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基于机器学习的磁流变弹性体磁致储能模量的快速准确表征

任航 赵丹 董立强 刘少刚 杨金水

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基于机器学习的磁流变弹性体磁致储能模量的快速准确表征

任航, 赵丹, 董立强, 刘少刚, 杨金水

Fast and accurate characterization of magnetorheological elastomers based on machine learning

Ren Hang, Zhao Dan, Dong Li-Qiang, Liu Shao-Gang, Yang Jin-Shui
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  • 磁流变弹性体在振动控制领域展现出巨大的潜力, 但其磁致力学性能的测量过程往往需投入较高的人工与时间成本. 本研究旨在利用机器学习方法在小样本试验数据驱动下实现磁流变弹性体磁致力学性能的快速准确预测. 基于加装可控磁场的剪切流变仪测试了磁流变弹性体 (9种配比, 4种加载频率)的磁致储能模量. 每种样品取5个测试点作为训练集并搭建支持向量回归机器学习模型, 从而表征磁流变弹性体的磁致储能模量. 结果表明, 相较于典型的理论模型, SVR模型仅使用5个样本点即可更准确表征磁流变弹性体磁致储能模量, 相关系数高达0.998. 另外, SVR模型训练时间仅为0.02 s, 可显著加速磁流变弹性体表征的进程. 更重要的是, SVR模型具有良好的泛化性, 对于不同硅油配比和不同加载频率的磁流变弹性体预测结果的相关系数仍可达 0.998 以上. 因此, 机器学习模型可实现磁流变弹性体磁致储能模量的快速准确表征, 为新型磁流变材料的研发提供参考.
    Magnetorheological elastomers (MREs) are smart materials with a wide range of applications, particularly in reducing vibrations and noise. Traditional methods of testing their magnetically-induced properties, although thorough, are labor-intensive and time-consuming. In this work, we introduce an innovative method that harnesses machine learning to rapidly characterize MREs by using a smallest dataset, thus simplifying the characterization process. Initially, 12 types of MREs are prepared and tested on a shear rheometer with a controllable magnetic field. From these data, we strategically select five representative data points from each sample to form a training dataset. Using this dataset, we develop a support vector regression (SVR) model to characterize the magnetically-induced storage modulus of the MRE. The SVR model exhibits remarkable accuracy, with a correlation coefficient (R2) of 0.998 or higher, exceeding the precision of traditional models. The training time of this model is very brief, only 0.02 seconds, thus greatly accelerating the characterization speed of MRE. Moreover, the SVR model demonstrates strong generalization ability, maintaining a high correlation coefficient of 0.998 or greater even when silicone oil is added to the MREs or tested under various loading frequencies. In a word, the machine learning model not only accelerates the evaluation process but also provides a valuable reference for developing innovative MREs, marking a significant advancement in the field of smart materials research.
      通信作者: 董立强, dongliqiang@hrbeu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 52275098, 52075111, 51675111)资助的课题.
      Corresponding author: Dong Li-Qiang, dongliqiang@hrbeu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52275098, 52075111, 51675111).
    [1]

    Vatandoost H, Hemmatian M, Sedaghati R, Rakheja S 2020 Compos. Part B Eng. 182 107648Google Scholar

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    Nam T H, Petríková I, Marvalová B 2020 Polym. Test. 81 106272Google Scholar

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    Kukla M, Warguła Ł, Talaśka K, Wojtkowiak D 2020 Materials 13 4795Google Scholar

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    Agirre-Olabide I, Elejabarrieta M J 2018 Polym. Test. 66 114Google Scholar

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    Zainudin A A, Yunus N A, Mazlan S A, Shabdin M K, Abdul Aziz S A, Nordin N A, Nazmi N, Abdul Rahman M A 2020 Appl. Sci. 10 1638Google Scholar

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    Jaafar M F, Mustapha F, Mustapha M 2021 J. Mater. Res. Technol. 15 5010Google Scholar

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    Leng D X, Zhu Z H, Liu G J, Li Y C 2022 Ocean Eng. 253 111293Google Scholar

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    Jin T H, Liu Z M, Sun S S, Ren Z S, Deng L, Yang B, Christie M D, Li W H 2020 Mech. Syst. Signal Process. 135 106338Google Scholar

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    Wang Q, Chen Z X, Wang Y H, Gong N, Yang J, Li W H, Sun S S 2024 Mech. Syst. Signal Process. 208 111029Google Scholar

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    Hu H S, Wang J, Qian S X, Li Y C, Shen N, Yan G B 2011 Chin. J. Mech. Eng. 47 84

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    文永蓬, 孙倩, 周伟浩, 尚慧琳, 郭林生 2018 机械工程学报 54 114

    Wen Y P, Sun Q, Zhou W H, Shang H L, Guo L S 2018 Chin. J. Mech. Eng. 54 114

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    Ivaneyko D, Toshchevikov V, Saphiannikova M, Heinrich G 2011 Macromol. Theory Simul. 20 411Google Scholar

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    Ivaneyko D, Toshchevikov V, Borin D, Saphiannikova M, Heinrich G 2014 Macromol. Symp. 338 96Google Scholar

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    Li W H, Zhou Y, Tian T F 2010 Rheol. Acta 49 733Google Scholar

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    Gu Z R, Luo Y P, Su Z B, Zhang L Y, Ren H J, Wang Y, Luo J 2023 J. Magn. Magn. Mater. 580 170795Google Scholar

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    Feng Y Y, Yang X J, Liu J G, Chen Z Q 2023 Phys. Stat. Mech. Its Appl. 621 128789Google Scholar

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    Chen L, Gong X L, Li W H 2008 Polym. Test. 27 340Google Scholar

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    Li Y C, Li J C, Li W H, Samali B 2013 Smart Mater. Struct. 22 035005Google Scholar

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    Ahmad Khairi M H, Abd Fatah A Y, Mazlan S A, Ubaidillah U, Nordin N A, Nik Ismail N I, Choi S B, Abdul Aziz S A 2019 Int. J. Mol. Sci. 20 4085Google Scholar

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    Gowda D K, Odenbach S 2023 J. Magn. Magn. Mater. 579 170856Google Scholar

    [25]

    刘浩, 须颖, 罗杨泉, 肖海善 2022 机械工程学报 58 328Google Scholar

    Liu H, Xu Y, Luo Y Q, Xiao S H 2022 Chin. J. Mech. Eng. 58 328Google Scholar

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    孙涛, 袁健美 2023 物理学报 72 218901Google Scholar

    Sun T, Yuan J M 2023 Acta Phys. Sin. 72 218901Google Scholar

    [27]

    寇雯博, 董灏, 邹岷强, 韩均言, 贾西西 2021 物理学报 70 030701Google Scholar

    Kou W B, Dong H, Zou M Q, Han J Y, Jia X X 2021 Acta Phys. Sin. 70 030701Google Scholar

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    Goodall R E A, Lee A A 2020 Nat. Commun. 11 6280Google Scholar

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    Goodall R E A, Parackal A S, Faber F A, Armiento R, Lee A A 2022 Sci. Adv. 8 eabn4117Google Scholar

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    Bessa M A, Bostanabad R, Liu Z, Hu A, Apley D W, Brinson C, Chen W, Liu W K 2017 Comput. Methods Appl. Mech. Eng. 320 633Google Scholar

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    Clément A, Soize C, Yvonnet J 2012 Int. J. Numer. Methods Eng. 91 799Google Scholar

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    Le B A, Yvonnet J, He Q C 2015 Int. J. Numer. Methods Eng. 104 1061Google Scholar

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    Shen L, Qian Q 2022 Comput. Mater. Sci. 211 111475Google Scholar

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    Jung J, Kim Y, Park J, Ryu S 2022 Compos. Struct. 285 115210Google Scholar

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    Huang D Z, Xu K, Farhat C, Darve E 2020 J. Comput. Phys. 416 109491Google Scholar

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    Li X, Liu Z, Cui S, Luo C, Li C, Zhuang Z 2019 Comput. Methods Appl. Mech. Eng. 347 735Google Scholar

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    Liu X, Yan Z, Zhong Z 2021 Int. J. Hydrog. Energy 46 22079Google Scholar

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    El Said B 2023 Int. J. Solids Struct. 276 112334Google Scholar

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    Li Z Q, Li X, Chen Y, Zhang C 2023 Compos. Struct. 323 117473Google Scholar

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    Nguyen X B, Komatsuzaki T, Iwata Y, Asanuma H 2018 Mech. Syst. Signal Process. 101 449Google Scholar

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    Wang L Z, Chen Z B, Jiang L K, Cheng L 2023 J. Magn. Magn. Mater. 570 170441Google Scholar

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    Kumbhar S B, Chavan S P, Gawade S S 2018 Mech. Syst. Signal Process. 100 208Google Scholar

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    Nguyen X B, Komatsuzaki T, Zhang N 2020 Mech. Syst. Signal Process. 141 106438Google Scholar

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  • 图 1  MRE制备流程

    Fig. 1.  Preparation process of MRE.

    图 2  MRE的磁致储能模量测试

    Fig. 2.  Magnetic storage modulus test of MRE.

    图 3  不同MRE样品的测试结果 (a)不同铁颗粒含量; (b) 不同硅油含量; (c) 不同加载频率

    Fig. 3.  Test results of different MRE samples: (a) Different iron particle content; (b) different silicon oil content; (c) different loading frequencies.

    图 4  典型的MRE力学模型 (a) 微观磁偶极子模型; (b) 宏观黏弹性模型

    Fig. 4.  Typical mechanical model of MRE: (a) Microscopic magnetic dipole model; (b) macroscopic viscoelastic model.

    图 5  SVR 模型机制

    Fig. 5.  Mechanism of SVR model.

    图 6  训练集采样过程

    Fig. 6.  Sampling process of training set.

    图 7  不同模型对MRE磁致储能模量的表征 (a) 磁偶极子模型与黏弹性模型; (b) SVR模型与对数模型

    Fig. 7.  Characterization of MRE magnetic induced storage modulus by different models: (a) Magnetic dipole model and viscoelastic model; (b) SVR model and logarithmic model.

    图 8  不同模型对不同样品预测的RMSE

    Fig. 8.  RMSE predicted by different models for different samples.

    图 9  不同模型对不同样品R2的对比 (a)不同铁颗粒含量; (b)不同硅油含量以及不同加载频率

    Fig. 9.  Comparison of different models on R2 of different samples: (a) Different iron particle contents; (b) different silicon oil contents and loading frequencies.

    图 10  SVR模型对不同MRE样品的预测结果 (a)不同铁颗粒含量; (b) 不同硅油含量; (c) 不同加载频率

    Fig. 10.  Prediction results of SVR model for different MRE samples: (a) Different iron particle content; (b) different silicone oil content; (c) different loading frequencies.

    表 1  MER样品配比及测试工况

    Table 1.  Ratio and testing conditions of MRE.

    S1S2S3S4S5S6S7S8S9S10S11S12
    铁磁颗粒/%121518212427272727272727
    硅油/%55555501015555
    加载频率/Hz757575757575757575306090
    下载: 导出CSV

    表 2  不同模型对S6样品的预测结果

    Table 2.  Prediction results of different models on S6 sample.

    训练样本数量451020
    train R20.9990.9990.9990.999
    test R20.8780.9980.9980.998
    RSME0.1120.01250.01330.0111
    下载: 导出CSV

    表 3  基于SVR模型预测不同MRE样品的RMSE与R2

    Table 3.  Prediction of RMSE and R2 for different MRE samples based on SVR model.

    样品RMSER2
    S133780.999
    S250060.999
    S342460.999
    S466710.998
    S585790.999
    S686690.998
    S722750.999
    S865470.999
    S936300.999
    S10171220.998
    S11126420.998
    S12104090.998
    下载: 导出CSV

    表 4  不同模型对S6样品的预测结果

    Table 4.  Prediction results of different models on S6 samples.

    模型 磁场范围/mT R2
    磁偶极子模型 0—1000 0.836
    动态黏弹性模型 0—326 0.93
    四参数分数阶导数黏弹性模型 0—150 0.97
    动态磁力学模型 90—178 0.99
    三参数本构模型(Maxwell形式) 125—540 0.958
    渗透模型 0—375 0.9
    Ramberg-Osgood模型 0—500 0.9
    修正Kelvin–Voigt黏弹模型 0—272 0.93
    自适应光滑库仑摩擦模型 0.92
    修正Bouc-Wen模型 0—545 0.9
    非线性流变模型 0—330 0.98
    SVR模型 0—1000 0.998
    下载: 导出CSV
  • [1]

    Vatandoost H, Hemmatian M, Sedaghati R, Rakheja S 2020 Compos. Part B Eng. 182 107648Google Scholar

    [2]

    Nam T H, Petríková I, Marvalová B 2020 Polym. Test. 81 106272Google Scholar

    [3]

    Kukla M, Warguła Ł, Talaśka K, Wojtkowiak D 2020 Materials 13 4795Google Scholar

    [4]

    Agirre-Olabide I, Elejabarrieta M J 2018 Polym. Test. 66 114Google Scholar

    [5]

    Zainudin A A, Yunus N A, Mazlan S A, Shabdin M K, Abdul Aziz S A, Nordin N A, Nazmi N, Abdul Rahman M A 2020 Appl. Sci. 10 1638Google Scholar

    [6]

    Jaafar M F, Mustapha F, Mustapha M 2021 J. Mater. Res. Technol. 15 5010Google Scholar

    [7]

    Leng D X, Zhu Z H, Liu G J, Li Y C 2022 Ocean Eng. 253 111293Google Scholar

    [8]

    Jin T H, Liu Z M, Sun S S, Ren Z S, Deng L, Yang B, Christie M D, Li W H 2020 Mech. Syst. Signal Process. 135 106338Google Scholar

    [9]

    刘少刚, 赵跃超, 赵丹 2019 物理学报 68 234301Google Scholar

    Liu S G, Zhao Y C, Zhao D 2019 Acta Phys. Sin. 68 234301Google Scholar

    [10]

    Wang Q, Chen Z X, Wang Y H, Gong N, Yang J, Li W H, Sun S S 2024 Mech. Syst. Signal Process. 208 111029Google Scholar

    [11]

    胡红生, 王炅, 钱苏翔, 李延成, 沈娜, 严拱标 2011 机械工程学报 47 84

    Hu H S, Wang J, Qian S X, Li Y C, Shen N, Yan G B 2011 Chin. J. Mech. Eng. 47 84

    [12]

    文永蓬, 孙倩, 周伟浩, 尚慧琳, 郭林生 2018 机械工程学报 54 114

    Wen Y P, Sun Q, Zhou W H, Shang H L, Guo L S 2018 Chin. J. Mech. Eng. 54 114

    [13]

    Jolly M R, Carlson J D, Muñoz B C 1996 Smart Mater. Struct. 5 607Google Scholar

    [14]

    Zhu Y S, Gong X L, Dang H, Zhang X Z, Zhang P Q 2006 Chin. J. Chem. Phys. 19 126Google Scholar

    [15]

    Li W H, Zhang X Z 2010 Smart Mater. Struct. 19 035002Google Scholar

    [16]

    Ivaneyko D, Toshchevikov V, Saphiannikova M, Heinrich G 2011 Macromol. Theory Simul. 20 411Google Scholar

    [17]

    Ivaneyko D, Toshchevikov V, Borin D, Saphiannikova M, Heinrich G 2014 Macromol. Symp. 338 96Google Scholar

    [18]

    Li W H, Zhou Y, Tian T F 2010 Rheol. Acta 49 733Google Scholar

    [19]

    Gu Z R, Luo Y P, Su Z B, Zhang L Y, Ren H J, Wang Y, Luo J 2023 J. Magn. Magn. Mater. 580 170795Google Scholar

    [20]

    Feng Y Y, Yang X J, Liu J G, Chen Z Q 2023 Phys. Stat. Mech. Its Appl. 621 128789Google Scholar

    [21]

    Chen L, Gong X L, Li W H 2008 Polym. Test. 27 340Google Scholar

    [22]

    Li Y C, Li J C, Li W H, Samali B 2013 Smart Mater. Struct. 22 035005Google Scholar

    [23]

    Ahmad Khairi M H, Abd Fatah A Y, Mazlan S A, Ubaidillah U, Nordin N A, Nik Ismail N I, Choi S B, Abdul Aziz S A 2019 Int. J. Mol. Sci. 20 4085Google Scholar

    [24]

    Gowda D K, Odenbach S 2023 J. Magn. Magn. Mater. 579 170856Google Scholar

    [25]

    刘浩, 须颖, 罗杨泉, 肖海善 2022 机械工程学报 58 328Google Scholar

    Liu H, Xu Y, Luo Y Q, Xiao S H 2022 Chin. J. Mech. Eng. 58 328Google Scholar

    [26]

    孙涛, 袁健美 2023 物理学报 72 218901Google Scholar

    Sun T, Yuan J M 2023 Acta Phys. Sin. 72 218901Google Scholar

    [27]

    寇雯博, 董灏, 邹岷强, 韩均言, 贾西西 2021 物理学报 70 030701Google Scholar

    Kou W B, Dong H, Zou M Q, Han J Y, Jia X X 2021 Acta Phys. Sin. 70 030701Google Scholar

    [28]

    Goodall R E A, Lee A A 2020 Nat. Commun. 11 6280Google Scholar

    [29]

    Goodall R E A, Parackal A S, Faber F A, Armiento R, Lee A A 2022 Sci. Adv. 8 eabn4117Google Scholar

    [30]

    Bessa M A, Bostanabad R, Liu Z, Hu A, Apley D W, Brinson C, Chen W, Liu W K 2017 Comput. Methods Appl. Mech. Eng. 320 633Google Scholar

    [31]

    Clément A, Soize C, Yvonnet J 2012 Int. J. Numer. Methods Eng. 91 799Google Scholar

    [32]

    Le B A, Yvonnet J, He Q C 2015 Int. J. Numer. Methods Eng. 104 1061Google Scholar

    [33]

    Shen L, Qian Q 2022 Comput. Mater. Sci. 211 111475Google Scholar

    [34]

    Jung J, Kim Y, Park J, Ryu S 2022 Compos. Struct. 285 115210Google Scholar

    [35]

    Huang D Z, Xu K, Farhat C, Darve E 2020 J. Comput. Phys. 416 109491Google Scholar

    [36]

    Li X, Liu Z, Cui S, Luo C, Li C, Zhuang Z 2019 Comput. Methods Appl. Mech. Eng. 347 735Google Scholar

    [37]

    Liu X, Yan Z, Zhong Z 2021 Int. J. Hydrog. Energy 46 22079Google Scholar

    [38]

    El Said B 2023 Int. J. Solids Struct. 276 112334Google Scholar

    [39]

    Li Z Q, Li X, Chen Y, Zhang C 2023 Compos. Struct. 323 117473Google Scholar

    [40]

    Nguyen X B, Komatsuzaki T, Iwata Y, Asanuma H 2018 Mech. Syst. Signal Process. 101 449Google Scholar

    [41]

    Wang L Z, Chen Z B, Jiang L K, Cheng L 2023 J. Magn. Magn. Mater. 570 170441Google Scholar

    [42]

    Kumbhar S B, Chavan S P, Gawade S S 2018 Mech. Syst. Signal Process. 100 208Google Scholar

    [43]

    Eem S H, Jung H J, Koo J H 2012 IEEE Trans. Magn. 48 3080Google Scholar

    [44]

    Norouzi M, Sajjadi Alehashem S M, Vatandoost H, Ni Y Q, Shahmardan M M 2016 J. Intell. Mater. Syst. Struct. 27 1121Google Scholar

    [45]

    Nguyen X B, Komatsuzaki T, Zhang N 2020 Mech. Syst. Signal Process. 141 106438Google Scholar

    [46]

    Yang S, Wang P, Liu Y, Dong X, Tong Y, Zhao Y 2021 Front. Mater. 8 743716Google Scholar

    [47]

    Wang Q, Dong X F, Li L Y, Ou J P 2017 Smart Mater. Struct. 26 065010Google Scholar

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出版历程
  • 收稿日期:  2024-04-08
  • 修回日期:  2024-06-20
  • 上网日期:  2024-07-18
  • 刊出日期:  2024-08-20

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