Influence of sampling length on estimated fractal dimension of surface profile. (June 2020) - Zuo, Xue
Highlights: The influence of sampling length on the estimated fractal dimension is analyzed. Estimated fractal dimension increases with sampling length and becomes stable. Sampling length should ensure that the fractal dimension reaches a stable value. Abstract: To study the influence of sampling length on estimated fractal dimension of surface profile, a series of profiles with same sampling interval and different lengths are generated by the Weierstrass-Mandelbrot function. The influence of sampling length on the estimated fractal dimension and the width of scaling region of both theoretical and real measured profiles are analyzed. The computing results show that the fractal dimension cannot be accurately calculated because of the fluctuation and narrow scaling region in the case of insufficient data points. This fluctuation tends to be weakened, and the linearity of the scaling region is improved with the increase of sampling length. The estimated fractal dimension increases with the sampling length, and eventually maintains at its theoretical value. Therefore, the sampling length should be more than the minimum length where the stable value can be achieved. Moreover, the sampling length should be appropriately increased for the smooth surface. This study provides basis for choosing sampling length appropriately to meet the requirements of computing accuracy and efficiency.