Research Article 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

License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals.Therefore they can produce opposite results in extreme signals.These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) andmodified time series signal with a robust algorithm and a running averagemethod, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by amultiplier, which has a non-linear effect on the signal’s time derivative.Theoptimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisationmethod provides an additional filter effect andmakes the fractal dimensions less noisy.Themethod is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals