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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.
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图 1 MRE制备流程
Figure 1. Preparation process of MRE.
图 2 MRE的磁致储能模量测试
Figure 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
Figure 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
Figure 4. Typical mechanical model of MRE: (a) Microscopic magnetic dipole model; (b) macroscopic viscoelastic model.
图 5 SVR 模型机制
Figure 5. Mechanism of SVR model.
图 6 训练集采样过程
Figure 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
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.
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.
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.
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.
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 
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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
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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
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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
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