Fractal analysis is one of the rapidly evolving branches of mathematics and finds its application in different analyses such as pore space description. It constitutes a new approach to the issue of their natural irregularity and roughness. To be properly applied, it should be encompassed by an error estimation. The article presents and verifies uncertainties along with imperfections connected with image analysis and expands on the possible ways of their correction. One of key aspects of such research is finding both appropriate place and the number of photos to take. A coarse- grained sandstone thin section was photographed and then pictures were combined into one, bigger image. Fractal parameters distributions show their change and suggest that the accurately gathered group of photos include both highly and less porous regions. Their amount should be representative and adequate to the sample. The resolution influence on the fractal dimension and lacunarity values was examined. For SEM limestone images obtained using backscattered electrons, magnification in the range of 120x to 2000x was used. Additionally, a single pore was examined. The acquired results point to the fact that the values of fractal dimension are similar to a wide range of magnifications, while lacunarity changes each time. This is connected with changing homogeneity of the image. The article also undertakes a problem of determining fractal parameters spatial distribution based on binarization. The available methods assume that it is carried out after or before the image division into rectangles to create fractal dimension and lacunarity values for interpolation. An individual binarization, although time consuming, provides better results that resemble reality to a closer degree. It is not possible to define a single, correct methodology of error elimination. A set of hints has been presented that can improve results of further image analysis of pore space.
The paper presents the results and provides an analyse of the geometric structure of Fe-Al protective coatings, gas-treated under specified GDS conditions. The analysis of the surface topography was conducted on the basis of the results obtained from the SEM data. Topographic images were converted to three-dimensional maps, scaling the registered amplitude coordinates of specific gray levels to the relative range of 0÷1. This allowed us to assess the degree of surface development by determining the fractal dimension. At the same time, the generated three-dimensional spectra of the autocorrelation function enabled the researchers to determine the autocorrelation length (Sal) and the degree of anisotropy (Str) of the surfaces, in accordance with ISO 25178. Furthermore, the reconstructed three-dimensional images of the topography allowed us to evaluate the functional properties o the studied surfaces based on the Abbott-Firestone curve (A-F), also known as the bearing area curve. The ordinate describing the height of the profile was replaced by the percentage of surface amplitude in this method, so in effect the shares of the height of the three-dimensional topographic map profiles of various load-bearing properties were determined. In this way, both the relative height of peaks, core and recesses as well as their percentages were subsequently established.
The paper presents results of a research on simulation of magnetic tip-surface interaction as a function of the lift height in the magnetic force microscopy. As expected, magnetic signal monotonically decays with increasing lift height, but the question arises, whether or not optimal lift height eventually exists. To estimate such a lift height simple procedure is proposed in the paper based on the minimization of the fractal dimension of the averaged profile of the MFM signal. In this case, the fractal dimension serves as a measure of distortion of a pure tip-surface magnetic coupling by various side effects, e.g. thermal noise and contribution of topographic features. Obtained simulation results apparently agree with experimental data.
Electrical Discharge Machining (EDM) process with copper tool electrode is used to investigate the machining characteristics of AISI D2 tool steel material. The multi-wall carbon nanotube is mixed with dielectric fluids and its end characteristics like surface roughness, fractal dimension and metal removal rate (MRR) are analysed. In this EDM process, regression model is developed to predict surface roughness. The collection of experimental data is by using L9 Orthogonal Array. This study investigates the optimization of EDM machining parameters for AISI D2 Tool steel using Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. Analysis of variance (ANOVA) and F-test are used to check the validity of the regression model and to determine the significant parameter affecting the surface roughness. Atomic Force Microscope (AFM) is used to capture the machined image at micro size and using spectroscopy software the surface roughness and fractal dimensions are analysed. Later, the parameters are optimized using MINITAB 15 software, and regression equation is compared with the actual measurements of machining process parameters. The developed mathematical model is further coupled with Genetic Algorithm (GA) to determine the optimum conditions leading to the minimum surface roughness value of the workpiece.
Based on recent advances in non-linear analysis, the surface electromyography (sEMG) signal has been studied from the viewpoints of self-affinity and complexity. In this study, we examine usage of critical exponent analysis (CE) method, a fractal dimension (FD) estimator, to study properties of the sEMG signal and to deploy these properties to characterize different movements for gesture recognition. SEMG signals were recorded from thirty subjects with seven hand movements and eight muscle channels. Mean values and coefficient of variations of the CE from all experiments show that there are larger variations between hand movement types but there is small variation within the same type. It also shows that the CE feature related to the self-affine property for the sEMG signal extracted from different activities is in the range of 1.855~2.754. These results have also been evaluated by analysis-of-variance (p-value). Results show that the CE feature is more suitable to use as a learning parameter for a classifier compared with other representative features including root mean square, median frequency and Higuchi's method. Most p-values of the CE feature were less than 0.0001. Thus the FD that is computed by the CE method can be applied to be used as a feature for a wide variety of sEMG applications.