Volume 44 Issue 7
Jul.  2023
Turn off MathJax
Article Contents
WANG Qingshan, YAN Bo, CHEN Yan, DENG Mao, CAI Yuanbin. Digital Twin Method for Dynamic Structures Based on Reduced Order Models and Data Driving[J]. Applied Mathematics and Mechanics, 2023, 44(7): 757-768. doi: 10.21656/1000-0887.430384
Citation: WANG Qingshan, YAN Bo, CHEN Yan, DENG Mao, CAI Yuanbin. Digital Twin Method for Dynamic Structures Based on Reduced Order Models and Data Driving[J]. Applied Mathematics and Mechanics, 2023, 44(7): 757-768. doi: 10.21656/1000-0887.430384

Digital Twin Method for Dynamic Structures Based on Reduced Order Models and Data Driving

doi: 10.21656/1000-0887.430384
  • Received Date: 2022-11-29
  • Rev Recd Date: 2022-12-09
  • Publish Date: 2023-07-01
  • A digital twin construction method based on the reduced order model library and machine learning was proposed for structures under dynamic loads. Firstly, the high-fidelity finite element models were established according to the possible damage states occurring during the service of the physical structures. Secondly, the Krylov subspace order reduction method was used to reduce the orders of the models and the reduced order models were assembled to a library. Finally, the random forest machine learning algorithm was used to train the model selector, infer the current state of the physical structure through the sensor data from the structure, and then drive the digital twin to evolve with the physical structure. A physical frame structure was designed and manufactured to simulate the damages of different degrees at different points, and verify the proposed digital twin construction method for dynamic structures.
  • (Contributed by YAN Bo, M.AMM Editorial Board)
  • loading
  • [1]
    GRIEVES M, VICKERS J. Digital twin: mitigating unpredictable, undesirable emergent behavior in complex systems[M]//Transdisciplinary Perspectives on Complex Systems. Springer, 2017: 85-113.
    [2]
    TAO F, XIAO B, QI Q, et al. Digital twin modeling[J]. Journal of Manufacturing Systems, 2022, 64: 372-389. doi: 10.1016/j.jmsy.2022.06.015
    [3]
    董雷霆, 周轩, 赵福斌, 等. 飞机结构数字孪生关键建模仿真技术[J]. 航空学报, 2021, 42(3): 113-141. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202103012.htm

    DONG Leiting, ZHOU Xuan, ZHAO Fubin, et al. Key modeling and simulation technology of aircraft structure digital twin[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(3): 113-141. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB202103012.htm
    [4]
    HAAG S, ANDERL R. Digital twin-proof of concept[J]. Manufacturing Letters, 2018, 15(B): 64-66.
    [5]
    MOI T, CIBICIK A, RØLVÅG T. Digital twin based condition monitoring of a knuckle boom crane: an experimental study[J]. Engineering Failure Analysis, 2020, 112(3): 104517.
    [6]
    WANG S, LAI X, HE X, et al. Building a trustworthy product-level shape-performance integrated digital twin with multifidelity surrogate model[J]. Journal of Mechanical Design, 2022, 144(3): 031703-0317114. doi: 10.1115/1.4052390
    [7]
    LAI X, HE X, WANG S, et al. Building a lightweight digital twin of a crane boom for structural safety monitoring based on a multifidelity surrogate model[J]. Journal of Mechanical Design, 2022, 144(6): 064502. doi: 10.1115/1.4053606
    [8]
    KAPTEYN M G, KNEZEVIC D J, HUYNH D, et al. Data-driven physics-based digital twins via a library of component-based reduced-order models[J]. International Journal for Numerical Methods in Engineering, 2022, 123(13): 2986-3003. doi: 10.1002/nme.6423
    [9]
    KAPTEYN M G, KNEZEVIC D J, WILLCOX K. Toward predictive digital twins via component-based reduced-order models and interpretable machine learning[C]//Proceedings of the AIAA Scitech 2020 Forum. Orlando, 2020.
    [10]
    MILANOSKI D P, GALANOPOULOS G K, LOUTAS T H. Digital-twins of composite aerostructures towards structural health monitoring[C]// 2021 IEEE 8th International Workshop on Metrology for AeroSpace (MetroAeroSpace). Naples, Italy, 2021.
    [11]
    WANG J, YE L, GAO R X, et al. Digital twin for rotating machinery fault diagnosis in smart manufacturing[J]. International Journal of Production Research, 2019, 57(12): 3920-3934. doi: 10.1080/00207543.2018.1552032
    [12]
    GANGULI R, ADHIKARI S. The digital twin of discrete dynamic systems: initial approaches and future challenges[J]. Applied Mathematical Modelling, 2020, 77(2): 1110-1128.
    [13]
    CHAKRABORTY S, ADHIKARI S. Machine learning based digital twin for dynamical systems with multiple time-scales[J]. Computers & Structures, 2021, 243: 106410.
    [14]
    赖学方, 王晓龙, 聂玉峰. 基于Mori-Zwanzig格式和偏最小二乘的非线性模型降阶[J]. 应用数学和力学, 2021, 42(6): 551-561. doi: 10.21656/1000-0887.410230

    LAI Xuefang, WANG Xiaolong, NIE Yufeng. Nonlinear model reduction based on Mori-Zwanzig scheme and partial least squares[J]. Applied Mathematics and Mechanics, 2021, 42(6): 551-561. (in Chinese) doi: 10.21656/1000-0887.410230
    [15]
    罗振东, 张博. Sobolev方程基于POD的降阶外推差分算法[J]. 应用数学和力学, 2016, 37(1): 107-116. doi: 10.3879/j.issn.1000-0887.2016.01.009

    LUO Zhendong, ZHANG Bo. Reduced order extrapolation difference algorithm based on pod for Sobolev equation[J]. Applied Mathematics and Mechanics, 2016, 37(1): 107-116. (in Chinese) doi: 10.3879/j.issn.1000-0887.2016.01.009
    [16]
    PATERA A T, ROZZA G. Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Partial Differential Equations[M]. Massachusetts Institute of Technology, 2007.
    [17]
    QUARTERONI A, MANZONI A, NEGRI F. Reduced Basis Methods for Partial Differential Equations: an Introduction[M]. Springer, 2015.
    [18]
    VALLAGHÉ S, HUYNH P, KNEZEVIC D J, et al. Component-based reduced basis for parametrized symmetric eigenproblems[J]. Advanced Modeling and Simulation in Engineering Sciences, 2015, 2(1): 1-30. doi: 10.1186/s40323-014-0017-1
    [19]
    张珺, 李立州, 原梅妮. 径向基函数参数化翼型的气动力降阶模型优化[J]. 应用数学和力学, 2019, 40(3): 250-258. doi: 10.21656/1000-0887.390187

    ZHANG Jun, LI Lizhou, YUAN Meini. Aerodynamic model optimization for radial basis function parameterized airfoils[J]. Applied Mathematics and Mechanics, 2019, 40(3): 250-258. (in Chinese) doi: 10.21656/1000-0887.390187
    [20]
    GUGERCIN S, ANTOULAS A C. A survey of model reduction by balanced truncation and some new results[J]. International Journal of Control, 2004, 77(8): 748-766. doi: 10.1080/00207170410001713448
    [21]
    KVRSCHNER P. Balanced truncation model order reduction in limited time intervals for large systems[J]. Advances in Computational Mathematics, 2018, 44(6): 1821-1844. doi: 10.1007/s10444-018-9608-6
    [22]
    GUYAN R J. Reduction of stiffness and mass matrices[J]. AIAA Journal, 1965, 3(2): 380. doi: 10.2514/3.2874
    [23]
    BAI Z. Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems[J]. Applied Numerical Mathematics, 2002, 43(1/2): 9-44.
    [24]
    BEATTIE C, GUGERCIN S. Model reduction by rational interpolation[M]//Model Reduction and Approximation. Society for Industrial and Applied Mathematics, 2017: 297-334.
    [25]
    SALIMBAHRAMI B, LOHMANN B. Order reduction of large scale second-order systems using Krylov subspace methods[J]. Linear Algebra and Its Applications, 2006, 415(2/3): 385-405.
    [26]
    ARNOLDI W E. The principle of minimized iterations in the solution of the matrix eigenvalue problem[J]. Quarterly of Applied Mathematics, 1951, 9(1): 17-29.
    [27]
    BREIMAN L. Random forests[J]. Machine Learning, 2001, 45(1): 5-32.
    [28]
    严波. 有限单元法基础[M]. 北京: 高等教育出版社, 2022: 396-397.

    YAN Bo. Foundation of Finite Element Method[M]. Beijing: Higher Education Press, 2022: 396-397. (in Chinese)
    [29]
    ADHIKARI S, BHATTACHARYA S. Dynamic analysis of wind turbine towers on flexible foundations[J]. Shock and Vibration, 2012, 19(1): 37-56.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(9)

    Article Metrics

    Article views (963) PDF downloads(245) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return