A new fractional fuzzy dispersion entropy and its application in muscle fatigue detection

Recently, fuzzy dispersion entropy (DispEn) has attracted much attention as a new nonlinear dynamics method that combines the advantages of both DispEn and fuzzy entropy. However, it suffers from limitation of insensitivity to dynamic changes. To solve this limitation, we proposed fractional fuzzy dispersion entropy (FFDispEn) based on DispEn, a novel fuzzy membership function and fractional calculus. The fuzzy membership function was defined based on the Euclidean distance between the embedding vector and dispersion pattern. Simulated signals generated by the one-dimensional (1D) logistic map were used to test the sensitivity of the proposed method to dynamic changes. Moreover, 29 subjects were recruited for an upper limb muscle fatigue experiment, during which surface electromyography (sEMG) signals of the biceps brachii muscle were recorded. Both simulated signals and sEMG signals were processed using a sliding window approach. Sample entropy (SampEn), DispEn and FFDispEn were separately used to calculate the complexity of each frame. The sensitivity of different algorithms to the muscle fatigue process was analyzed using fitting parameters through linear fitting of the complexity of each frame signal. The results showed that for simulated signals, the larger the fractional order q, the higher the sensitivity to dynamic changes. Moreover, DispEn performed poorly in the sensitivity to dynamic changes compared with FFDispEn. As for muscle fatigue detection, the FFDispEn value showed a clear declining tendency with a mean slope of −1.658 × 10⁻³ as muscle fatigue progresses; additionally, it was more sensitive to muscle fatigue compared with SampEn (slope: −0.4156 × 10⁻³) and DispEn (slope: −0.1675 × 10⁻³). The highest accuracy of 97.5% was achieved with the FFDispEn and support vector machine (SVM). This study provided a new useful nonlinear dynamic indicator for sEMG signal processing and muscle fatigue analysis. The proposed method may be useful for physiological and biomedical signal analysis.