- Research Article
- 10.3934/bioeng.2026003
Real-time fatigue curve extraction algorithm for wearable sEMG devices based on fast variational mode decomposition
- Jan 01, 2026
- AIMS bioengineering
- Tianshun Li + 3 more +3
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.
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