构分析计算加速(Senhora et al. 2022a), (b)构建近实时物理响应分析代理模型(Lee et al. 2020), (c)引入内嵌物理知识神经网络替代有限元法(Jeong et al. 2023b).
图 11基于子结构法的PIML(Huang et al. 2023)框架. 借助子结构法或EMsFEM思想能够在粗网格下实现细网格的分析精度, 从而大幅减少方程组求解自由度. 但在线生成粗网格单元数值基函数同样是非常耗时的. 已有研究表明: 这部分操作导致的额外计算时间可能使得方法效率优势显著降低甚至消失殆尽. 基于神经网络构建粗网格数值基函数代理模型实时计算数值基函数, 实现EMsFEM粗网格刚度阵或子结构边界刚度阵的快速生成.
图 12PINN框架示意图(Lu et al. 2021b). 其原理可以概括为: 通过训练神经网络最小化损失函数近似PDE求解, 损失函数项包括初始和边界条件的残差项, 以及区域中选定点 (对应于传统数值方法中的“配点”概念) 处的PDE残差. 在训练完成后即可得到任意一点处的响应值.
图 13采用PINN替代有限元分析的拓扑优化. (a)典型的双网络架构, 其中密度网络采用重参数化思想(Zhang et al. 2021c,2023b)用于表征结构拓扑, 位移网络用于结构物理响应分析(Joglekar et al. 2023); (b)PINN TO(Jeong et al. 2023a)方法3D悬臂梁优化结果, (c)DMF-TONN(Joglekar et al. 2023)方法3D悬臂梁优化结果, (d)CPINN TO(Jeong et al. 2023b)方法3D悬臂梁优化结果, (e)NTopo(Zehnder et al. 2021)方法3D悬臂梁优化结果, (f)(He et al. 2022)方法3D桥状结构优化.
图 14深度学习应用于拓扑优化灵敏度分析环节的两类典型技术路线. (a)构建近实时灵敏度分析代理模型(Takahashi et al. 2019), (b)基于多分辨率思想的精细结构灵敏度快速生成模型(Xia et al. 2023).
图 15神经网络重参数化方法. 典型的重参数化建模正向计算流程可分为四个环节(Zhang et al. 2021c,2023b): 结构拓扑的神经网络表征 (neural representations), 设计模型向分析模型映射 (mapping)、物理响应分析 (physics model)、目标函数及约束计算 (objective function). 反向过程即为灵敏度分析.
图 16采用重参数化方法的优化结果. (a)结构刚度设计(Chandrasekhar & Suresh 2021a), (b)多材料设计(Chandrasekhar & Suresh 2021b); (c)纤维连续增强结构设计(Chandrasekhar et al. 2023a); (d)复杂设计域设计(Zhang et al. 2023b); (e)超弹性结构设计(Zhang et al. 2021c); (f)微结构设计(Sridhara et al. 2022); (g)功能梯度结构设计(Chandrasekhar et al. 2023b); (h)三维结构设计(Chen et al. 2023a); (i)应力约束设计(Deng & To 2020); (j)大跨径桥梁结构设计(Qian et al. 2022).
图 17基于神经网络的拓扑结构超分辨率设计. (a)典型超分辨率设计流程(Xue et al. 2021), (b)超分辨率设计效果, SIMP结果为代表原始低分辨设计, 其它为采用不同神经网络架构得到的超分辨率设计结果, 结构清晰度得到显著提升(Lee et al. 2023).
图 18典型在线训练流程图(Xia et al. 2023). 蓝色模块对应的迭代步进行数据收集, 黄色模块对应的迭代步进行代理模型的初始训练以及调整, 橙色模块对应的迭代步应用代理模型.
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