• Journal of the Korean Society for Precision Engineering
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• v.16 no.12
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• pp.143-151
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• 1999

The shape of surface micro-crack is very irregular due to nonhomogeneous microstructure but is very important in respect to qualitative estimation of fatigue life. Fractal geomety can quantify the shape of surface mciro-crack. Fractal dimension is measured for surface micro-cracks with coast line and box counting method and estimates cycle ration in Al 2024-T3. The average fractal dimension $D_{favg}$ of surface micro-cracks has 3-parameter weibull distribution and location parameter is nearly constant but shape parameter decreases as cycle ration increases. The fractal dimension by coast line method is measured for individual surface micro-crack but the fractal dimension by box countin method is measured for all the surface micro-cracks under sampling area. Therefore, This paper shows fractal dimension $D_{fb}$ can predict cycle ratio $N/N_f$ more convenient than fractal dimension $D_{favg}$.

• Geomechanics and Engineering
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• v.9 no.5
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• pp.619-629
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• 2015

Influenced by various mining activities, fractures in rock masses have different densities, set numbers and lengths, which induce different mechanical properties and failure modes of rock masses. Therefore, precisely expressing the failure criterion of the fractured rock influenced by coal mining is significant for the support design, safety assessment and disaster prevention of underground mining engineering subjected to multiple mining activities. By adopting PFC2D particle flow simulation software, this study investigated the propagation and fractal evolution laws of the micro cracks occurring in two typical kinds of rocks under uniaxial compressive condition. Furthermore, it calculated compressive strengths of the rocks with different confining pressures and box-counting dimensions. Moreover, the quantitative relation between the box-counting dimension of the rocks and the empirical parameters m and s in Hoek-Brown strength criterion was established. Results showed that with the increase of the strain, the box-counting dimension of the rocks first increased slowly at the beginning and then exhibited an exponential increase approximately. In the case of small strains of same value, the box-counting dimensions of hard rocks were smaller than those of weak rocks, while the former increased rapidly and were larger than the latter under large strain. The results also presented that there was a negative correlation between the parameters m and s in Hoek-Brown strength criterion and the box-counting dimension of the rocks suffering from variable mining activities. In other words, as the box-counting dimensions increased, the parameters m and s decreased linearly, and their relationship could be described using first order polynomial function.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10c
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• pp.636-638
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• 1998

여러 다양한 프랙탈 구조의 차원을 측정하는 개량된 프랙탈 차원 측정 방법을 제안하였다. 기존의 box counting 방법은 사용상의 편리성은 있으나 측정에 사용되는 데이터에 의존적이어서 기존 box counting방법의 약점을 보완, 개량한 방법의 적용으로 프랙탈 차원의 보다 정확한 측정결과를 얻었다.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.9
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• pp.710-715
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• 2016

Due to its simplicity and high reliability, the box-counting(BC) method is one of the most frequently used techniques to estimate the fractal dimensions of a binary image with a self-similarity property. The fractal calculation requires data sampling that determines the size of boxes to be sampled from the given image and directly affects the accuracy of the fractal dimension estimation. There are three non-overlapping regular grid methods: geometric-step method, arithmetic-step method and divisor-step method. These methods have some drawbacks when the image size M becomes large. This paper presents a BC algorithm for enhancing the accuracy of the fractal dimension estimation based on a new sampling method. Instead of using the geometric-step method, the new sampling method, called the coverage ratio-step method, selects the number of steps according to the coverage ratio. A set of experiments using well-known fractal images showed that the proposed method outperforms the existing BC method and the triangular BC method.

• Architectural research
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• v.16 no.4
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• pp.175-183
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• 2014

Contemporary architecture tends to deconstruct modern architecture based on rationalization just like reductionism and functionalism and secedes from it. It means change from mechanical to organic and ecological view of the world. According to these changes, consideration of a compositive relationship presented variety and complexity in architecture. Thus, the modern speculation based on rationalism cannot provide an alternative interpretation about complicated architectural phenomena. At this point in time, the purpose of this study is to investigate the possibilities of the fractal as an alternative tool of analysis and design in contemporary architecture. In this study, two major aspects are discussed. First, the fractal concepts just like 'fractal dimension', 'box-counting dimension' and 'fractal rhythm' can be applied to analysis in architecture. Second, the fractal formative principles just like 'scaling', 'superimposition trace', 'distortion' and 'repetition' can be applied to design in architecture. Fractal geometry similar to nature's patterned order can provide endless possibilities for analysis and design in architecture. Therefore further study of fractal geometry should be conducted synthetically from now on.

• Journal of the Korean Society of Safety
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• v.17 no.4
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• pp.38-44
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• 2002

The application of fractal concept provides an useful method in the study for the quantitative analysis of irregular variations like the fracture surfaces and crack profiles. Fractal curves have characteristics that represents a self-similarity based on the fractal dimension. The fractal dimensions were obtained by the box counting method. In this report, we obtained the nearly stable fractal dimensions of fracture crack profiles for STS316 with CT specimen as the crack advances and the relationships between crack length and fractal dimension. Moreover fractal fracture parameter that corresponds to J-R curve is shown by the relationships between fractal dimension and crack extension. From the results, we concluded that crack extension of high toughness material also shows the fractal characteristics, which can be used in order to evaluate the crack life precisely.

• Proceedings of the KSEEG Conference
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• 2005.04a
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• pp.160-160
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• 2005

• Journal of Advanced Marine Engineering and Technology
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• v.22 no.4
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• pp.522-528
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• 1998

This paper presents a fundamental fractal characteristics of the growing crack that has an irregularity producing a zigzag crack contour. This irregularity is analysed by a fractal geometry in a box counting method that is a very simple technique. First the fractal dimensions and actual fractal extensive crack length are obtained. Also a fractal fracture energy relation with a fractal dimension is found so as to get fractal crack behaviors. Thus it can be shown that the fractal dimension has a possibility as a fracture parameter in a real crack growth length meaning.

• Wind and Structures
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• v.31 no.4
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• pp.363-371
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• 2020

Proper understanding of offshore wind speed variability is of essential importance in practice, which provides useful information to a wide range of coastal and marine activities. In this paper, long-term wind speed data recorded at various offshore stations are analyzed in the framework of fractal dimension analysis. Fractal analysis is a well-established data analysis tool, which is particularly suitable to determine the complexity in time series from a quantitative point of view. The fractal dimension is estimated using the conventional box-counting method. The results suggest that the wind speed data are generally fractals, which are likely to exhibit a persistent nature. The mean fractal dimension varies from 1.31 at an offshore weather station to 1.43 at an urban station, which is mainly associated with surface roughness condition. Monthly variability of fractal dimension at offshore stations is well-defined, which often possess larger values during hotter months and lower values during winter. This is partly attributed to the effect of thermal instability. In addition, with an increase in measurement interval, the mean and minimum fractal dimension decrease, whereas the maximum and coefficient of variation increase in parallel.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.2
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• pp.121-125
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• 2015

In this paper, we propose a method that extracts features from character patterns using the fractal dimension of chaos theory. The input character pattern image is converted into time-series data. Then, using the modified Henon system suggested in this paper, it determines the last features of the character pattern image after calculating the box-counting dimension, natural measure, information bit, and information (fractal) dimension. Finally, character pattern recognition is performed by statistically finding each information bit that shows the minimum difference compared with a normalized character pattern database.