A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications

Figure 1

Acceleration of a wheelchair recorded at 60 Hz during a wheelchair rugby match (data from [15]) against time (bottom subfigure); fractal dimension 𝐷_𝐻 (running average with a window width of 151 data points over 2.5 s) of the acceleration signal calculated with three different methods (middle subfigure): Higuchi’s [7] method, Raghavendra and Dutt’s [9] MRBC, and the method developed in this study (cf. Section 4); top subfigure: absolute difference in 𝐷_𝐻 between the three methods.