留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

理论辅助的弹塑性本构关系小样本深度学习

王琛 何有泉 宋凌寒 樊健生

王琛, 何有泉, 宋凌寒, 樊健生. 理论辅助的弹塑性本构关系小样本深度学习[J]. 工程力学, 2023, 40(9): 29-36. doi: 10.6052/j.issn.1000-4750.2021.12.1012
引用本文: 王琛, 何有泉, 宋凌寒, 樊健生. 理论辅助的弹塑性本构关系小样本深度学习[J]. 工程力学, 2023, 40(9): 29-36. doi: 10.6052/j.issn.1000-4750.2021.12.1012
WANG Chen, HE You-quan, SONG Ling-han, FAN Jian-sheng. A THEORY-AIDED FEW-SHOT DEEP LEARNING ALGORITHM FOR ELASTOPLASTIC CONSTITUTIVE RELATIONSHIPS[J]. Engineering Mechanics, 2023, 40(9): 29-36. doi: 10.6052/j.issn.1000-4750.2021.12.1012
Citation: WANG Chen, HE You-quan, SONG Ling-han, FAN Jian-sheng. A THEORY-AIDED FEW-SHOT DEEP LEARNING ALGORITHM FOR ELASTOPLASTIC CONSTITUTIVE RELATIONSHIPS[J]. Engineering Mechanics, 2023, 40(9): 29-36. doi: 10.6052/j.issn.1000-4750.2021.12.1012

理论辅助的弹塑性本构关系小样本深度学习

doi: 10.6052/j.issn.1000-4750.2021.12.1012
基金项目: 国家杰出青年科学基金项目(51725803)
详细信息
    作者简介:

    王 琛(1993−),男,浙江人,博士,主要从事结构工程研究(E-mail: qtwjy309@163.com)

    何有泉(2002−),男,河北人,本科生,主要从事结构工程研究(E-mail: he-yq19@mails.tsinghua.edu.cn)

    宋凌寒(1997−),男,福建人,博士生,主要从事结构工程研究(E-mail: songlh19@mails.tsinghua.edu.cn)

    通讯作者:

    樊健生(1975−),男,山东人,教授,博士,主要从事结构工程研究(E-mail: fanjsh@tsinghua.edu.cn)

  • 中图分类号: TU501

A THEORY-AIDED FEW-SHOT DEEP LEARNING ALGORITHM FOR ELASTOPLASTIC CONSTITUTIVE RELATIONSHIPS

  • 摘要: 该文提出了一种引入经典弹塑性力学理论知识作为辅助驱动的小样本深度学习算法,适用于土木工程任意材料弹塑性本构关系,能够有效缓解大规模深度学习模型实际应用时常见的数据量匮乏瓶颈。该文简要概述了通用的经典弹塑性力学框架;在此基础上详细阐释了将弹塑性力学方程引入到常规深度学习模型中的方法与流程,该过程无需关心底层理论本构模型的具体形式与传统的复杂数值实现,保留了数据驱动技术简单、直接、高效的优点;为缓解优化目标复杂化所导致的训练不收敛问题,提出了一种与理论辅助驱动相适应的训练策略“过拟合-修正法”,能够稳定并加速收敛过程;基于结构钢材精细弹塑性本构模型开展了数值试验,验证了理论辅助的小样本学习算法的有效性,能够实现大规模深度学习模型在少量训练样本情形下获得优异的泛化性,相较纯粹数据驱动模型准确性提升38.9%。该文采用的理论辅助思想具有可借鉴性,后续可应用于结构层次的深度学习代理模型研究,促进未来更为先进、大型的智能算法落地土木工程计算领域。
  • 图  1  理论辅助的小样本学习算法

    Figure  1.  Theory-aided few-shot learning scheme

    图  2  数值试验采用的深度学习模型

    Figure  2.  The deep learning model adopted in the numerical experiment

    图  3  数据集构成示例

    Figure  3.  Examples of the dataset

    图  4  理论辅助的小样本学习算法模拟结果

    Figure  4.  Simulation results of the theory-aided few-shot learning

    图  5  理论辅助驱动模型与纯粹数据驱动模型模拟结果对比

    Figure  5.  Comparison of the simulation results between the theory-aided model and the pure data-driven model

  • [1] 聂建国, 王宇航. ABAQUS中混凝土本构模型用于模拟结构静力行为的比较研究[J]. 工程力学, 2013, 30(4): 59 − 67, 82. doi: 10.6052/j.issn.1000-4750.2011.07.0420

    NIE Jianguo, WANG Yuhang. Comparison study of constitutive model of concrete in ABAQUS for static analysis of structures [J]. Engineering Mechanics, 2013, 30(4): 59 − 67, 82. (in Chinese) doi: 10.6052/j.issn.1000-4750.2011.07.0420
    [2] 许立言. 低屈服点钢剪切型阻尼器的力学性能及理论模型研究[D]. 北京: 清华大学, 2017.

    XU Liyan. Research on mechanical behavior and theoretical model of low-yield-point steel shear panel dampers [D]. Beijing: Tsinghua University, 2017. (in Chinese)
    [3] 骆晶, 施刚, 毛灵涛, 等. 双相型不锈钢S22053循环本构关系研究[J]. 工程力学, 2021, 38(9): 171 − 181. doi: 10.6052/j.issn.1000-4750.2020.09.0659

    LUO Jing, SHI Gang, MAO Lingtao, et al. Constitutive relation of duplex stainless steel S22053 under cyclic loading [J]. Engineering Mechanics, 2021, 38(9): 171 − 181. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.09.0659
    [4] 班慧勇, 梅镱潇, 石永久. 不锈钢复合钢材钢结构研究进展[J]. 工程力学, 2021, 38(6): 1 − 23. doi: 10.6052/j.issn.1000-4750.2020.04.ST01

    BAN Huiyong, MEI Yixiao, SHI Yongjiu. Research advances of stainless-clad bimetallic steel structures [J]. Engineering Mechanics, 2021, 38(6): 1 − 23. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.04.ST01
    [5] 刘晓刚, 樊健生, 聂建国, 等. 剪切型消能连梁的塑性强化特性研究[J]. 土木工程学报, 2017, 50(3): 1 − 11. doi: 10.15951/j.tmgcxb.2017.03.001

    LIU Xiaogang, FAN Jiansheng, NIE Jianguo, et al. Research on plastic overstrength of energy-dissipation shear links [J]. China Civil Engineering Journal, 2017, 50(3): 1 − 11. (in Chinese) doi: 10.15951/j.tmgcxb.2017.03.001
    [6] 侯帅, 朱有利, 王燕礼, 等. 基于多晶体塑性与唯象学本构模型的纯铝与单晶铝的有限变形分析与对比[J]. 稀有金属材料与工程, 2017, 46(12): 3760 − 3766.

    HOU Shuai, ZHU Youli, WANG Yanli, et al. Analysis and comparison of finite deformation of pure aluminum and single crystal aluminum based on polycrystal plasticity and phenomenological constitutive models [J]. Rare Metal Materials and Engineering, 2017, 46(12): 3760 − 3766. (in Chinese)
    [7] 王元清, 关阳, 刘明, 等. 建筑结构钢材及其焊缝循环微观损伤模型的韧性参数校正分析[J]. 工程力学, 2020, 37(增刊): 20 − 31. doi: 10.6052/j.issn.1000-4750.2019.04.S019

    WANG Yuanqing, GUAN Yang, LIU Ming, et al. Correction analysis of toughness parameters of cyclic microscopic damage model for building structural steel and its welds [J]. Engineering Mechanics, 2020, 37(Suppl): 20 − 31. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.04.S019
    [8] WANG C, XU L, FAN J. Cyclic softening behavior of structural steel with strain range dependence [J]. Journal of Constructional Steel Research, 2021, 181: 106658. doi: 10.1016/j.jcsr.2021.106658
    [9] TANG M, LIU Y, DURLOFSKY L J. A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems [J]. Journal of Computational Physics, 2020, 413: 109456. doi: 10.1016/j.jcp.2020.109456
    [10] WANG C, XU L, FAN J. A general deep learning framework for history-dependent response prediction based on UA-Seq2Seq model [J]. Computer Methods in Applied Mechanics and Engineering, 2020, 372: 113357. doi: 10.1016/j.cma.2020.113357
    [11] HORNIK K, STINCHCOMBE M, WHITE H. Multilayer feedforward networks are universal approximators [J]. Neural Networks, 1989, 2(5): 359 − 366. doi: 10.1016/0893-6080(89)90020-8
    [12] LEFIK M, SCHREFLER B A. Artificial neural network as an incremental non-linear constitutive model for a finite element code [J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(28/29/30): 3265 − 3283. doi: 10.1016/S0045-7825(03)00350-5
    [13] GHAVAMIAN F, SIMONE A. Accelerating multiscale finite element simulations of history-dependent materials using a recurrent neural network [J]. Computer Methods in Applied Mechanics and Engineering, 2019, 357: 112594. doi: 10.1016/j.cma.2019.112594
    [14] 王琛, 樊健生. 具有历史依赖效应的材料及结构响应预测通用深度学习模型MechPerformer[J]. 建筑结构学报, 2022, 43(8): 209 − 219. doi: 10.14006/j.jzjgxb.2021.0115

    WANG Chen, FAN Jiansheng. A general deep learning model MechPerformer for history-dependent response prediction in structural engineering [J]. Journal of Building Structures, 2022, 43(8): 209 − 219. (in Chinese) doi: 10.14006/j.jzjgxb.2021.0115
    [15] MOZAFFAR M, BOSTANABAD R, CHEN W, et al. Deep learning predicts path-dependent plasticity [J]. Proceedings of the National Academy of Sciences, 2019, 116(52): 26414 − 26420. doi: 10.1073/pnas.1911815116
    [16] WANG J J, WANG C, FAN J S, et al. A deep learning framework for constitutive modeling based on temporal convolutional network [J]. Journal of Computational Physics, 2022, 449: 110784. doi: 10.1016/j.jcp.2021.110784
    [17] RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations [J]. Journal of Computational physics, 2019, 378: 686 − 707. doi: 10.1016/j.jcp.2018.10.045
    [18] KARNIADAKIS G E, KEVREKIDIS I G, LU L, et al. Physics-informed machine learning [J]. Nature Reviews Physics, 2021, 3(6): 422 − 440. doi: 10.1038/s42254-021-00314-5
    [19] CAI S, MAO Z, WANG Z, et al. Physics-informed neural networks (PINNs) for fluid mechanics: A review [J]. Acta Mechanica Sinica, 2021, 37(12): 1 − 12. doi: 10.48550/arXiv.2105.09506
    [20] HAGHIGHAT E, JUANES R. Sciann: A keras/tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks [J]. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113552. doi: 10.1016/j.cma.2020.113552
    [21] RAISSI M, YAZDANI A, KARNIADAKIS G E. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations [J]. Science, 2020, 367(6481): 1026 − 1030. doi: 10.1126/science.aaw4741
    [22] SIMO J C, HUGHES T J R. Computational inelasticity [M]. Berlin, Germany: Springer Science & Business Media, 2006.
    [23] WANG C, FAN J, XU L, et al. Cyclic hardening and softening behavior of the low yield point steel: Implementation and validation [J]. Engineering Structures, 2020, 210: 110220. doi: 10.1016/j.engstruct.2020.110220
    [24] BOYD S, BOYD S P, VANDENBERGHE L. Convex optimization [M]. London, UK: Cambridge University Press, 2004.
    [25] WANG Y, YAO Q, KWOK J T, et al. Generalizing from a few examples: A survey on few-shot learning [J]. ACM Computing Surveys (CSUR), 2020, 53(3): 1 − 34.
    [26] CHABOCHE J L. Time-independent constitutive theories for cyclic plasticity [J]. International Journal of Plasticity, 1986, 2(2): 149 − 188. doi: 10.1016/0749-6419(86)90010-0
    [27] CHABOCHE J L. Constitutive equations for cyclic plasticity and cyclic viscoplasticity [J]. International Journal of Plasticity, 1989, 5(3): 247 − 302. doi: 10.1016/0749-6419(89)90015-6
    [28] CHABOCHE J L. On some modifications of kinematic hardening to improve the description of ratchetting effects [J]. International Journal of Plasticity, 1991, 7(7): 661 − 678. doi: 10.1016/0749-6419(91)90050-9
    [29] NAIR V, HINTON G E. Rectified linear units improve restricted Boltzmann machines [C]// The 27th International Conference on Machine Learning (ICML). Haifa Israel, Omnipress, 2010: 807 − 814.
    [30] BOCHKOVSKIY A, WANG C Y, LIAO H Y M. Yolov4: Optimal speed and accuracy of object detection [J]. Computer Vision and Pattern Recognition, 2020, 23: 1 − 17. doi: 10.48550/arXiv.2004.10934
    [31] XU L, NIE X, FAN J, et al. Cyclic hardening and softening behavior of the low yield point steel BLY160: Experimental response and constitutive modeling [J]. International Journal of Plasticity, 2016, 78: 44 − 63. doi: 10.1016/j.ijplas.2015.10.009
    [32] CHO K, VAN MERRIËNBOER B, GULCEHRE C, et al. Learning phrase representations using RNN encoder-decoder for statistical machine translation [C]// Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP). Doha Qatar, Association for Computational Linguistics, 2014: 1724 − 1734.
    [33] SUTSKEVER I, VINYALS O, LE Q V. Sequence to sequence learning with neural networks [C]// Twenty-eighth Conference on Neural Information Processing Systems (NIPS). Montréal Canada, MIT Press, 2014: 3104 − 3112.
    [34] KINGMA D P, BA J. Adam: A method for stochastic optimization [C]// The 3rd International Conference for Learning Representations (ICLR). San Diego US, OpenReview.net, 2015.
    [35] PASZKE A, GROSS S, MASSA F, et al. Pytorch: An imperative style, high-performance deep learning library [C]// Thirty-third Conference on Neural Information Processing Systems (NIPS). Vancouver Canada, MIT Press, 2019: 8026 − 8037.
  • 加载中
图(5)
计量
  • 文章访问数:  418
  • HTML全文浏览量:  97
  • PDF下载量:  130
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-12-27
  • 修回日期:  2022-06-09
  • 录用日期:  2022-06-24
  • 网络出版日期:  2022-06-24
  • 刊出日期:  2023-09-06

目录

    /

    返回文章
    返回