• 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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.1
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• pp.145-149
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• 2023

High-resolution images of surfaces provide detailed information on pores or shapes with specific sizes ranging from nano sizes to micrometers. However, it is not yet clear to determine an efficient association for pores or shapes from high-resolution images of surfaces. For the efficient association of pores and shapes, the surface characteristics of the device were considered as fractal dimensions by taking SEM photographs and binarizing the images. The fractal program was directly coded for surface analysis of the device. The device surface characteristics and electrical characteristics are thought to be related to the fractal dimension. The fractal dimension decreased with an increase in internal pores. The density and grain boundary of particles, which are structural characteristics of the device surface, were related to the fractal dimension. The particle size decreased with an increase in the fractal dimension and was uniformly formed. When the particles were uniformly formed, fewer pores were present and the fractal dimension increased.

• ETRI Journal
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• v.33 no.6
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• pp.849-856
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• 2011

This research introduces three new fractal array configurations that have superior performance over the well-known Sierpinski fractal array. These arrays are based on the fractal shapes Dragon, Twig, and a new shape which will be called Flap fractal. Their superiority comes from the low side lobe level and/or the wide angle between the main lobe and the side lobes, which improves the signal-to-intersymbol interference and signal-to-noise ratio. Their performance is compared to the known array configurations: uniform, random, and Sierpinski fractal arrays.

• 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.

• Proceedings of the KIEE Conference
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• 2006.07e
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• pp.55-56
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• 2006

In prevention and diagnostic system of GIS, pattern classification is focused on the detection of unnatural patterns in PD(Partial discharge) image data. Fractals have been used extensively to provide a description and to model mathematically many of the naturally occurring complex shapes, such as coastlines, mountain ranges, clouds, etc., and have also received increased attention in the field of image processing, for purposes of segmentation and recognition of regions and objects present in natural scenes. Among the numerous fractal features that could be defined and used for image data, fractal dimension and lacunarity have been found to be useful for recognition purposes Partial discharge(PD) occuring in GIS system is a very complex phenomenon, and more so are the shapes of the various 2-d patterns obtained during routine tests and measurements. It has been fairly well established that these pattern shapes and underlying defects causing PD have a 1:1 correspondence, and therefore methods to describe and qunatify these pattern shapes must be explored, before recognition systems based on them could be developed. The computed fractal features(fractal dimension and lacunarity) for standard library of PD data were analyzed and found to possess fairly reasonable pattern discriminating abilities. This new approach appears promising, and further research is essential before any long-term predictions can be made.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.333-338
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• 2001

Fractal geometry is a non-Euclidean geometry which has been developed to quantitative analysis irregular or fractional shapes. Fractal dimension of irregular surface has fractal values ranging from 2 to 3 and of irregular line profile has fractal values ranging from 1 to 2. In this paper, quantitative analysis of crack growth patterns during the fracture processing of fiber-reinforced cement composites based on fractal geometry. The fracture behaviors of fiber reinforced mortar beams subjected to three-point loading in flexure. The beams all had a single notch depth, but varing volume fractions of polypropylene, cellulose fibers. The crack growth behaviors, as observed through the image processing system, and the box counting method was used to determine the fractal dimension, Df. The results showed that the linear correlation exists between fractal dimension and fracture energy of the fiber reinforced cement mortar.

• Korean Institute of Interior Design Journal
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• no.37
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• pp.12-20
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• 2003

The purpose of this study is to propose a new design principles and to analyze the pattern of art and architecture applying fractal concepts. As this study is based on fractal geometry as a natural science, 1 intented to explain the concepts and provide some methods of generating fractal properties. Two major aspects are discussed. Frist, fractals are geometric shapes that are self-similar, in other words, they iterate a basic shape at ever increasing a decreasing dimensions. Self-similarity, irregularity, and scaling are fundamental characteristics of fractal geometry. Second, the fractal concepts of art and design can be analyzed and used as a critical tool. In both criticism and design, fractals provides a tool In fine, fractal geometry can be provided endless possibilities for artists and designers intended in expressing the more complex underlying rhythms and organic patterns of nature.

• Korean Institute of Interior Design Journal
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• v.23 no.1
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• pp.88-95
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• 2014

This study intended arousal of other viewpoints that deal with and understand spaces and shapes, by describing the concept of 'dimensions' into visual patterns. Above all, the core concept of spatial dimensions was defined as 'expandability'. Then, first, the 'golden ratio', 'Fibonacci sequence', and 'fractal theory' were defined as elements of each dimension by stage. Second, a 'unit cell' of one dimension as 'minimum unit particles' was set. Next, Fibonacci sequence was set as an extended concept into two dimensions. Expansion into three dimensions was applied to the concept of 'self-similarity repetition' of 'Fractal'. In 'fractal dimension', the concept of 'regularity of irregularity' was set as a core attribute. Plus, Platonic solids were applied as a background concept of the setting of the 'unit cell' from the viewpoint of 'minimum unit particles'. Third, while 'characteristic patterns' which are shown in the courses of 'expansion' of each dimension were embodied for the visual expression forms of dimensions, expansion forms of dimensions are based on the premise of volume, directional nature, and concept of axes. Expressed shapes of each dimension are shown into visually diverse patterns and unexpected formative aspects, along with the expression of relative blank spaces originated from dualism. On the basis of these results, the 'unit cell' that is set as a concept of theoretical factor can be defined as a minimum factor of a basic algorism caused by other purpose. In here, by applying diverse pattern types, the fact that meaning spaces, shapes, and dimensions can be extracted was suggested.

• Journal of Fashion Business
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• v.22 no.1
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• pp.135-147
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• 2018

Since the 20th century, there has been a growing interest in the new concept of fractals, a combination of mathematics and art, and the attempt to study the creative spatial aspects of the concept is being made. The purpose of this research is to examine artistic characteristics of fractal dimension and then analyze the types of fractal dimensions expressed in the fashion. Previous literature on fractals and dimension, and visual data on art and fashion collected over the Internet were used for analysis. Fractal dimension refers to the spatial concept of structural dimension of geometrical self-similarity. An analysis of the types of fractals seen in fashion revealed spatial expansion, the repetition in continual figures, superposition accordant to different sizes, and shades of different shapes. The aesthetic characteristics of fractal dimension appearing in fashions were examined based on analyses of fractal dimension types; the inherent characteristics of self-similarity, superimposition, and atypicality were found. Results obtained from this study are expected to be used as basic materials for the application of the design of fractal dimension into various perspectives of fashion.

• Journal of Korea Game Society
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• v.16 no.1
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• pp.119-128
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• 2016

In this paper, we consider an improved deformation method of IFS(iterated function system) fractal using codes of fractal points. In the existing deformation methods, the intermediate results of position dependent partial deformation propagate randomly due to the randomly selected maps of iteration. Therefore, in many cases, the obtained results become somewhat monotonous feeling shapes. To improve these limitations, we propose a method in which the selection of maps are controlled by codes of fractal points. Applying this method, we can obtain interesting fractal deformation conforming with its fractal features. Also, we propose a simple method, incorporating state variables, that can be applied to deformation of some fractal features other than position coordinates.