Fast and accurate characterization of magnetorheological elastomers based on machine learning

Ren Hang; Zhao Dan; Dong Li-Qiang; Liu Shao-Gang; Yang Jin-Shui

doi:10.7498/aps.73.20240482

Abstract

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.

Keywords:

Authors and contacts

1.
School of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150000, China
2.
Qingdao Innovation and Development Base, Harbin Engineering University, Qingdao 266000, China

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).

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References

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[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 106338 Google Scholar
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[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 111029 Google Scholar
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[21]	Chen L, Gong X L, Li W H 2008 Polym. Test. 27 340 Google Scholar
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[34]	Jung J, Kim Y, Park J, Ryu S 2022 Compos. Struct. 285 115210 Google Scholar
[35]	Huang D Z, Xu K, Farhat C, Darve E 2020 J. Comput. Phys. 416 109491 Google Scholar
[36]	Li X, Liu Z, Cui S, Luo C, Li C, Zhuang Z 2019 Comput. Methods Appl. Mech. Eng. 347 735 Google Scholar
[37]	Liu X, Yan Z, Zhong Z 2021 Int. J. Hydrog. Energy 46 22079 Google Scholar
[38]	El Said B 2023 Int. J. Solids Struct. 276 112334 Google Scholar
[39]	Li Z Q, Li X, Chen Y, Zhang C 2023 Compos. Struct. 323 117473 Google Scholar
[40]	Nguyen X B, Komatsuzaki T, Iwata Y, Asanuma H 2018 Mech. Syst. Signal Process. 101 449 Google Scholar
[41]	Wang L Z, Chen Z B, Jiang L K, Cheng L 2023 J. Magn. Magn. Mater. 570 170441 Google Scholar
[42]	Kumbhar S B, Chavan S P, Gawade S S 2018 Mech. Syst. Signal Process. 100 208 Google Scholar
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[44]	Norouzi M, Sajjadi Alehashem S M, Vatandoost H, Ni Y Q, Shahmardan M M 2016 J. Intell. Mater. Syst. Struct. 27 1121 Google Scholar
[45]	Nguyen X B, Komatsuzaki T, Zhang N 2020 Mech. Syst. Signal Process. 141 106438 Google Scholar
[46]	Yang S, Wang P, Liu Y, Dong X, Tong Y, Zhao Y 2021 Front. Mater. 8 743716 Google Scholar
[47]	Wang Q, Dong X F, Li L Y, Ou J P 2017 Smart Mater. Struct. 26 065010 Google Scholar

Cited By

图 1 MRE制备流程

Figure 1. Preparation process of MRE.

DownLoad: Full-Size Img PowerPoint

图 2 MRE的磁致储能模量测试

Figure 2. Magnetic storage modulus test of MRE.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

图 5 SVR 模型机制

Figure 5. Mechanism of SVR model.

DownLoad: Full-Size Img PowerPoint

图 6 训练集采样过程

Figure 6. Sampling process of training set.

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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

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

DownLoad: Full-Size Img PowerPoint

图 8 不同模型对不同样品预测的RMSE

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

表 1 MER样品配比及测试工况

Table 1. Ratio and testing conditions of MRE.

	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10	S11	S12
铁磁颗粒/%	12	15	18	21	24	27	27	27	27	27	27	27
硅油/%	5	5	5	5	5	5	0	10	15	5	5	5
加载频率/Hz	75	75	75	75	75	75	75	75	75	30	60	90

DownLoad: 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	4	5	10	20
train R²	0.999	0.999	0.999	0.999
test R²	0.878	0.998	0.998	0.998
RSME	0.112	0.0125	0.0133	0.0111

DownLoad: 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	RMSE	R²
S1	3378	0.999
S2	5006	0.999
S3	4246	0.999
S4	6671	0.998
S5	8579	0.999
S6	8669	0.998
S7	2275	0.999
S8	6547	0.999
S9	3630	0.999
S10	17122	0.998
S11	12642	0.998
S12	10409	0.998

DownLoad: 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

DownLoad: CSV

[1]	Vatandoost H, Hemmatian M, Sedaghati R, Rakheja S 2020 Compos. Part B Eng. 182 107648 Google Scholar
[2]	Nam T H, Petríková I, Marvalová B 2020 Polym. Test. 81 106272 Google Scholar
[3]	Kukla M, Warguła Ł, Talaśka K, Wojtkowiak D 2020 Materials 13 4795 Google Scholar
[4]	Agirre-Olabide I, Elejabarrieta M J 2018 Polym. Test. 66 114 Google 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 1638 Google Scholar
[6]	Jaafar M F, Mustapha F, Mustapha M 2021 J. Mater. Res. Technol. 15 5010 Google Scholar
[7]	Leng D X, Zhu Z H, Liu G J, Li Y C 2022 Ocean Eng. 253 111293 Google 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 106338 Google Scholar
[9]	刘少刚, 赵跃超, 赵丹 2019 物理学报 68 234301 Google Scholar Liu S G, Zhao Y C, Zhao D 2019 Acta Phys. Sin. 68 234301 Google 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 111029 Google 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. 5 607 Google Scholar
[14]	Zhu Y S, Gong X L, Dang H, Zhang X Z, Zhang P Q 2006 Chin. J. Chem. Phys. 19 126 Google Scholar
[15]	Li W H, Zhang X Z 2010 Smart Mater. Struct. 19 035002 Google Scholar
[16]	Ivaneyko D, Toshchevikov V, Saphiannikova M, Heinrich G 2011 Macromol. Theory Simul. 20 411 Google Scholar
[17]	Ivaneyko D, Toshchevikov V, Borin D, Saphiannikova M, Heinrich G 2014 Macromol. Symp. 338 96 Google Scholar
[18]	Li W H, Zhou Y, Tian T F 2010 Rheol. Acta 49 733 Google 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 170795 Google Scholar
[20]	Feng Y Y, Yang X J, Liu J G, Chen Z Q 2023 Phys. Stat. Mech. Its Appl. 621 128789 Google Scholar
[21]	Chen L, Gong X L, Li W H 2008 Polym. Test. 27 340 Google Scholar
[22]	Li Y C, Li J C, Li W H, Samali B 2013 Smart Mater. Struct. 22 035005 Google 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 4085 Google Scholar
[24]	Gowda D K, Odenbach S 2023 J. Magn. Magn. Mater. 579 170856 Google Scholar
[25]	刘浩, 须颖, 罗杨泉, 肖海善 2022 机械工程学报 58 328 Google Scholar Liu H, Xu Y, Luo Y Q, Xiao S H 2022 Chin. J. Mech. Eng. 58 328 Google Scholar
[26]	孙涛, 袁健美 2023 物理学报 72 218901 Google Scholar Sun T, Yuan J M 2023 Acta Phys. Sin. 72 218901 Google Scholar
[27]	寇雯博, 董灏, 邹岷强, 韩均言, 贾西西 2021 物理学报 70 030701 Google Scholar Kou W B, Dong H, Zou M Q, Han J Y, Jia X X 2021 Acta Phys. Sin. 70 030701 Google Scholar
[28]	Goodall R E A, Lee A A 2020 Nat. Commun. 11 6280 Google Scholar
[29]	Goodall R E A, Parackal A S, Faber F A, Armiento R, Lee A A 2022 Sci. Adv. 8 eabn4117 Google 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. 320 633 Google Scholar
[31]	Clément A, Soize C, Yvonnet J 2012 Int. J. Numer. Methods Eng. 91 799 Google Scholar
[32]	Le B A, Yvonnet J, He Q C 2015 Int. J. Numer. Methods Eng. 104 1061 Google Scholar
[33]	Shen L, Qian Q 2022 Comput. Mater. Sci. 211 111475 Google Scholar
[34]	Jung J, Kim Y, Park J, Ryu S 2022 Compos. Struct. 285 115210 Google Scholar
[35]	Huang D Z, Xu K, Farhat C, Darve E 2020 J. Comput. Phys. 416 109491 Google Scholar
[36]	Li X, Liu Z, Cui S, Luo C, Li C, Zhuang Z 2019 Comput. Methods Appl. Mech. Eng. 347 735 Google Scholar
[37]	Liu X, Yan Z, Zhong Z 2021 Int. J. Hydrog. Energy 46 22079 Google Scholar
[38]	El Said B 2023 Int. J. Solids Struct. 276 112334 Google Scholar
[39]	Li Z Q, Li X, Chen Y, Zhang C 2023 Compos. Struct. 323 117473 Google Scholar
[40]	Nguyen X B, Komatsuzaki T, Iwata Y, Asanuma H 2018 Mech. Syst. Signal Process. 101 449 Google Scholar
[41]	Wang L Z, Chen Z B, Jiang L K, Cheng L 2023 J. Magn. Magn. Mater. 570 170441 Google Scholar
[42]	Kumbhar S B, Chavan S P, Gawade S S 2018 Mech. Syst. Signal Process. 100 208 Google Scholar
[43]	Eem S H, Jung H J, Koo J H 2012 IEEE Trans. Magn. 48 3080 Google Scholar
[44]	Norouzi M, Sajjadi Alehashem S M, Vatandoost H, Ni Y Q, Shahmardan M M 2016 J. Intell. Mater. Syst. Struct. 27 1121 Google Scholar
[45]	Nguyen X B, Komatsuzaki T, Zhang N 2020 Mech. Syst. Signal Process. 141 106438 Google Scholar
[46]	Yang S, Wang P, Liu Y, Dong X, Tong Y, Zhao Y 2021 Front. Mater. 8 743716 Google Scholar
[47]	Wang Q, Dong X F, Li L Y, Ou J P 2017 Smart Mater. Struct. 26 065010 Google Scholar

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