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.Abstract: In addition to the complexity of meshfree approximation that needs extra computational effort, the dynamic meshfree analysis requires the computation of dynamic response recursively at each time step, which significantly lowers the overall computational efficiency. In this work, the intrinsic relationships are established between meshfree discrete data and machine learning training samples, and recursive computational procedure of dynamic meshfree analysis and temporal sequence information transmission mode of recurrent convolution neural networks. With the aid of these intrinsic links, a recurrent convolutional neural network structure design method for meshfree discretization is proposed, which is then used to develop a recurrent convolution neural network surrogate model for dynamic meshfree analysis. This surrogate model takes full advantage of the flexibility of meshfree discretization. Meanwhile, meshfree analysis can provide versatile and highly accurate numerical samples, which then enhance the generality and applicability of the proposed surrogate model for dynamic meshfree analysis. Besides, the unique historical memory characteristics of the recurrent module embedded in the recurrent convolution neural network surrogate model enable an effective processing of the sequence information, and then accelerate the dynamic meshfree computational procedure with accuracy guarantee. The efficiency and accuracy of the recurrent convolution neural network surrogate model for dynamic meshfree analysis are validated through representative examples.
-
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 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
Items Meshfree simulation/min Meshfree surrogate model/min off-line generation of 9600 sets data — 7520.25 off-line training — 605.30 on-line simulation of 400 sets data 313.34 0.25 
下载: 导出CSV
-
[1] Belytschko T, Kronggauz Y, Organ D, et al. Meshless methods: an overview and recent developments. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 3-47 doi: 10.1016/S0045-7825(96)01078-X [2] Liu WK, Jun S, Zhang YF. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids, 1995: 1081-1106 [3] Chen JS, Pan C, Wu CT, et al. Reproducing kernel particle methods for large deformation analysis of non-linear structures. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1-4): 195-227 doi: 10.1016/S0045-7825(96)01083-3 [4] 张雄, 刘岩, 马上. 无网格法的理论及应用. 力学进展, 2009, 39(1): 1-36 (Zhang Xiong, Liu Yan, Ma Shang. Meshfree methods and their applications. Advances in Mechanics, 2009, 39(1): 1-36 (in Chinese) doi: 10.3321/j.issn:1000-0992.2009.01.001 [5] 吴俊超, 邓俊俊, 王家睿等. 伽辽金型无网格法的数值积分方法. 固体力学学报, 2016, 37(3): 208-233 (Wu Junchao, Deng Junjun, Wang Jiarui, et al. A review of numerical integration approaches for Galerkin meshfree methods. Chinese Journal of Solid Mechanics, 2016, 37(3): 208-233 (in Chinese) [6] Chen JS, Hillman M, Chi SW. Meshfree methods: progress made after 20 years. Journal of Engineering Mechanics-ASCE, 2017, 143(4): 04017001 doi: 10.1061/(ASCE)EM.1943-7889.0001176 [7] 高效伟, 徐兵兵, 吕军等. 自由单元法及其在结构分析中的应用. 力学学报, 2019, 51(3): 703-713 (Gao Xiaowei, Xu Bingbing, Lü Jun, et al. Free element method and its application in structural analysis. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 703-713 (in Chinese) doi: 10.6052/0459-1879-19-011 [8] 王莉华, 李溢铭, 褚福运. 基于分区径向基函数配点法的大变形分析. 力学学报, 2019, 51(3): 743-753 (Wang Lihua, Li Yiming, Zhu Fuyun. Finite subdomain radial basis collocation method for the large deformation analysis. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 743-753 (in Chinese) [9] Wu J, Wang D, Lin Z, et al. An efficient gradient smoothing meshfree formulation for the fourth-order phase field modeling of brittle fracture. Computational Particle Mechanics, 2020, 7(2): 193-207 doi: 10.1007/s40571-019-00240-5 [10] Wang D, Wu J. An inherently consistent reproducing kernel gradient smoothing framework toward efficient Galerkin meshfree formulation with explicit quadrature, Computer Methods in Applied Mechanics and Engineering, 2019. 349: 628-672 [11] Wu J, Wang D. An accuracy analysis of Galerkin meshfree methods accounting for numerical integration. Computer Methods in Applied Mechanics and Engineering, 2021, 375: 113631 [12] Kirchdoerfer T, Ortiz M. Data-driven computational mechanics. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 81-101 doi: 10.1016/j.cma.2016.02.001 [13] 王东东, 章靑, 柳占立. 人工智能计算力学专辑序言. 固体力学学报, 2021, 42(3): 封2Wang Dongdong, Zhang Qing, Liu Zhanli. Preface for the special issue artificial intelligence-based computational mechanics. Chinese Journal of Solid Mechanics, 2021, 42(3): cover 2 (in Chinese)). [14] Oishi A, Yagawa G. Computational mechanics enhanced by deep learning. Computer Methods in Applied Mechanics and Engineering, 2017, 327: 327-351 doi: 10.1016/j.cma.2017.08.040 [15] 李想, 严子铭, 柳占立. 机器学习与计算力学的结合及应用初探. 科学通报, 2019, 64(7): 635-648 (Li Xiang, Yan Ziming, Liu Zhanli. Combination and application of machine learning and computational mechanics. Chinese Science Bulletin, 2019, 64(7): 635-648 (in Chinese) doi: 10.1360/N972019-00005 [16] Tang S, Zhang G, Yang H, et al. MAP123: a data-driven approach to use id data for 3 d nonlinear elastic materials modeling. Computer Methods in Applied Mechanics and Engineering, 2019, 357: 112587 doi: 10.1016/j.cma.2019.112587 [17] Feng S, Xu Y, Han X, et al. A phase field and deep-learning based approach for accurate prediction of structural residual useful life. Computer Methods in Applied Mechanics and Engineering, 2021, 383: 113885 doi: 10.1016/j.cma.2021.113885 [18] 严子铭, 王涛, 柳占立等. 基于机器学习的页岩气采收率预测方法. 固体力学学报, 2021, 42(3): 221-232 (Yan Ziming, Wang Tao, Liu Zhanli, et al. Machine-learning-based prediction methods on shale gas recovery. Chinese Journal of Solid Mechanics, 2021, 42(3): 221-232 (in Chinese) [19] 阳杰, 白晓伟, 颜巍等. 基于分层数据搜索的数据驱动算法研究. 固体力学学报, 2021, 42(3): 241-248 (Yang Jie, Bai Xiaowei, Yan Wei, et al. An efficient hierarchical data searching scheme for data-driven computational mechanics. Chinese Journal of Solid Mechanics, 2021, 42(3): 241-248 (in Chinese) [20] 黄钟民, 谢臻, 张易申等. 面内变刚度薄板弯曲问题的挠度-弯矩耦合神经网络方法. 力学学报, 2021, 53(9): 2541-2553 (Huang Zhongmin, Xie Zhen, Zhang Yishen, et al. Deflection-bending moment coupling neural network method for the bending problem of thin plates with in-plane stiffness gradient. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2541-2553 (in Chinese) doi: 10.6052/0459-1879-21-273 [21] Wang Z, Zhang Z. A mesh-free method for interface problems using the deep learning approach. Journal of Computational Physics, 2020, 400: 108963 doi: 10.1016/j.jcp.2019.108963 [22] Brink AR, Najera-Flores DA, Martinez C. The neural network collocation method for solving partial differential equations. Neural Computing and Applications, 2020, 33(11): 5591-5608 [23] 刘宇翔, 王东东, 樊礼恒等. 基于卷积神经网络的无网格形函数影响域优化研究. 固体力学学报, 2021, 42(3): 302-319 (Liu Yuxiang, Wang Dongdong, Fan Liheng, et al. CNN-based optimized support selection for meshfree methods. Chinese Journal of Solid Mechanics, 2021, 42(3): 302-319 (in Chinese) [24] Hochreiter S, Schmidhuber J. Long short-term memory. Neural Computation, 1997, 9(8): 1735-1780 doi: 10.1162/neco.1997.9.8.1735 [25] Sherstinsky A. Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network. Physica D:Nonlinear Phenomena, 2020, 404: 132306 doi: 10.1016/j.physd.2019.132306 [26] Liu G, Guo JB. Bidirectional LSTM with attention mechanism and convolutional layer for text classification. Neurocomputing, 2019, 337: 325-338 doi: 10.1016/j.neucom.2019.01.078 [27] Bin Y, Yang Y, Shen F, et al. Describing video with attention-based bidirectional LSTM. IEEE Transactions on Cybernetics, 2019, 49(7): 2631-2641 doi: 10.1109/TCYB.2018.2831447 [28] Shi XJ, Chen ZR, Wang H, et al. Convolutional LSTM network: a machine learning approach for precipitation nowcasting. Advances in Neural Information Processing Systems, 2015, 28: 802-810 [29] Moishin M, Deo RC, Prasad R, et al. Designing deep-based learning flood forecast model with ConvLSTM hybrid algorithm. IEEE Access, 2021, 9: 50982-50993 doi: 10.1109/ACCESS.2021.3065939 [30] Fernández-Méndez S, Huerta A. Imposing essential boundary conditions in mesh-free methods. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12-14): 1257-1275 doi: 10.1016/j.cma.2003.12.019 [31] Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications, 2000 [32] Maas AL, Hannun AY, Ng AY. Rectifier nonlinearities improve neural network acoustic models//Proceedings of the International Conference on Machine Learning, Atlanta, GA, 2013: 1-6 -
下载:
点击查看大图
计量
- 文章访问数: 434
- HTML全文浏览量: 85
- PDF下载量: 125
- 被引次数: 0
