Real-time fatigue curve extraction algorithm for wearable sEMG devices based on fast variational mode decomposition

Tianshun Li; Donghao Lv; Dahua Yu; Xiaowei Du; Tianshun Li; Donghao Lv; Dahua Yu; Xiaowei Du

doi:10.3934/bioeng.2026003

AIMS Bioengineering

2026, Volume 13, Issue 1: 43-61. doi: 10.3934/bioeng.2026003

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Research article

Real-time fatigue curve extraction algorithm for wearable sEMG devices based on fast variational mode decomposition

1.
School of Automation and Electrical Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China
2.
School of Automation, China University of Geosciences, Wuhan 430074, China
3.
Key Laboratory of Synthetical Automation for Process Industries at Universities of Inner Mongolia Autonomous Region, Inner Mongolia University of Science and Technology, Baotou 014010, Inner Mongolia, China
4.
Department of Physical Education (Institute of Physical Education), Inner Mongolia University of Science and Technology, Baotou 014010, China

Received: 03 November 2025 Revised: 31 December 2025 Accepted: 26 January 2026 Published: 02 February 2026

Wearable devices are widely utilized in the field of health monitoring. Given the real-time requirements of wearable devices for dynamic tracking of muscle fatigue, and addressing the issues of prolonged computation time and failure to extract fatigue-related modal information when applying the variational mode decomposition (VMD) algorithm to surface electromyography (sEMG) signals, this paper proposes the fast VMD (FVMD) algorithm. The objective was to rapidly decompose fatigue-related modal information and extract a complete fatigue curve to alert users. The proposed algorithm is an engineering acceleration of the VMD algorithm. FVMD extends the original signal and applies the Fourier transform to convert the time-domain variational problem into the frequency domain. The optimization problem was constrained to the positive frequency range to simplify calculations while leveraging the unilateral spectrum characteristics to streamline optimization and focus on narrowband modes. The alternating direction method of multipliers framework was employed to decompose the problem into subproblems solvable in closed form, with modal updates inspired by Wiener filtering. The Lagrange multipliers were iteratively updated, and convergence criteria were established to ensure stability. The time-domain signal was reconstructed via the inverse Fourier transform. According to the experimental results, the proposed algorithm exhibits a substantial improvement in processing time compared to the original algorithm and other enhanced algorithms. Compared with other VMD variant algorithms using the same experimental data, the fast recursive VMD (FRVMD) algorithm takes 9.93 s. In contrast, the FVMD method can complete the same task in a shorter time. An evaluation metric was used to select the muscle fatigue modal component most correlated with the original signal and extract the muscle fatigue curve. The FVMD algorithm enhances computational efficiency, overcoming the computational limitations of wearable devices, and provides reliable technical support for real-time muscle fatigue quantification and early warning in scenarios such as sports rehabilitation and occupational health.
- wearable devices,
- sEMG,
- fast variational mode decomposition,
- muscle fatigue curve
Citation: Tianshun Li, Donghao Lv, Dahua Yu, Xiaowei Du. Real-time fatigue curve extraction algorithm for wearable sEMG devices based on fast variational mode decomposition[J]. AIMS Bioengineering, 2026, 13(1): 43-61. doi: 10.3934/bioeng.2026003

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Abstract

Wearable devices are widely utilized in the field of health monitoring. Given the real-time requirements of wearable devices for dynamic tracking of muscle fatigue, and addressing the issues of prolonged computation time and failure to extract fatigue-related modal information when applying the variational mode decomposition (VMD) algorithm to surface electromyography (sEMG) signals, this paper proposes the fast VMD (FVMD) algorithm. The objective was to rapidly decompose fatigue-related modal information and extract a complete fatigue curve to alert users. The proposed algorithm is an engineering acceleration of the VMD algorithm. FVMD extends the original signal and applies the Fourier transform to convert the time-domain variational problem into the frequency domain. The optimization problem was constrained to the positive frequency range to simplify calculations while leveraging the unilateral spectrum characteristics to streamline optimization and focus on narrowband modes. The alternating direction method of multipliers framework was employed to decompose the problem into subproblems solvable in closed form, with modal updates inspired by Wiener filtering. The Lagrange multipliers were iteratively updated, and convergence criteria were established to ensure stability. The time-domain signal was reconstructed via the inverse Fourier transform. According to the experimental results, the proposed algorithm exhibits a substantial improvement in processing time compared to the original algorithm and other enhanced algorithms. Compared with other VMD variant algorithms using the same experimental data, the fast recursive VMD (FRVMD) algorithm takes 9.93 s. In contrast, the FVMD method can complete the same task in a shorter time. An evaluation metric was used to select the muscle fatigue modal component most correlated with the original signal and extract the muscle fatigue curve. The FVMD algorithm enhances computational efficiency, overcoming the computational limitations of wearable devices, and provides reliable technical support for real-time muscle fatigue quantification and early warning in scenarios such as sports rehabilitation and occupational health.

Acknowledgments

This research received partial funding from the Natural Science Foundation of the Inner Mongolia Autonomous Region (2024MS06024), the Special Fund for Basic Research Operations at Inner Mongolia University of Science and Technology (2023QNJS194), and the Special Research Project for the First-Level Discipline of Metallurgical Engineering from the Department of Education of the Inner Mongolia Autonomous Region (YLXKZX-NKD-020).

Conflict of interest

The authors declare no conflict of interest.

Author contributions

All authors contributed to the conceptualization and design of the study. Material preparation and data analysis were performed by Tianshun Li and Donghao Lv. Tianshun Li completed the initial draft and experimental work. Dahua Yu provided experimental guidance, while Xiaowei Du contributed data support. All authors reviewed earlier versions of the manuscript. All authors read and approved the final manuscript.

Novelty claim

The proposed algorithm is an engineering acceleration of the VMD algorithm.

Ethics approval of research

The Ethics Committee of the People's Hospital of Linhe District, Bayannur City, approved all procedures. All individual participants in the study provided informed consent and obtained a paper-based informed consent form.

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