The Refined Composite Downsampling Permutation Entropy Is a Relevant Tool in the Muscle Fatigue Study Using sEMG Signals

Figures

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  Figure 1. Principles of the composite coarse-graining procedure ( m=3 ). Nonoverlapping segments of size m are obtained from the raw signal. This leads to the original MPE estimation procedure using the single x1(m) data vector. By shifting the initial positions, a set of coarse signals x1(m) , x2(m) , and x3(m) is obtained. This leads to variant MPE estimation procedures using the set of m data vectors xk(m) , with k=1,…,m .

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  Figure 2. Principles of the composite downsampling procedure ( τ=3 ). Downsampled signals are obtained by taking data points spaced by τ . By shifting the initial positions between 1 and τ , a set of downsampling signals is obtained without any common data points.

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  Figure 3. Left column: mean entropy values as a function of scale m for the fatigue steps (from W1 to W4 ). Right column: variation in entropy mean values as a function of scale m on the pairwise differences between steps of fatigue (only W1−W3 , W2−W4 , and W1−W4 are shown). From top to bottom: MPE (a,b), rcMPE (c,d) and rcDPE (e,f). All values at dimension d = 3.

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  Figure 4. Left column: mean entropy values as a function of scale m for the fatigue steps (from W1 to W4 ). Right column: variation in entropy mean values as a function of scale m on the pairwise differences between steps of fatigue ( W1−W3 , W2−W4 , and W1−W4 ). Dimension values, from top to bottom: d=4 (a,b) and d=5 (c,d).

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  Figure 5. Effective hypothesis decomposition for fatigue isometric contraction for the following factors: (a) PE-based methods and (b) dimension. The vertical lines denote 95% confidence intervals for the ANOVA F distribution.

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  Figure 6. Range boxplots for rcDPE measurements from isometric contractions with dimension d=4 . Four activity windows from sustained 70% MVC at scale m=τ=10 . From the repeated ANOVA test measurements, all the pairwise comparisons are statistically significant ( p<0.001 ), shown globally with **.

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  Figure 7. PSD averaged over the ten studied subjects (thick line) with the standard deviation (thin lines) in x-axis semilog representation. Integrated normalized PSDs are in unity.

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  Figure 8. PSD for the ten subjects in a linear representation. The thick line is the averaged curve over the ten subjects. Integrated normalized PSDs are in unity.