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Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (12): 2483-2494    DOI: 10.3785/j.issn.1008-973X.2025.12.003
    
Upper-limb muscle fatigue assessment in overhead work based on Hammerstein model and surface electromyography
Yanpu YANG(),Zhihong WU,Wenhao MENG,Yueming ZHUO,Jialing LIU
Key Laboratory of Road Construction Technology and Equipment of MOE, Chang’an University, Xi’an 710064, China
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Abstract  

A novel muscle fatigue assessment method integrating the Hammerstein model with surface electromyography (sEMG) signals was proposed, to address the effective identification of dynamic upper-limb muscle fatigue during overhead work. An overhead work experiment was designed to acquire sEMG signals from participants during sustained tasks, followed by signal preprocessing. The sEMG median frequency and root mean square were selected as the model input and output, respectively, to construct a nonlinear system based on the Hammerstein structure. Key model parameters were identified using recursive least squares with a forgetting factor combined with singular value decomposition. The K-means++ clustering algorithm was applied to perform unsupervised classification on the identified parameters, enabling differentiation of distinct fatigue levels. The electromyographic fatigue threshold (EMGFT) was further introduced to determine the exact onset time of muscle fatigue by integrating clustering results. Experimental results demonstrated that the method effectively captured the nonlinear dynamic characteristics of upper-limb muscles during overhead work. The clustering outcomes exhibit strong correlation with Borg CR10 subjective fatigue ratings, indicating good physiological interpretability. Combined with EMGFT analysis, the approach accurately characterized the progression of fatigue, providing a quantifiable technical pathway for upper-limb muscle fatigue monitoring in dynamic overhead work.



Key wordsoverhead work      upper-limb muscle fatigue assessment      Hammerstein model      surface electromyography (sEMG) signal      K-means++ clustering     
Received: 26 November 2024      Published: 25 November 2025
CLC:  TP 393  
Fund:  基础加强计划技术领域基金资助项目(2021-JCJQ-JJ-1018);长安大学中央高校基金资助项目(300102253107).
Cite this article:

Yanpu YANG,Zhihong WU,Wenhao MENG,Yueming ZHUO,Jialing LIU. Upper-limb muscle fatigue assessment in overhead work based on Hammerstein model and surface electromyography. Journal of ZheJiang University (Engineering Science), 2025, 59(12): 2483-2494.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.12.003     OR     https://www.zjujournals.com/eng/Y2025/V59/I12/2483


基于Hammerstein模型和表面肌电的过头作业上肢肌肉疲劳评估

针对过头作业场景下上肢肌肉疲劳动态变化的有效识别问题,提出融合Hammerstein模型与表面肌电(sEMG)信号的新型肌肉疲劳评估方法. 通过设计过头作业实验获取被试者在持续作业过程中的sEMG信号并预处理,选取sEMG中位频率与均方根值分别作为模型输入与输出,构建基于Hammerstein结构的非线性系统模型. 采用带遗忘因子的递推最小二乘法结合奇异值分解辨识模型关键参数,利用K-means++聚类算法对辨识所得参数进行无监督分类,划分出不同疲劳等级. 进一步引入肌电疲劳阈值(EMGFT),结合聚类结果确定肌肉进入疲劳状态的具体时间. 实验验证显示,该方法可有效捕捉上肢肌肉在过头作业中的非线性动态特征;所提取参数的聚类结果与Borg CR10主观疲劳评分呈强相关性,表明其具备良好的生理意义解释能力;联合EMGFT分析可有效刻画疲劳发展进程,为动态过头作业中的上肢肌肉疲劳监测提供可量化的技术路径.


关键词: 过头作业,  上肢肌肉疲劳评估,  Hammerstein模型,  表面肌电(sEMG)信号,  K-means++聚类 
Fig.1 Hammerstein model structure
Fig.2 EMGFT calculation process
Fig.3 Overhead work platform
肌肉实验过程示意
斜方肌被试站姿,手臂伸直自然下垂,掌心朝内. 实验人员双手下按肩部,被试者用力抬肩5 s,记录肌电数据,完成一次MVC测量
肱桡肌被试者坐姿,前臂置于桌面,掌心朝下. 实验人员按住手背,被试腕关节用力抬起5 s,记录肌电数据,完成一次MVC测量
肱二头肌被试者坐姿,上臂平放桌面,前臂竖直,掌心向内. 实验人员双手拉住被试者前臂,被试者紧缩肱二头肌保持5 s,记录肌电数据,完成一次MVC测量
三角肌被试者站姿,手臂伸直抬起与身体垂直,掌心向下. 实验人员双手下按其大臂,被试者手臂努力保持原状态5 s,记录肌电数据,完成一次MVC测量
Tab.1 Experimental description of MVC
数值疲劳等级
0完全没有
0.5极其轻微,难以察觉
1非常轻微,没有作业压力
2轻微,感觉进入作业状态
3温和,上肢有少许酸
4稍稍强烈,开始出现轻微酸痛
5强烈,上肢开始轻微抖动,仍能完成作业
6~8非常强烈,上肢较强抖动,出现短暂无法完成作业
9极其强烈,已经处于极度疲劳,无法完成作业
10最大值,处于脱力状态
Tab.2 Borg CR10 subjective fatigue assessment scale
Fig.4 Overhead work experiment process
Fig.5 Comparison of before and after denoising for m4
被试者Pm/%
m1m2m3m4m5m6m7m8
114.9617.7810.6820.2112.387.359.886.76
215.2519.9910.9424.2110.457.895.236.04
314.6212.2012.2117.3115.0414.927.725.98
410.2513.3311.7227.9615.1311.475.664.48
510.3012.2712.6826.4312.7712.284.049.23
615.6015.7010.7317.8314.3312.337.156.33
79.2514.869.6321.9716.828.7710.528.18
817.4913.9213.3621.0814.714.479.335.64
915.0819.6112.7320.2515.145.466.685.05
1014.4514.2612.1815.5415.1410.1510.218.07
平均13.7315.3911.6821.2814.199.517.646.58
Tab.3 Muscle contribution rate of each channel
被试者R2
RMS-MFRMS-MPFIEMG-MFIEMG-MPFRMS-IEMGMF-MPF
1)注:*表示为p<0.05,**表示为p<0.01.
10.554**1)0.373*0.3410.3140.3100.321
20.514**0.414*0.3110.3320.352*0.325
30.536**0.434*0.368*0.357*0.3210.256
40.607**0.498*0.423*0.3120.3210.416*
50.621**0.409*0.482*0.387*0.3320.337
60.593**0.421*0.378*0.3260.394*0.407*
70.542**0.3170.411*0.3040.415*0.356*
80.575**0.403*0.498*0.386*0.391*0.315
90.578**0.432*0.394*0.3150.3250.346
100.569**0.411*0.437*0.3090.3240.362*
Tab.4 Determination coefficient R2 of different feature combinations
Fig.6 Parameter identification results
Fig.7 SSE change curve
Fig.8 Clustering fatigue level
被试者皮尔逊相关系数被试者皮尔逊相关系数
1)注:**表示p<0.01
10.910**1)70.928**
20.861**80.901**
30.884**90.894**
40.919**100.911**
50.889**平均值0.904**
60.941**
Tab.5 Pearson correlation coefficient between fatigue segments and clustering results in group 65
Fig.9 Comparison between clustered fatigue levels and fatigue classification of group 65
Fig.10 Comparison analysis of fatigue grade, MF, RMS and each parameter
Fig.11 Overall fluctuation statistics of parameters a, b, and c at different fatigue stages
Fig.12 Pole change map
被试者EMGFT/s作业时间
预备疲劳轻度疲劳中度疲劳重度疲劳
152.79141.55346.89559.6912 min 11 s
241.69168.95280.42830.0515 min 18 s
332.91150.22254.58565.6313 min 18 s
4150.16175.49290.68410.6010 min 11 s
546.54151.51340.67537.5111 min 36 s
639.89163.90528.18647.7715 min 6 s
740.73166.93447.24738.2117 min 24 s
836.05119.29287.72576.9415 min 54 s
923.36110.11367.11707.5914 min 24 s
1063.42145.72344.16685.1213 min 30 s
Tab.6 Total time and EMGFT of each fatigue stage
因素SSMSFp
1) 注:**表示p<0.01
截距3461916.133461916.13597.110.000**1)
疲劳阶段1922927.24640975.75110.560.000**
被试者51665.355740.600.990.47
误差156539.455797.76
Tab.7 Intersubjective effects
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