Many types of tribological surfaces have been observed to exhibit a multiscale nature, i.e. topographical features over different scales ranging from nanometers to hundreds of micrometers. Consequently, recent developments in the characterization of tribological surfaces have concentrated on wavelet transformation and fractal-based methods. The wavelet methods are used due to their ability to decompose surface data into different scale components and to characterize surface data at each individual scale. On the other hand, fractal methods are used due to their ability to characterize surface data in a scale-invariant manner. It has been shown that these two capabilities of (i) decomposition of surface data and (ii) scale-invariant analysis are essential in the characterization of 3-D surface topography. Thus, it is apparent that a characterization method which exhibits both of these capabilities would yield the best results. Developing such a method is not an easy task. This problem in the characterization of tribological surfaces is addressed in our paper. A new method, called a hybrid fractal-wavelet method, is proposed. This method is a combination of a partition iterated function system (PIFS) and a symmetric wavelet transform (SWT). The PIFS is used to scale-invariantly characterize the surface topography over a wide range of different scales, while the SWT is used to characterize the surface topography at each individual scale. This multiscale characterization ability of the newly developed method is demonstrated on a tribological surface example.
Podsiadlo, P., & Stachowiak, G. (2002). Hybrid Fractal-Wavelet Method for Characterization of Tribological Surfaces - a Preliminary Study. Tribology Letters, 13(4), 241-250. https://doi.org/10.1023/A:1021059108478