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Set of Suffosion Holes Occurring After a Water Supply Failure as a Structure with Fractal Features

Iwanek Małgorzata

Journal of Ecological Engineering

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2022

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Vol. 23, nr 6

164--171

EN

As a result of a buried water pipe unsealing, water often flows from the pipe to the soil surface, washing out the solid particles of soil and creating the so-called suffosion holes. It is a dangerous phenomenon, especially in urbanized areas, where it poses a threat to human safety and the stability of infrastructure. Uncontrolled outflows of water from water pipes belong to the main causes of suffosion in cities, occur in all water networks around the world and are difficult to predict. Therefore, it seems to be important to determine the size of the so-called the protection zone, which is the area around the potential leak where, in the event of a water pipe failure, it would be possible for water to flow in the soil. The analysis of the suffosion holes distribution around the place of leakage may be helpful in determining the size of the protection zone. Previous studies have shown that this distribution is random. Thus, the structure consisting of suffusion holes creates a certain geometric shape, which is difficult to describe using the classical concepts of Euclidean geometry. The study showed that this structure meets the conditions for probabilistic fractals, which means that elements of fractal geometry can be used to determine the size of the protection zone.

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Fractal Geometry in Designing and Operating Water Networks

Iwanek Małgorzata, Kowalski Dariusz, Kowalska Beata, Suchorab Paweł

Journal of Ecological Engineering

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2020

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Vol. 21, nr 6

229--236

EN

Fractals are self-similar sets that cannot be easily described by classical geometry. Fractal sets have been implemented in almost all areas of human activity since they were introduced to science by Mandelbrot in 1982. For the last 10 years, the interest in fractal geometry has increased by the issues connected with water distribution networks (WDNs). The aim of this paper was to review the application of fractal geometry in designing and operating WDNs. Treating a WDN as a fractal pattern enables its description and classification, simplifies the assessment of a network reliability, helps to solve the problems of routing and dimensioning WDN, as well as enables to select the places to locate measurement points in a network to control water quality, pressure in pipes and water flow rate. Moreover, the application of tree-shaped fractal patterns to reflect WDNs helps to solve the problems of their optimization. Fractal geometry can be also applied to investigate the results of WDNs failures connected with leakage of water to the ground. Using fractal dimension of a pattern created by points reflecting places of water outflow on the soil surface after a prospective pipe breakage enables to determine the zone near a pipe, where the outflow of water on the soil surface is possible. It is an important approach for the security of humans and existing infrastructure. Usage of fractal geometry in description, optimisation and operation analysis of WDNs still continues, which confirms the efficiency of fractal geometry as a research tool. On the other hand, it can be supposed that fractal geometry possibilities have still not been fully used.

3

Classification of abnormalities in mammograms by new asymmetric fractal features

Beheshti S. M. A., Noubari H. A., Fatemizadeh E., Khalili M.

Biocybernetics and Biomedical Engineering

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2016

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Vol. 36, no. 1

56--65

EN

In this paper we use fractal method for detection and diagnosis of abnormalities in mammograms. We have used 168 images that were carefully selected by a radiologist and their abnormalities were also confirmed by biopsy. These images included asymmetric lesions, architectural distortion, normal tissue and mass lesion where in case of mass lesion they included circumscribed benign, ill-defined and spiculated malignant masses. At first, by using wavelet transform and piecewise linear coefficient mapping, image enhancement were done. Secondly detection of lesions was done by fractal method as a ROI. Since in investigation of breast cancer, it is important that fibroglandular tissues in both breasts be symmetric and for each asymmetric density, evaluation for malignancy is necessary, we define new fractal features based on extracting asymmetric information from lesions. The fractal features were evaluated on 5 data sets using SVM classifier which enabled to achieve high accuracy in classification of mammograms and diagnostic results. We have also investigated the performance of image enhancement in classification of each data set which shows different effects of enhancement on different lesion types.

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Wykorzystanie cech fraktalnych ekstrahowanych z sygnałów radarowych w procesie specyficznej identyfikacji

Dudczyk J., Kawalec A.

Przegląd Elektrotechniczny

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2014

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R. 90, nr 11

212--215

PL

W artykule przedstawiono procedurę rozpoznawania źródeł emisji radarowych o śladowo dystynktywnych cechach pierwotnych sygnału. Wykorzystano w tym celu cechy fraktalne ekstrahowane z sygnałów radarowych pochodzących od tych źródeł emisji. Procedura ta jest specyficznym rodzajem identyfikacji, znana jako Specific Emitter Identification. W wyniku zastosowanej procedury, możliwa jest jednoznaczna identyfikacja źródła sygnału radarowego co do jego egzemplarza.

EN

This article presents the procedure of radar emitter sources identification with low distinctive primary features of a signal. Fractal features extracted from incoming radar signals have been used during this method. This procedure is a specific type of recognition called Specific Emitter Identification. As a result of this procedure it is possible to identify a radar copy of the same type more precisely.

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Identification of emitter sources in the aspect of their fractal features

Dudczyk J., Kawalec A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2013

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Vol. 61, nr 3

623--628

EN

This article presents the procedure of identification radar emitter sources with the trace distinctive features of original signal with the use of fractal features. It is a specific kind of identification called Specific Emitter Identification, where as a result of using transformations, which change measure points, a transformation attractor was received. The use of linear regression and the Lagrange polynomial interpolation resulted in the estimation of the measurement function. The method analysing properties of the measurement function which has been suggested by the authors caused the extraction of two additional distinctive features. These features extended the vector of basic radar signals’ parameters. The extended vector of radar signals’ features made it possible to identify the copy of radar emitter source.