EEE – METHOD BASED ON FRACTAL DIMENSION FOR ANALYSIS OF TIME SERIES

Abstract eng:
In our research we have developed a new analysis of topological one-dimensional objects (especially time series or dividing lines): Evaluation of length changes with Elimination of insignificant Extremes. The method, useful for complex data, stems from an estimation of the fractal dimension, so it measures changes of lengths in sequential steps. The EEE method does not use a “ruler” for measurement, but the line is defined by local extremes (maxima and minima). The extremes are eliminated and the length of the function, which is linear by parts, is measured. The lengths are plotted in relation to the number of all steps and the plot is evaluated. Mathematically generated functions (e.g. based on the Hurst coefficient), time series from real production processes and dividing lines (surface profiles and surface roughness) were used for the first experiment. The results show good potential for applications in measurement in off-line evaluations of data sets and on-line monitoring and control.

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