Muscle fatigue characterization method based on Tsallis entropy and fluctuation-based dispersion entropy

doi:10.3785/j.issn.1008-973X.2025.12.004

Journal of ZheJiang University (Engineering Science)

2025, Vol. 59

Issue (12): 2495-2505 DOI: 10.3785/j.issn.1008-973X.2025.12.004

Muscle fatigue characterization method based on Tsallis entropy and fluctuation-based dispersion entropy

Bo DONG(

),Donghao LV*(

),Keyang XI,Jiahao LI

School of Automation and Electrical Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China

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Abstract

To address the issues of information loss and insufficient sensitivity in the feature extraction of surface electromyography (sEMG) signals, which resulted in low classification accuracy, a smooth enhanced refined composite multiscale Tsallis fluctuation-based dispersion entropy (RCMTFDE) was proposed based on Tsallis entropy and fluctuation-based dispersion entropy (FDE). The issue of discontinuity in sEMG signals caused by FDE in discrete classification was addressed by introducing a fuzzy membership function. Additionally, Tsallis entropy was combined with FDE to enhance its sensitivity to nonlinear complex systems. Considering that single time-scale analysis could not accurately characterize the signals, a smooth enhanced coarse-graining method was proposed. Signal information leakage and entropy instability during the coarse-graining process were reduced, allowing the extraction of optimal muscle fatigue features across multiple scales. Experimental results showed that RCMTFDE demonstrated significant entropy value differences when distinguishing between non-fatigue and fatigue signals, and exhibited clear fatigue gradient characteristics in the muscle fatigue quantification curve. Compared to the reference algorithms, the proposed method achieved the highest accuracy in muscle fatigue classification, reaching 96.667%.

Key words： muscle fatigue surface electromyography signal fluctuation-based dispersion entropy Tsallis entropy multiscale analysis

Received: 08 December 2024 Published: 25 November 2025

CLC:

TN 911.7

Fund: 内蒙古自治区自然科学基金资助项目(2024MS06024)；内蒙古自治区一流学科科研专项项目(YLXKZX-NKD-020)；内蒙古自治区直属高校基本科研业务费资助项目(2023QNJS194).

Corresponding Authors: Donghao LV E-mail: 2023023236@stu.imust.edu.cn;wsldh2016957@imust.edu.cn

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Cite this article:

Bo DONG,Donghao LV,Keyang XI,Jiahao LI. Muscle fatigue characterization method based on Tsallis entropy and fluctuation-based dispersion entropy. Journal of ZheJiang University (Engineering Science), 2025, 59(12): 2495-2505.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.12.004 OR https://www.zjujournals.com/eng/Y2025/V59/I12/2495

融合Tsallis熵和波动分散熵的肌肉疲劳表征方法

针对目前表面肌电(sEMG)信号在肌肉疲劳识别中存在特征提取信息丢失、灵敏性不足的问题，进而影响分类精度的问题，提出基于Tsallis熵和波动分散熵(FDE)的平滑增强精细复合多尺度Tsallis波动分散熵(RCMTFDE). 该算法通过引入模糊隶属函数，解决了FDE在离散分类中影响sEMG信号连续性的问题，并结合Tsallis熵提升了FDE对非线性复杂系统的灵敏性. 考虑到单一时间尺度分析难以准确表征信号的问题，提出平滑增强的粗粒化方法，来减少粗粒化过程中信号信息泄露和熵值不稳定性，在多尺度下提取出最佳肌肉疲劳特征. 实验结果表明，RCMTFDE在区分非疲劳和疲劳信号时，展示了显著的熵值差异，且在肌肉疲劳量化曲线中表现出明显的疲劳梯度特征. 相较对比算法，该方法在肌肉疲劳分类中取得最高准确率，达到了96.667%.

关键词： 肌肉疲劳, 表面肌电信号, 波动分散熵, Tsallis熵, 多尺度分析

Fig.1 Comparison of coarse-graining methods

Fig.2 Mean distribution of indicators varying with q

Fig.3 Distribution of entropy value under different noise lengths

Fig.4 Error bars of entropy methods across noise variations

Fig.5 Comparison of entropy values in non-fatigue and fatigue signals across scale factors and lengths

Fig.6 Subject 1 analysis results

Tab.1 Quantification of muscle fatigue in each subject

Tab.2 Mann-Kendall trend test results

Tab.3 Results of muscle fatigue classification with different features

Fig.7 ROC curve results of each method in muscle fatigue classification

Tab.4 Ablation experiments results of RCMTFDE


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