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无网格动力分析的循环卷积神经网络代理模型

陈健 王东东 刘宇翔 陈俊

陈健, 王东东, 刘宇翔, 陈俊. 无网格动力分析的循环卷积神经网络代理模型. 力学学报, 2022, 54(3): 732-745 doi: 10.6052/0459-1879-21-565
引用本文: 陈健, 王东东, 刘宇翔, 陈俊. 无网格动力分析的循环卷积神经网络代理模型. 力学学报, 2022, 54(3): 732-745 doi: 10.6052/0459-1879-21-565
Chen Jian, Wang Dongdong, Liu Yuxiang, Chen Jun. A recurrent convolutional neural network surrogate model for dynamic meshfree analysis. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 732-745 doi: 10.6052/0459-1879-21-565
Citation: Chen Jian, Wang Dongdong, Liu Yuxiang, Chen Jun. A recurrent convolutional neural network surrogate model for dynamic meshfree analysis. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 732-745 doi: 10.6052/0459-1879-21-565

无网格动力分析的循环卷积神经网络代理模型

doi: 10.6052/0459-1879-21-565
基金项目: 国家自然科学基金(12072302, 11772280)和福建省自然科学基金(2021J02003)资助项目
详细信息
    作者简介:

    王东东, 教授, 主要研究方向: 计算力学与结构工程. E-mail: ddwang@xmu.edu.cn

  • 中图分类号: O242.2

A RECURRENT CONVOLUTIONAL NEURAL NETWORK SURROGATE MODEL FOR DYNAMIC MESHFREE ANALYSIS

  • 摘要: 在无网格动力分析中, 除了无网格形函数本身构造复杂引入的计算成本, 还需要逐步递推求解每个时间步的动力响应, 因而计算效率较为低下. 本文通过研究无网格离散数据与机器学习训练样本、无网格动力分析递推计算过程与循环卷积神经网络序列信息传递模式之间的本征联系, 构建了与无网格法相匹配的循环卷积神经网络设计方法, 进而提出了一种无网格动力分析的循环卷积神经网络代理模型. 该模型充分融合了无网格离散模型节点布置灵活的优点, 同时无网格法能够提供具有泛化特征的高精度数值样本, 增强循环卷积神经网络的泛化性和适用性. 此外, 循环卷积神经网络代理模型特有的循环模块历史记忆特性使其可以有效地处理序列信息, 在保证精度的前提下加速无网格动力分析计算过程. 文中通过系列算例验证了所提出的无网格动力分析的循环卷积神经网络代理模型的精度和效率.

     

  • 图  1  全卷积神经网络中的卷积与转置卷积操作

    Figure  1.  Convolution and transpose convolution operations in full convolution neural networks

    图  2  LSTM循环神经网络结构框架与循环模块

    Figure  2.  Schematic illustartion of LSTM and recurrent module

    图  3  数值计算产生数据与机器学习训练样本之间的对应关系

    Figure  3.  Schemetic illustration of the corresponding relationship between the data generated by numerical simulations and the machine learning training samples

    图  4  无网格动力分析与长短期记忆神经网络之间的本征联系

    Figure  4.  Intrinsic relationships between dynamic meshfree analysis and long short-term memory neural network

    图  5  无网格动力分析的循环卷积神经网络代理模型框架

    Figure  5.  The structure of recurrent convolution neural network surrogate model for dynamic meshfree analysis

    图  6  无网格动力分析训练集包含的计算模型与离散模型

    Figure  6.  Computational models and discretizations for the training set of dynamic meshfree analysis

    图  7  无网格动力分析的循环卷积神经网络代理模型具体数据传递过程

    Figure  7.  Detailed data transfer process of the recurrent convolution neural network surrogate model for dynamic meshfree analysis

    图  8  无网格动力分析的循环卷积神经网络代理模型训练历史

    Figure  8.  Training history of the recurrent convolution neural network surrogate model for dynamic meshfree analysis

    9  方形区域弹性力学问题代理模型预测解与无网格数值解对比

    9.  Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the square region

    图  9  方形区域弹性力学问题代理模型预测解与无网格数值解对比(续)

    Figure  9.  Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the square region (continued)

    图  10  L形区域弹性力学问题代理模型预测解与无网格数值解对比

    Figure  10.  Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the L-shape region

    图  11  圆形区域弹性力学问题代理模型预测解与无网格数值解对比

    Figure  11.  Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the circular region

    图  12  四分之一环形区域弹性力学问题代理模型预测解与无网格数值解对比

    Figure  12.  Comparison between the predicted solution of the recurrent convolution neural network surrogate model and the meshless numerical solution of the elasticity problem in the quarter annular region

    表  1  弹性问题下无网格法动力分析与循环卷积神经网络代理模型训练预测时间对比

    Table  1.   Comparison of the training and prediction cost between dynamic meshfree analysis and recurrent convolution neural network surrogate model for elastic problems

    ItemsMeshfree simulation/minMeshfree surrogate model/min
    off-line generation of 9600 sets data7520.25
    off-line training605.30
    on-line simulation of 400 sets data313.340.25
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-11-01
  • 录用日期:  2021-12-29
  • 网络出版日期:  2021-12-30
  • 刊出日期:  2022-03-18

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