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 analysis of the fractal dimension becomes one of the new approach features in spatial research. This approach bases on the perception of space as a living structure, an organism which in its complexity and heterogeneity is a multi-scale creation although holistically perceived. The aim of the authors was to determine the nationwide fractal dimensions for the distinguished construction categories and designation of general regularities in these layout.
Combine harvesters are the source a large amount of noise in agriculture. Depending on different working conditions, the noise of such machines can have a significant effect on the hearing condition of drivers. Therefore, it is highly important to study the noise signals caused by these machines and find solutions for reducing the produced noise. The present study was carried out is order to obtain the fractal dimension (FD) of the noise signals in Sampo and John Deere combine harvesters in different operational conditions. The noise signals of the combines were recorded with different engine speeds, operational conditions, gear states, and locations. Four methods of direct estimations of the FD of the waveform in the time domain with three sliding windows with lengths of 50, 100, and 200 ms were employed. The results showed that the Fractal Dimension/Sound Pressure Level [dB] in John Deere and Sampo combines varied in the ranges of 1.44/96.8 to 1.57/103.2 and 1.23/92.3 to 1.51/104.1, respectively. The cabins of Sampo and John Deere combines reduced and enhanced these amounts, respectively. With an increase in the length of the sliding windows and the engine speed of the combines, the amount of FD increased. In other words, the size of the suitable window depends on the extraction method of calculating the FD. The results also showed that the type of the gearbox used in the combines could have a tangible effect on the trend of changes in the FD.
Lower Carboniferous limestone has been extracted in the “Czatkowice” open-pit hill-slope quarry in southern Poland since 1947, for the needs of metallurgical and building industries, as well as farming. We can distinguish two aquifers in the Czatkowice area: the Quaternary porous aquifer and the Carboniferous fissure-porous one. Two vertical zones representing different hydrodynamic characteristics can be indentified in the Carboniferous formations. One is a weathering zone and the other one the zone of fissures and interbedding planes. Groundwater inflows into the quarry workings have been observed at the lowest mining level (+315 m above the sea level (asl)) for over 30 years. This study concerns two hypotheses of the sources of such inflows originating either from (a) the aeration zone or from (b) the saturation zone. Inflows into the quarry combine into one stream flowing gravitationally to the doline under the pile in the western part of the quarry. This situation does not cause a dewatering need. Extending eastward mining and lowering of the exploitation level lead to increased inflows.
The analysis of particle size in suspensions carried out with use of the laser diffraction method enables us to obtain not only information about the size of particles, but also about their properties, shape and spatial structure, determined basing on fractal dimension. The fractal dimension permits the evaluation of the interior of aggregates, at the same time showing the degree of complexity of the matter. In literature, much attention is paid to the evaluation of the fractal dimension of flocs in activated sludge, in the aspect of control of single processes, i.e. sedimentation, dehydration, coagulation or flocculation. However, results of research concerning the size of particles and the structure of suspensions existing in raw and treated sewage are still lacking. The study presents optical fractal dimensions D3 and particle size distributions measured with use of laser granulometer in raw and treated sewage and activated sludge collected from six mechanical-biological wastewater treatment plants located in the Lower Silesian region. The obtained test results demonstrate that wastewater treatment plants that use both sequencing batch reactors and continuous flow reactors are more efficient at capturing suspension particles of a size up to 30 μm and are characterized by an increased removal of particles of a size ranging from 30 μm to 550 μm to the outflow. Additionally, in the case of samples of treated sewage and activated sludge collected at the same location, at short intervals, similar particle distributions were observed. As far as the analysis of fractal dimensions is concerned, particles contained in the raw sewage suspension were characterized by the lowest values of the fractal dimension (median equals 1.89), while the highest values occurred in particles of activated sludge (median equals 2.18). This proves that the spatial structure of suspension particles contained in raw sewage was similar to a linear structure, with a large amount of open spaces, while the structure of particles contained in the activated sludge suspension was significantly more complex in the spatial aspect.
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.