Influence of noise on the fractal dimension of measured surface topography. (February 2020) - Zuo, Xue; Peng, Minglong; Zhou, Yuankai
Highlights: Noise influences the amplitude and estimated fractal dimension of the surfaces. Estimated fractal dimension decreases with SNR and becomes stable. Noise has relatively little influence on the high-dimensional surfaces. Denoising for low-dimensional surfaces is required prior to fractal analysis. Abstract: The influence of noise on the estimated fractal dimension (EFD) was investigated based on theoretical and experimental surfaces. White and pink noise with predefined SNR (signal-to-noise ratio) were added to Weierstrass-Mandelbrot (W-M) and fractional Brownian motion (fBm) surfaces, respectively. The EFD decreases with the growth in SNR. The noise has significant influence on the EFD of low-dimensional surfaces, but has relatively less influence on the high-dimensional surfaces. Thus, denoising for low-dimensional surfaces is required prior to fractal analysis. To verify this conclusion, worn and grinding surfaces obtained under different experimental conditions are studied. The results show that the fractal dimensions of experimental surfaces decrease after denoising. There is a reasonable agreement between the theoretical and experimental surfaces, which ensures the broad applicability of presented results.