Scale Interval Method for Calculating the Fractal Parameter: Fractal Roughness

Abstract

The Weierstrass-Mandelbrot (W-M) function method is commonly used in surface reconstruction, which integrates parameters such as fractal dimension (D) and fractal roughness (G). The parameter G is typically calculated using the power spectral density (PSD) method. This study identifies deviations in the G calculations. These deviations arise from simplifications made during the derivation process when applying the PSD method. To address this issue, this paper introduces a novel approach based on statistical methods to define the scale interval. This approach involves calculating the G post-alignment of the generated target profile within this interval, followed by surface generation using the W-M function. A comparison between the scale interval method (SI) and the PSD method reveals that the SI method demonstrates better accuracy. A comparative analysis between the generated and actual surfaces substantiates the accuracy of the G calculations using the SI method. This method provides a theoretical foundation for subsequent fractal surface measurements, reconstructions, contact calculations, and dynamic characterizations.