• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2001.11a
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• pp.53-58
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• 2001

Fractal dimension is the method to measure the roughness and the irregularity of something that cannot be defined obviously by Euclidean dimension. And the analysis method of this dimension don't need perfect, accurate boundary and color like analysis lot diameter, perimeter, aspect or reflectivity of wear particles or surface. If we arranged the morphological characteristic of various wear particle by using the characteristic of fractal dimension, it might be very efficient to the diagnosis of driving condition. In order to describe morphology of various wear particle, the wear test was carried out under friction experimental conditions. And fractal descriptors was applied to boundary and surface of wear particle with image processing system. These descriptors to analyze shape and surface wear particle are boundary fractal dimension and surface fractal dimension.

• KCI Concrete Journal
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• v.14 no.1
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• pp.30-35
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• 2002

The fractal geometry is a non-Euclidean geometry which describes the naturally irregular or fragmented shapes, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cementitious composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is apparent.ent.

• Speech Sciences
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• v.10 no.2
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• pp.45-55
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• 2003

Strange attractor can be used as a presentation method for signal processing. Fractal dimension is well known method that extract features from attractor. Even though the method provides powerful capabilities for speech processing, there is drawback which should be solved in advance. Normally, the size of the raw signal should be long enough for processing if we use the fractal dimension method. However, in the area of connected-digits problem, normally, syllable or semi-syllable based processing is applied. In this case, there is no evidence that we have sufficient data or not to extract characteristics of attractor. This paper discusses the relationship between the size of the signal data and the calculation result of fractal dimension, and also discusses the efficient way to be applied to connected-digit recognition.

• Journal of Electrical Engineering and Technology
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• v.6 no.3
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• pp.391-396
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• 2011

The tracking pattern formed on the dielectric surface due to a surface electrical discharge exhibits fractal structure. In order to quantitatively investigate the fractal characteristics of the surface tracking pattern, the dielectric breakdown model has been employed to numerically generate the surface tracking pattern. In dielectric breakdown model, the pattern growth is determined stochastically by a probability function depending on the local electric potential difference. For the computation of the electric potential for all points of the lattice, a two-dimensional discrete Laplace equation is solved by mean of the successive over-relaxation method combined to the Gauss-Seidel method. The box counting method has been used to calculate the fractal dimensions of the simulated patterns with various exponent $\eta$ and breakdown voltage $\phi_b$. As a result of the simulation, it is found that the fractal nature of the surface tracking pattern depends strongly on $\eta$ and $\phi_b$.

• Smart Structures and Systems
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• v.13 no.6
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• pp.975-991
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• 2014

The objective of this study is to develop a reliable method for locating cracks in a beam using data fusion of fractal dimension features of operating deflection shapes. The Katz's fractal dimension curve of an operating deflection shape is used as a basic feature of damage. Like most available damage features, the Katz's fractal dimension curve has a notable limitation in characterizing damage: it is unresponsive to damage near the nodes of structural deformation responses, e.g., operating deflection shapes. To address this limitation, data fusion of Katz's fractal dimension curves of various operating deflection shapes is used to create a sophisticated fractal damage feature, the 'overall Katz's fractal dimension curve'. This overall Katz's fractal dimension curve has the distinctive capability of overcoming the nodal effect of operating deflection shapes so that it maximizes responsiveness to damage and reliability of damage localization. The method is applied to the detection of damage in numerical and experimental cases of cantilever beams with single/multiple cracks, with high-resolution operating deflection shapes acquired by a scanning laser vibrometer. Results show that the overall Katz's fractal dimension curve can locate single/multiple cracks in beams with significantly improved accuracy and reliability in comparison to the existing method. Data fusion of fractal dimension features of operating deflection shapes provides a viable strategy for identifying damage in beam-type structures, with robustness against node effects.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.5 no.1
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• pp.7-12
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• 2006

Recently, the fractal interpolation methods have been widely introduced and used to estimate and analyze various theoretical and experimental data. Because of the chaotic behaviors of dynamic cutting force data, some method for end-milling force analysis must be used. The fractal analysis used in this paper is fractal linear interpolation and fractal dimension. Also, several methods for computing fractal dimensions have been used in which the fractal dimension of the typical dynamic end-milling force was calculated according to number of data points that are generally lower than 200 data points sampled. This fractal analysis shows a possible prediction of end-milling force that has some dynamic chatter property or stationary property in endmilling operation.

• Structural Engineering and Mechanics
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• v.57 no.3
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• pp.529-541
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• 2016

Under the interaction between dam body, dam foundation and external environment, the dam structural behavior presents the time-varying nonlinear characteristics. According to the prototypical observations, the correct identification on above nonlinear characteristics is very important for dam safety control. It is difficult to implement the description, analysis and diagnosis for dam structural behavior by use of any linear method. Based on the rescaled range analysis approach, the algorithm is proposed to identify and extract the fractal feature on observed dam structural behavior. The displacement behavior of one actual dam is taken as an example. The fractal long-range correlation for observed displacement behavior is analyzed and revealed. The feasibility and validity of the proposed method is verified. It is indicated that the mechanism evidence can be provided for the prediction and diagnosis of dam structural behavior by using the fractal identification method. The proposed approach has a high potential for other similar applications.

• Journal of Broadcast Engineering
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• v.4 no.2
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• pp.127-133
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• 1999

The conventional fractal image compression based on discrete wavelet transform uses the fixed block size in fractal coding and reduces PSNR at low bit rate. This paper proposes a fractal image coding based on discrete wavelet transform which improves PSNR by using variable block size in fractal coding. In the proposed method. the absolute values of discrete wavelet transform coefficients are computed. and the discrete wavelet transform coefficients of different highpass subbands corresponding to the same spatial block are assembled. and the fractal code for the range block of each range block level is assigned. and then a decision tree C. the set of choices among fractal coding. "0" encoding. and scalar quantization is generated and a set of scalar quantizers q is chosen. And then the wavelet coefficients. fractal codes. and the choice items in the decision tree are entropy coded by using an adaptive arithmetic coder. This proposed method improved PSNR at low bit rate and could achieve a blockless reconstructed image. As the results of experiment. the proposed method obtained better PSNR and higher compression ratio than the conventional fractal coding method and wavelet transform coding.rm coding.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.6D
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• pp.905-913
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• 2008

Recently, concrete tracks are introduced into high-speed railroads as an alternative to ballast tracks. Concrete tracks are superior to ballast tracks in the aspect of durability, maintenance and safety. However, deteriorated stiffness of railroad bed and settlement of soft ground induced by trapped or seepage water lead to problems in safety of train operation. In this research, flexural rigidity of concrete tracks was employed as an index of track displacement and a new seismic technique called FRACTAL (Flexural-Rigidity Assessment of Concrete Tracks by Antisymmetric Lamb Waves) method was proposed to delineate flexural rigidity of concrete tracks in a 2-D image. In this paper, to establish theoretical background, parametric research was performed using numerical simulations of stress-wave tests at concrete tracks. Feasibility of the FRACTAL technique was proved at a real concrete track for Korean high-speed trains. Validity of the FRACTAL technique was also verified by comparing the results of impulse-response tests performed at the same measurement array and the results of DC resistivity survey performed at a shoulder nearby the track.

• Journal of the Korean association of regional geographers
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• v.11 no.6
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• pp.530-542
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• 2005

In this study, GIS method has been used to get fractal characteristics. Using the projected area and surface area, 2 dimensional fractal characteristic of terrain was found out. Correlation of fractal dimension and mean slope were also checked over. Results are as below. 1) To get a fractal dimension, the method which is using the surface area is also directly proportional to complexity of the terrain as other fractal dimension. 2) Fractal dimensions using the surface area, that is proposed in this thesis are carried out as below : Uiseong : $2.02{\sim}2.15$ Yeongcheon : $2.10{\sim}2.24$. These values are in a range of fractal $2.10{\sim}2.20$ dimensions which has known. 3) Correlation of mean slope and fractal dimension is diminished about 30% in a region which is more than $25^{\circ}$ of mean slope. So, in this region using the fractal dimension method is better than using the mean slope. From this study, on formula using the projected area and surface area is still good to get a fractal dimension that has been found. But to confirm this method the region of research should be wider and be set up the correlation of mean slope, surface area and fractal dimension. It can be applicable to restoration of terrain and traffic flow analysis in the future research.