机器学习辅助的三周期极小曲面结构逆设计研究进展

尹兴鹏; 李俊豪; 唐新桢; 李洲

doi:10.7513/j.issn.1004-7638.2025.05.014

机器学习辅助的三周期极小曲面结构逆设计研究进展

doi: 10.7513/j.issn.1004-7638.2025.05.014

1.
株洲齿轮有限责任公司, 湖南株洲 412007
2.
中南大学机电学院, 湖南长沙 410017

基金项目: 湖南省优秀青年基金项目（2023JJ20069）。

详细信息

作者简介:
尹兴鹏，1987年7月出生，男，山东潍坊人，大学本科，工程师。研究方向：高性能金属材料应用，345019320@qq.com

通讯作者:
李洲，1987年出生，男，湖南岳阳人，博士，副教授，从事先进结构与复合材料研究工作，E-mail：221029@csu.edu.cn

中图分类号: TB383,TP181
计量
- 文章访问数: 31
- HTML全文浏览量: 12
- PDF下载量: 10
- 被引次数: 0
出版历程
- 收稿日期: 2025-06-13
- 录用日期: 2025-07-07
- 修回日期: 2025-07-02
- 刊出日期: 2025-10-30

Research progress on machine learning-assisted inverse design of triply periodic minimal surface structures

1.
Zhuzhou Gear Co., Ltd., Zhuzhou 412007, Hunan, China
2.
College of Mechanical and Electrical Engineering, Central South University, Changsha 410017, Hunan, China

摘要

摘要: 三周期极小曲面（Triply periodic minimal surface, TPMS）结构是一类由数学隐式函数生成的仿生多孔结构，具有连续光滑、自支撑性强、比强度高和能量吸收性能优异等特点，适用于钛合金等轻质高性能金属材料的结构设计，广泛应用于航空航天和先进制造领域。系统综述了TPMS金属结构设计方法与力学性能研究进展，重点梳理了TPMS结构的几何建模算法、梯度与组合类型的构建策略。进一步总结了机器学习方法在TPMS金属结构设计中的应用现状，涵盖了正向机器学习的结构力学性能预测与逆向机器学习的目标导向TPMS金属结构设计方法。最后，分析了当前复杂TPMS金属结构逆向设计在高效映射、数据集构建等方面存在的不足，指出未来亟需通过生成式人工智能（Generative artificial intelligence，Generative AI）与逆向建模的深度融合，以推动TPMS金属结构逆向设计的工程化应用。
- 三周期极小曲面(TPMS) /
- 机器学习 /
- 逆设计 /
- 性能预测 /
- 金属多孔结构
Abstract: Triply periodic minimal surface (TPMS) structures are a class of bio-inspired porous architectures generated through mathematical implicit functions, known for their continuous smooth surfaces, self-supporting characteristics, high specific strength, and excellent energy absorption capabilities. These features make TPMS structures particularly suitable for lightweight, high-performance materials such as titanium alloys used in aerospace and advanced manufacturing applications. This work provides a comprehensive review of the design methodologies and advancements in the mechanical performance analysis of TPMS metal structures, with particular emphasis on the geometric modeling algorithms and the construction strategies for gradient and combined structural configurations. It further synthesizes the current state of machine learning applications in the design of TPMS metal structure, encompassing forward machine learning approaches for performance prediction and inverse machine learning frameworks for goal-oriented structural design. The review concludes with a critical assessment of existing challenges in inverse design of TPMS metal structures, particularly regarding efficient mapping and dataset generation. Finally, it highlights the urgent need for deep integrating generative artificial intelligence (Generative AI) techniques with inverse modeling strategies to facilitate the practical engineering implementation of TPMS metal structure inverse design.
- triply periodic minimal surface (TPMS) /
- machine learning /
- inverse design /
- performance prediction /
- metal porous structures

HTML全文

图 1 三周期极小曲面（TPMS）结构的应用^[17-34]

Figure 1. Applications of triply periodic minimal surface (TPMS) structure^[17-34]

下载: 全尺寸图片幻灯片

图 2 复杂TPMS结构的建模算法

(a) 基于区域的TPMS建模算法^[40]；(b) 基于Voronoi的建模算法^[42-44]

Figure 2. Modeling algorithms for complex TPMS

下载: 全尺寸图片幻灯片

图 3 梯度与组合TPMS结构建模研究

(a) 梯度TPMS建模研究^[46,48,52]；(b) 组合TPMS建模研究^[53-57]

Figure 3. Gradient and combined TPMS structure modeling

下载: 全尺寸图片幻灯片

图 4 结构参数、梯度类型与组合方式等对结构性能的影响

(a) 不同梯度对结构性能影响^[58-59]；(b) 不同参数对结构性能影响^[60-61]；(c) 不同组合方式对结构性能影响^[62-63]

Figure 4. Influence of structural parameters, gradient types and combinations on performance

下载: 全尺寸图片幻灯片

图 5 机器学习辅助的TPMS结构性能预测与参数设计

(a) 正向机器学习研究^{[66, 67]}；(b) 逆向机器学习研究^{[68, 70]}

Figure 5. Machine learning-assisted TPMS structural performance prediction and parameter design

下载: 全尺寸图片幻灯片

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