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

Abstract Background The complexity analysis of neuroelectrophysiological signals has been widely applied in the field of biomedical engineering and muscle fatigue detection using the complexity analysis of surface electromyographic (sEMG) signals is one of the hot research topics. Recently, fuzzy dispersion entropy has attracted more and more attention as a new nonlinear dynamics method for complexity analysis which combines the advantages of both dispersion entropy(DispEn) and fuzzy entropy. However, it suffers from limitation of sensitivity to dynamic changes. In this study, fractional fuzzy dispersion entorpy (FFDispEn) is proposed based on DispEn, a new fuzzy membership function and fractional calculus to solve this limitation. Fuzzy membership function is defined based on Euclidean distance between embdding vector and dispersion pattern in this study. Methods Simulated signals generated by 1D Logistic map were used to test the sensitivity of the proposed method to dynamic changes. Moreover, ten subjects were recruited for upper limb muscle fatigue exprienment while sEMG signals of the biceps brachii muscle were recorded. Both simulated signals and sEMG signals were processed using sliding window approach. Sample entropy(SampEn), DispEn and FFDispEn were respectively used to calculate the complexity of each frame. The sensitivity of different algorithms to muscle fatigue process was analyzed using fitting parameters through linear fitting of the complexity of each frame signal. Results The results show that for simulated signals, the larger the fractional order q, the higher the sensitivity to dynamic changes. Moreover, DispEn performs poorly in the sensitivity to dynamic changes compared with FFDispEn. As for the muscle fatigue detection, FFDispEn value shows a clear declining tendency as muscle fatigue progresses and is more sensitive to muscle fatigue compared with SampEn and DispEn. Conclusions This study provides a new useful nonlinear dynamic indicator for sEMG signal preprocessing and muscle fatigue analysis. The proposed method may be useful for physiological and biomedical signal analysis.