Surface Evaluation by Estimation of Fractal Dimension and Statistical Tools

Abstract

Structured and complex data can be found in many applications in research and development, and also in industrial practice. We developed a methodology for describing the structured data complexity and applied it in development and industrial practice. The methodology uses fractal dimension together with statistical tools and with software modification is able to analyse data in a form of sequence (signals, surface roughness), 2D images, and dividing lines. The methodology had not been tested for a relatively large collection of data. For this reason, samples with structured surfaces produced with different technologies and properties were measured and evaluated with many types of parameters. The paper intends to analyse data measured by a surface roughness tester. The methodology shown compares standard and nonstandard parameters, searches the optimal parameters for a complete analysis, and specifies the sensitivity to directionality of samples for these types of surfaces. The text presents application of fractal geometry (fractal dimension) for complex surface analysis in combination with standard roughness parameters (statistical tool).

Evolution of Joint Roughness Degradation from Cyclic Loading and Its Effect on the Elastic Wave Velocity

“…However, the validity of techniques and the accuracy of measurement methods for identifying and classifying rock joint surfaces are generally questioned because of the subjectivity of JRC results. The undulation and unevenness of a rock joint surface are recognized by its peak-to-valley height (Hotar and Novotny 2005) to classify the rock joint surface profile. In particular, Mohd-Nordin et al (2014) applied the JRC to naturally fractured rock surfaces using the scan line technique through the implementation of the peak-to-valley height.…”

Surface Fractal Analysis for Estimating the Fracture Energy Absorption of Nanoparticle Reinforced Composites

“…Beginning with the pioneering work by Mandelbrot et al [ 1 ], numerous investigators have focused on statistical characterization of the roughness of fractured surfaces [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ]. It is now evident that the topography of crack surfaces can be described as being self-affine [ 10 ].…”

“…Cherepanov et al [ 3 ] discussed several achievements in the field of fractal geometry that influenced fracture mechanics. Hotar et al [ 4 ] applied fractal geometry in combination with statistical tools for the classification of surface roughness. Mecholosky [ 5 ] showed how fractal geometry can be used in estimating the theoretical strength of materials based on crack tip geometry and generated fracture surface.…”

Fractal and stereological analyses of insulin-induced rat exocrine pancreas remodelling

“…All these changes may increase the level of detail during binarisation and outline of the digital images; therefore, the values of fractal dimension and lacunarity. Any change in acinus shape could have a significant impact on the complexity of the exocrine pancreas tissue [18].…”