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1

Performance evaluation of the suspension system on Maglev trains based on measurement data

Ni Fei, Dai Yawen, Xu Junqi, Rong Lijun, Zheng Qinghua

Metrology and Measurement Systems

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2024

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Vol. 31, nr 1

115--133

EN

In order to ensure the safe operation of electromagnetic suspension (EMS) maglev trains, it is necessary to pay attention to the control loop performance of the suspension system. The suspension system with closed-loop control is tuned to achieve excellent performance at its early stage of operation. After running for a period of time, the control loop may encounter problems e.g., degraded operation, and paralysis may occur in severe cases. In order to quantify the control performance of the suspension system in an explicable manner, this paper proposed a data-driven control loop performance evaluation method based on fractal analysis, which does not require any external sensors and can be applied without data source restrictions such as dimension, volume and resolution. The control loop performances of such suspension systems were monitored, analysed, and evaluated by cross-sectional study, based on the field data of a commercial operation line in the commissioning stage. Furthermore, the track condition was revealed by capturing performance changes of the suspension system running on different guideway girders. The results demonstrate that the proposed method enables early warning of the degeneration of the suspension systems and the track.

2

Fractal dimensions analysis of branching streamers propagating in mineral oil

Dang Viet-Hung, Beroual Abderrahmane, Rózga Paweł

Archives of Electrical Engineering

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2022

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Vol. 71, nr 3

659--669

EN

This article deals with the analysis of the fractal dimension of streamers propagating in mineral oil, under lightning impulse voltage, using the box counting method; the method and technique of calculation are described therein. In the considered experimental conditions, the average velocities of recorded streamers are of 2.4 km/s and 1.8 km/s for positive and negative streamers, respectively; these velocities correspond to the 2nd mode of streamers propagation. It is shown that the streamers present the fractal dimension D ; and the higher D is the bushier are the streamers (i.e. with high branch density). The positive streamers can have higher D than the negative ones, if they are bushier.

3

Assessment of the Possibility of Using Fractal Analysis to Describe the Surface Aluminum Composites After Turning

Karolczak P., Kowalski M., Raszka K.

Advances in Science and Technology. Research Journal

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2021

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Vol. 15, no 4

49--60

EN

The description of the characteristics of the surface using standardized roughness parameters can not fully predict its performance properties. One of the tools supporting the assessment of the surface layer of the treated surface may be fractal analysis. This applies both to surfaces with machining traces, which are created under conditions of high randomness and variability of process conditions, and to surfaces with directional traces and their distinct periodicity. The paper presents the results of surface roughness measurements of turned aluminium matrix composites reinforced with ceramic fibers. Carbide and diamond tools were used for turning the tested material. The trials were carried out under dry machining conditions and with minimal lubrication in the cutting zone. Surfaces were measured by the contact method, and surface roughness parameters were calculated by Gaussian filtration. Then, the values of the fractal dimension were calculated using the enclosing box method. On the basis of these calculations, the influence of machining conditions on the values of selected roughness parameters and the box fractal dimension was determined. It was found that the fractal dimension, i.e. the irregularity of the geometric structure of the surface after turning of composites, changes with the change of cutting parameters, the tool and the method of lubricating the cutting zone. Of these factors, the feed has the greatest influence. As it grows, the irregularity of the machined surface structure decreases. In addition, the correlation coefficients between the fractal dimension and the measured roughness parameters were determined. It was noticed that the fractal dimension, in the case of turning aluminum composites, best correlates with the roughness parameters Sa and Ssk and thus describes features similar to these parameters. Therefore, it was assumed that it is possible to use fractal analysis as a supplementary tool for the description of the surface condition of aluminum composites after turning in various machining conditions. On the other hand, the fractal dimension can be treated as an additional tool to describe the surface condition, especially its irregularity, which is not described by other standard roughness parameters.

4

Wykorzystanie analizy fraktalnej oraz adaptacyjnej krzywej mocy do krótkoterminowych prognoz mocy elektrowni wiatrowych

Popławski Tomasz, Szeląg Piotr

Rynek Energii

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2020

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Nr 1

25--30

PL

Powstała stosunkowo niedawno teoria fraktalna ukazała odmienne od klasycznego podejście do opisu otaczającego nas świata. Zostały wykształcone nowe narzędzia pozwalające opisywać procesy dotąd trudne do zbadania. Analiza fraktalna jest wykorzystywana w wielu dziedzinach naukowych od biologii i medycyny poprzez geografię, a na informatyce kończąc. W artykule podjęto próbę wykorzystania pewnych elementów tej teorii, z powodzeniem stosowanych w innych dziedzinach nauki do analizy procesów związanych z generowaniem energii elektrycznej przez farmy wiatrowe. Skupiono się głównie na zbadaniu podobieństwa oraz samopodobieństwa procesów. Sprawdzano związki zachodzące między przebiegami prędkości wiatru oraz wytworzonej mocy, a wykładnikiem Hursta. Przeprowadzono badania dotyczące podobieństwa między stochastycznymi szeregami czasowymi jakimi są przebiegi prędkości wiatru oraz generowanej mocy dla danej turbiny wiatrowej. Opracowano model celem stworzenia krótkoterminowych prognoz produkcji energii elektrycznej w farmach wiatrowych. Wykorzystano podejście statystyczne, w którym głównym celem jest uchwycenie relacji między procesami (prędkość wiatru, a moc elektrowni wiatrowej).

EN

The relatively recent fractal theory has disclosed a description of the Word surrounding us different from the classical owe. New tools to describe processes difficult to be examined so far, have been developed. Fractal analysis is used in many areas of science, from biology and medicine to geography and computer science. In the paper an attempt has been made to avail of certain components of this theory, successfully applied in others fields of science, in order to analyze the processes of generating electricity by wind farms. Attention has been focused on examination of similarity and self-similarity. Relation-ships between power versus wind velocity dependencies and hurst exponent have been checked. Studies on similarity between stochastic time series (wind velocity time dependencies) and generated power for a given wind turbine have been carried out. On the basis of the studies a model has been developed in order to create short-term forecasts of electric energy production in wind farms. A statistical approach has been used, whose main goal is to find a relationship between the pro-cesses wind speed – generated energy.

5

Atomic force microscopy with fractal studies of temperature induced changes in the surface topography of polymeric materials

Rydzkowski Tomasz, Kulesza Sławomir, Bramowicz Mirosław, Michalska-Pożoga Iwona

Polimery

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2020

|

T. 65, nr 1

25--32

EN

Changes in the surface topography of polymeric materials can be analyzed to find the correspondence between observed surface features and specific external factors that might also influence physical and functional properties of the investigated material. In this work, atomic force microscopy (AFM) measurements were carried out to investigate the thermal changes in the surface topography as well as in the inner structure of the low density polyethylene (LDPE) samples subjected to 10 recirculations (rLDPE). For better assessment, fractal analysis and AFM results were additionally compared to DSC tests results.

PL

Analiza zmian topografii powierzchni materiałów polimerowych pozwala wyznaczyć zależności między obserwowanymi cechami powierzchni a określonymi czynnikami zewnętrznymi, które mogą wpływać na właściwości fizyczne i funkcjonalne badanego materiału. W niniejszej pracy metodą mikroskopii sił atomowych (AFM) oceniano zmiany termiczne topografii powierzchni, a także wewnętrznej struktury próbek polietylenu małej gęstości (LDPE) poddanych 10-krotnej recyrkulacji (rLDPE). Wyniki AFM i analizy fraktalnej porównywano z wynikami badań metodą różnicowej kalorymetrii skaningowej (DSC).

6

Surface micromorphology characterization of PDI8-CN2 thin films on H-Si by AFM analysis

Ţălu Ştefan, Kulesza Slawomir, Bramowicz Miroslaw, Solaymani Shahram, Ţălu Mihai, Nezafat Negin Beryani, Rezaee Sahar

Materials Science Poland

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2020

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Vol. 38, No. 2

334--340

EN

A nanoscale investigation of three-dimensional (3-D) surface micromorphology of archetypical N, N0- bis (n-etyl) x:y, dicyanoperylene- 3, 4:9, 10 bis (dicarboximide) (PDI8-CN2) thin films on H-Si substrates, which are applicable in n-type semiconducting compounds, has been performed by using fractal analysis. In addition, surface texture characteristics of the PDI8-CN2 thin films have been characterized by using atomic force microscopy (AFM) operated in tapping-mode in the air. These analyses revealed that all samples can be described well as fractal structures at nanometer scale and their three dimensional surface texture could be implemented in both graphical models and computer simulations.

7

Methods of fractal analysis and phase trajectories for the improvement of identification of complex technical systems

Chovnyuk Y. V., Gumenyuk Y. O., Djachenko L. A., Ivanov E. A., Kravchyuk V. T.

Zeszyty Naukowe. Quality. Production. Improvement

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2019

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No. 2 (11)

41--50

EN

The procedure of the qualitative analysis of complex technical systems is discussed. One may use such methods of analysis for time series characterized the functioning of such systems. These time serious aren’t confirmed the hypothesis of trend existence. One may use at this qualitative analysis the methods of nonlinear dynamics and the theory of chaos. The basis for similar researches is Takens’s theorem. The randomness of the studied dynamical system as the model of the complex technical system given by time realizations is established by means of Lyapunov’s indicator. The state stability is estimated by Hausdorf’s fractal dimension and the fractality index. Visual evaluation of the time series was carried out by means of the phase trajectory restoration procedure. As a result of the analysis of the phase points in the phase space the split attractor is indicated, which gives the chance to speak about its bifurcation.

8

Influence of gas detonation spraying parameters on the geometrical structure of Fe-Al intermetallic protective coatings

Chrostek Tomasz, Bramowicz Mirosław, Rychlik Kazimierz, Wojtkowiak Adam, Senderowski Cezary

Technical Sciences / University of Warmia and Mazury in Olsztyn

|

2019

|

nr 22(3)

249--262

EN

The paper presents the results of an analysis of the geometrical structure of Fe-Al intermetallic protective coatings sprayed under specified gun detonation spraying (GDS) conditions. Two barrel lengths, two powder injection positions (PIP) at the moment of spark detonation, and two numbers of GDS shots with 6.66 Hz frequency were applied as variable parameters in the GDS process. Surface profile measurements were conducted by contact profilometry with the use of the TOPO-01 system and the Mitutoyo SJ 210 profilometer. The measured parameters were used to analyze surface topography in two-dimensional (2D) and three-dimensional (3D) systems. It was assumed that roughness can be regarded as a non-stationary parameter of variance in surface amplitude which is highly dependent on the sampling rate and spraying distance. Therefore, changes in surface amplitude parameters and functional properties were analyzed across segments with a length (ln) of 1.25, 4 and 12.5 mm. The development of the geometric structure of the surface was analyzed with the RMS (Root Mean Square) fractal method, and the geometric structure of the surface stretched by several orders of magnitude was evaluated based on the correlation between roughness (Rq), segment length (ln) and fractal dimension (D). The RMS method and the calculated fractal dimension (D) supported the characterization of the geometric structure of intermetallic Fe-Al protective coatings subjected to GDS under the specified process conditions based on the roughness profiles of surface segments with a different length (ln).

9

Zastosowanie wymiaru fraktalnego do analizy obrazów płomienia w procesie współspalania

Sawicki D., Omiotek Z., Kotyra A.

Przegląd Elektrotechniczny

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2018

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R. 94, nr 7

142--145

PL

W pracy przedstawiono możliwość zastosowania wymiaru fraktalnego do identyfikacji stanu procesu współspalania pyłu węglowego i biomasy. Przebadano dziewięć wariantów (klas) procesu współspalania z różnymi wartościami mocy cieplnej, wydatku powietrza i paliwa, przy 30% udziale biomasy. Wyniki pokazały, że wartość średnia wymiaru fraktalnego (szacowanego różnymi metodami) wykazuje tendencję do grupowania, co stwarza możliwości wykorzystania tego narzędzia w systemie automatycznej klasyfikacji.

EN

This paper presents use of the fractal dimension to identify co-firing pulverized coal and biomass process state. In research nine variants (classes) of co-firing process with different heating power, fuel at 30% of the biomass share and air flow were tested. Experimental results show that average value of fractal dimensions (estimated by various methods) tends to group, which makes possibilities to use this implements as the automatic classification system.

10

Peculiarities of the radio signals and hindrances in the navigation system of the remote-piloted vehicles

Mykyjchuk M., Markiv V.

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2018

|

T. 8, nr 1

40--43

EN

The article dwells upon the peculiarities of radio signals concerning the use of remote-piloted vehicles. It is highlighted that it is important take into consideration the fractal analysis of remote-piloted vehicles based on diverse fractal dimensions. The significance of remote-piloted vehicle control system investigation based on radio signals is presented. Also it is highlighted that there are many hindrances during the remote-piloted vehicle flight and it is important to take them into consideration and develop methods in order to omit them. Also the vital role of remote-piloted vehicles in different spheres of life, for example, in environment research is depicted.

PL

W artykule został poruszony temat cech sygnałów radiowych w przypadku ich zastosowania w bezzałogowych statkach powietrznych. W pracy podkreśla się istotność bazowania na fraktalnych wymiarach podczas analizy fraktalnej bezzałogowych statków powietrznych. Podkreślono znaczenie sygnałów radiowych w systemach sterowania. Przedstawiono istnienie wielu utrudnień podczas lotów bezzałogowych statków powietrznych oraz wskazano na konieczność uwzględniania i opracowania metod uniknięcia tych utrudnień. Podkreślono również istotną rolę bezzałogowych statków powietrznych w różnych sferach życia, na przykład w badaniach środowiska.

11

Functional and Fractal Properties of Fe-Al Coatings After Gas Detonation Spraying (GDS)

Chrostek T., Rychlik K., Bramowicz M., Senderowski C.

Archives of Metallurgy and Materials

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2018

|

Vol. 63, iss. 4

1993--1999

EN

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 of 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.

12

Application of Fractal Analysis Methods for Lift Height Optimization in Magnetic Force Microscopy Measurements

Bramowicz M., Kulesza S., Chrostek T., Sendrowski C.

Archives of Metallurgy and Materials

|

2018

|

Vol. 63, iss. 3

1109--1113

EN

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 aris es, 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 ser ves 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.

13

Fractal and frequency based analysis of rough surfaces produced by different machining operations on hardened alloy steel parts

Żak K.

Advances in Manufacturing Science and Technology

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2018

|

Vol. 42, nr 1-4

43--53

EN

The paper presents an original approach to the characterization of the surface profiles/surface topographies produced on hardened steel parts using CBN tools. The experimental investigations involve recording of surface profiles and surface topographies for three different machining operations, namely hard turning, ball burnishing and superfinish in order to obtain a comparable value of the Sa (Ra) parameter of 0.2 μm. Both fractal and frequency analysis were performed in order to obtain the fractal dimension (Sfd) and the signal amplitude and the wavelength which were estimated from the power spectral density (PSD) spectra. The correlations between the Sz (Sa) roughness parameter and the fractal dimension were documented as well as appropriate relations with the frequency characteristics. In particular, the multi-fractal approach to the complex machined surfaces was discussed.

PL

W artykule przedstawiono opracowane nowe podejście do charakterystyki profili powierzchni/topografii powierzchni hartowanych stalowych elementów maszyn obrabianych przy użyciu narzędzi CBN. Badania eksperymentalne obejmowały określenie profili powierzchni i topografii powierzchni dla trzech różnych operacji obróbki – toczenia na twardo, nagniatania i dogładzania oscylacyjnego w celu uzyskania porównywalnej wartości parametru Sa (Ra) – 0,2 μm. Analizę fraktalną i częstotliwościową prowadzono dla ustalenia wymiaru fraktalnego (Sfd) oraz amplitudy sygnału i długości fali. Zostały oszacowane na podstawie gęstości widmowej mocy (PSD). Określono korelację pomiędzy parametrem chropowatości Sz (Sa) i wymiarem fraktalnym. Także ustalono ich zależności od charakterystyk częstotliwości. W szczególności uwzględniono w prowadzonej analizie multifraktalne podejście dla powierzchni złożonych.

14

A single scaling parameter as a first approximation to describe the rainfall pattern of a place: application on Catalonia

Casas-Castillo M. C., Llabrés-Brustenga A., Rius A., Rodríguez-Solà R., Navarro X.

Acta Geophysica

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2018

|

Vol. 66, no. 3

415--424

EN

As well as in other natural processes, it has been frequently observed that the phenomenon arising from the rainfall generation process presents fractal self-similarity of statistical type, and thus, rainfall series generally show scaling properties. Based on this fact, there is a methodology, simple scaling, which is used quite broadly to find or reproduce the intensity–duration–frequency curves of a place. In the present work, the relationship of the simple scaling parameter with the characteristic rainfall pattern of the area of study has been investigated. The calculation of this scaling parameter has been performed from 147 daily rainfall selected series covering the temporal period between 1883 and 2016 over the Catalonian territory (Spain) and its nearby surroundings, and a discussion about the relationship between the scaling parameter spatial distribution and rainfall pattern, as well as about trends of this scaling parameter over the past decades possibly due to climate change, has been presented.

15

Characteristics of porous beds based on fractal parameters

Bramowicz M., Kulesza S., Sobieski W.

Technical Sciences / University of Warmia and Mazury in Olsztyn

|

2017

|

nr 20(2)

171--179

EN

The paper presents the results of a fractal analysis of the cross-sections of a porous mineral deposit consisting of spherical elements which formed a spatial system with varying porosity (0.4 to 0.95). The virtual deposit was generated using the Discrete Element Method in the YADE code by means of the so-called Radius Expansion Method. The fractal analysis was carried out using the structure function method, determining the fractal dimension (D), the topothesy (L) and the corner frequency (l) (MAINSAH et al. 2001). The conducted simulations have confirmed to a considerable extent the test results available in the literature involving the fractal analysis of mineral deposits with varying porosity. They clearly indicate that the fractal dimension does not change along with the porosity of the deposit, if the autocorrelation function or their transformations (e.g. structure function) methods are used. Moreover, based on the information available in the literature, it can be concluded that the value of the fractal dimension corresponds to mineral deposits with the specified geometric shapes of the elements which form them.

16

Fractal analysis of the grey and binary images in diagnosis of Hashimoto's thyroiditis

Omiotek Z.

Biocybernetics and Biomedical Engineering

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2017

|

Vol. 37, no. 4

655--665

EN

In the study, a fractal analysis of thyroid ultrasound images was applied. This method has not been too often used for testing such kind of images so far. Its advantage is a tool in a form of a fractal dimension, which easily quantifies a complexity of an image texture surface. There is a close relationship between the lesions and an ultrasound image texture in a case of a diffuse form of the Hashimoto's disease. As a result of the analysis, a set of nine fractal descriptors was obtained which made it possible to distinguish healthy cases from sick ones that suffer from the diffuse form of the Hashimoto's thyroiditis. The Hellwig's method for feature selection was utilised. It found the combinations of features of the highest value of the information capacity index. These combinations were applied to build and test five popular classifiers. The following methods were implemented: decision tree, random forests, K-nearest neighbours, linear and quadratic discriminant analysis. The best results were achieved with a combination of three descriptors – fractal dimension and intercept obtained by the power spectral density method and fractal dimension estimated by the box counting method. The LDA (linear discriminant analysis) classifier based on them was characterised by a sensitivity of 96.88%, a specificity at a level of 98.44%, and its overall classification accuracy was equal to 97.66%. These results are similar to the best results of other authors cited in the work where the greyscale image analysis was used.

17

Improvement of the vibration diagnostics of rotation shaft damage based on fractal analysis

Bouraou N., Pavlovskyi O., Pazdrii O.

Vibrations in Physical Systems

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2016

|

Vol. 27

61--66

EN

This work is devoted to further research and improvement of the vibration diagnostics of the initial crack-like damage of rotation shaft in aviation gas-turbine engines (GTE). We propose to use fractal analysis of the accelerating shaft response in order to increase the damage detection efficiency. Responses of the accelerating shaft are derived by using simulation in absence and in presence of the initial traverse crack. The responses of the cracked shaft have sub-critical peaks; the increase in size of a crack leads to the increase in peak values of the vibration amplitude in the range of sub-harmonic resonances. The Hurst exponent is obtained for the time series in the range of sub-harmonic resonances. The research shows that a small change in the crack size results in considerable change of the Hurst exponent, which allows to detect the mentioned sub-harmonic resonances of the measured signal in order to identify the initial crack-like damage of the rotation shaft.

18

Comparison of efficiency of extraction of built-up areas in aerial images using fractal analysis and morphological granulometry

Kupidura P., Popławski W., Sitko P.

Teledetekcja Środowiska

|

2015

|

T. 52

29--37

EN

The paper presents a comparison of results of the automatic extraction of built-up areas, based on fractal analysis and granulometric maps, in the aerial images. Built-up areas as a land-use class can be clearly seen in an aerial or satellite image, due to its high granularity, but for the same reason they are very difficult to extract using a “traditional” non-contextual, pixel-based classification. Both approaches presented in the paper, using fractal analysis and morphological granulometry, base generally on a pixel-based classification, but performed on images reviously processed using these two types of processes. Fractal analysis consists in an empirical computing of fractal dimension of parts of an image, using a box-counting method. Such an approach generates an image where pixel values are equal to a fractal dimension values of their neighbourhood. Since we can interpret a fractal dimension as a level of granularity, a simple reclassification of such an image can improve a performance of an automatic extraction of built-up area effectively. The approach based on a morphological granulometry creates a number of granulometric maps – images where pixel values mean an amount of objects of certain size in a set neighbouring fragment of an image. This way a number of these images can be processed using a pixel-based classification, to perform an effective extraction of built-up areas in an image. The results of the presented approaches have been compared to the reference mask obtained basing on a visual interpretation of the image.

19

Surface morphology of titanium nitride thin films synthesized by DC reactive magnetron sputtering

Talu S., Stach S., Valedbagi S., Elahi S. M., Bavadi R.

Materials Science Poland

|

2015

|

Vol. 33, No. 1

137--143

EN

In this paper the influence of temperature on the 3-D surface morphology of titanium nitride (TiN) thin films synthesized by DC reactive magnetron sputtering has been analyzed. The 3-D morphology variation of TiN thin films grown on p-type Si (100) wafers was investigated at four different deposition temperatures (473 K, 573 K, 673 K, 773 K) in order to evaluate the relation among the 3-D micro-textured surfaces. The 3-D surface morphology of TiN thin films was characterized by means of atomic force microscopy (AFM) and fractal analysis applied to the AFM data. The 3-D surface morphology revealed the fractal geometry of TiN thin films at nanometer scale. The global scale properties of 3-D surface geometry were quantitatively estimated using the fractal dimensions D, determined by the morphological envelopes method. The fractal dimension D increased with the substrate temperature variation from 2.36 (at 473 K) to 2.66 (at 673 K) and then decreased to 2.33 (at 773 K). The fractal analysis in correlation with the averaged power spectral density (surface) yielded better quantitative results of morphological changes in the TiN thin films caused by substrate temperature variations, which were more precise, detailed, coherent and reproducible. It can be inferred that fractal analysis can be easily applied for the investigation of morphology evolution of different film/substrate interface phases obtained using different thin-film technologies.

20

Wpływ warunków flokulacji na cechy morfologiczne i wymiary fraktalne agregatów komórek glonów

Jodłowski A., Gutkowska E.

Instal

|

2015

|

nr 12

79--82

PL

W pracy przedstawiono wyniki badań nad zmianami parametrów morfologicznych oraz wymiarów fraktalnych agregatów komórek zielenicy Monoraphidium contortum powstających w wyniku koagulacji prowadzonej chlorkiem żelaza (III). Prowadząc badania z użyciem mikroskopowego analizatora obrazu stwierdzono, że zwiększanie czasu flokulacji wpływało na zmiany wymiaru fraktalnego D2 oraz kolistości i wypukłości agregatów, a wzrost intensywności wolnego mieszania powodował wydłużanie agregatów, o czym świadczyły zmniejszające się wartości D1, D2 oraz zwiększanie parametru wydłużenia.

EN

This paper presents results of the research on morphological parameters and fractal dimensions changes of Monoraphidium contortum cell aggregates resulting from coagulation conducted using ferric chloride (III). Microscopic image analyzer was used during the studies. Effect of flocculation time on particle morphology was particularly noticeable in relation to the fractal dimension D2 and morphological parameters as circularity andconvexity. Mixing intensity intensification a tendency towards an increase in the agglomerates elongation expressed as decreasing values of D1, D2, and increasing the parameter elongation.