• Structural Engineering and Mechanics
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• 제23권2호
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• pp.147-161
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• 2006

Recent developments in fractal theory suggest that fractal may provide a more realistic representation of characteristics of cementitious materials. In this paper, the roughness of fracture surfaces in cementitious material has been characterized by fractal theory. A systematic experimental investigation was carried out to examine the dependency of fracture parameters on the aggregate sizes as well as the loading rates. Three maximum aggregate sizes (4.76 mm, 12.7 mm, and 19.1 mm) and two loading rates (slow and fast loading rate) were used. A total of 25 compression tests and 25 tension tests were performed. All fracture parameters exhibited an increase, to varying degrees, when aggregates were added to the mortar matrix. The fracture surfaces of the specimens were digitized and analyzed. Results of the fractal analysis suggested that concrete fracture surfaces exhibit fractal characteristics, and the fractal geometry provide a useful tool for characterizing nonlinear fracture behavior of concrete. Fractal dimension D was monotonically increased as maximum aggregate sizes increase. A new fractal fracture model was developed which considers the size and shape of aggregate, and the crack paths in the constituent phases. Detailed analyses were given for four different types of fracture paths. The fractal fracture model can estimate fractal dimension for multiphase composites.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2007년도 Proceedings of ISRS 2007
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• pp.616-619
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• 2007

Nowadays, urbanized area expands its boundary, and distribution of urbanized area is gradually transformed into more complicated pattern. In Korea, SMA(Seoul Metropolitan Area) has outstanding urbanized area since 1950s. But it is ambiguous whether urban distribution is clustered or dispersed. This study aims to show the way in which expansion of urbanized area impacts on spatial distribution pattern of urbanized area. We use quadrat analysis, nearest-neighbor analysis and fractal analysis to know distribution pattern of urbanized area in time-series urban growth. The quadrat analysis indicates that distribution pattern of urbanized area is clustered but the cohesion is gradually weakened. And the nearest-neighbor analysis shows that point patterns are changed that urbanized area distribution pattern is progressively changed from clustered pattern into dispersed pattern. The fractal dimension analysis shows that 1972's distribution dimension is 1.428 and 2000's dimension is 1.777. Therefore, as time goes by, the complexity of urbanized area is more increased through the years. As a result, we can show that the cohesion of the urbanized area is weakened and complicated.

• Journal of the Korean Data and Information Science Society
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• 제24권1호
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• pp.53-62
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• 2013

현재 세계기상기구에 등록되어 있는 우리나라 기후관측소는 11개 지점이다. 11개 지점의 분포를 보면 지리적으로 균일하지 못하고 대부분이 해안에 위치하는 편중된 분포를 보이고 있다. 따라서 기후관측소 자료를 바탕으로 하는 전국 기후자료 생산 및 특성 산출을 위해서는 관측소 밀도에 관한 분석을 통해 기후자료 분포에 대한 균형도의 측정이 필요하다. 본 연구에서는 상관적분 기법을 이용한 프랙탈 차원의 추정을 통해 우리나라 기후관측소 밀도를 측정하였다. 상관적분 기법 적용시 회귀분석을 통하여 추정된 회귀계수로 프랙탈 차원을 추정한다. 추정된 프랙탈 차원을 이용해 전국의 기상관서들 중 지리적으로 기후관측소 구성의 균형도를 가장 높여 줄 수 있는 기후관측소 후보지점을 선정하였다. 이 때 후보지점을 순차적으로 선택하는 방식과 조합의 형태로 여러 후보지점을 한 번에 선택하는 방식으로 각각 최적의 후보지점들을 선택하였다.

• Computers and Concrete
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• 제2권3호
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• pp.239-248
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• 2005

The article presents the results of examination of the fractal dimension D of concrete specimen fracture surfaces obtained in fracture toughness tests. The concretes were made from three different types of coarse aggregate: gravel, dolomite and basalt aggregate. Ordinary concretes (C40) and high-performance concretes (HPC) were subjected to testing after 7, 14, 28 and 90 days of curing, respectively. In fracture toughness and compressive tests, different behaviours of concretes were found, depending on the type of aggregate and class of concrete (C40, HPC). A significant increase in the strength parameters tested occurred also after a period of 28 days (up to the $90^{th}$ day of curing) and was particularly large for concretes C40. Fractal examinations performed on fracture replicas showed that the fractal dimension D was diverse, depending on the coarse aggregate type and concrete class being, however, statistically constant after 7 and 14 days for respective concretes during curing. The fractal dimension D was the greater, the worse strength properties were possessed by the concrete. A cross-grain crack propagation occurred in that case, due to weak cohesion forces at the coarse aggregate/mortar interface. A similar effect was observed for C40 and HPC made from the same aggregate. A greater dimension D was exhibited by concretes C40, in which case the fracture was easier to form compared with high-performance concretes, where, as a result of high aggregate/mortar cohesion forces, the crack propagation was of inter-granular type, and the resulted fracture was flatter.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1997년도 하계학술대회 논문집 E
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• pp.1758-1760
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• 1997

Automatic detection system to detect acoustic emission pulse and fractal dimension were developed, to observe tree deterioration phenomena in LDPE. The purpose of our work are to use acoustic emission system and fractal dimension and to investigate the treeing phenomena in polymeric insulation under applied AC voltage 11[kV] with an artificial needle-shaped void(1.5[mm]) using the above system. We analyzed and phase angle-acoustic emission pulse amplitude-deterioration time ($\Phi$-AEA-t) pattern and phase angle-acoustic emission pulse number-deterioration time($\Phi$-AEN-t) pattern using statistical operators such as skewness, fractal dimension. In this paper show that the correlation of $\Phi$-AEA-t, $\Phi$-AEN-t, fractal dimension using regression analysis by the method of least squares can be used to predict the breakdown just before the breakdown occurs.

• 조명전기설비학회논문지
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• 제24권1호
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• pp.124-129
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• 2010

페놀수지가 그 표면에 흐르는 누설전류에 의하여 탄화되는 경우 탄화패턴은 페놀수지의 탄화특성을 결정하는 가장 중요한 인자 중의 하나이다. 그러나 전형적인 페놀수지의 탄화패턴은 매우 복잡하기 때문에 종래의 유클리드 기하학을 이용하여 해석하는 것은 어려운 일이다. 이와 같이 복잡한 형태는 대부분의 경우 프랙탈 구조를 나타낸다. 따라서 주어진 페놀수지에 대한 탄화패턴의 특성을 프랙탈 해석으로 규명할 수 있다. 본 논문에서는 누설전류에 의하여 탄화된 페놀수지의 탄화패턴을 정량적으로 조사하기 위하여 누설전류의 크기와 전극간격의 함수로서 탄화패턴의 프랙탈 차원을 계산하였다. 계산의 신뢰성을 위하여 박스 카운팅 방법뿐만 아니라 상관함수를 이용하여 프랙탈 차원을 구하였다. 계산 결과에 따르면 전극간격을 일정하게 유지한 상태에서 전류가 증가하면 프랙탈 차원은 증가하였다. 반면, 전류가 일정할 때 전극간격과 프랙탈 차원 사이에는 큰 관련성이 없었다.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• 제38권2호
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• pp.96-100
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• 2012

Objectives: This study sought to evaluate trabecular changes in the mandible using fractal analysis and to explain the transient osteopenia related to rapid orthodontic tooth movement after orthognathic surgery. Materials and Methods: Panoramic radiographs were taken of 26 patients who underwent bilateral sagittal split ramus osteotomy. Radiographs taken before the surgery and 1 month after surgery were overlapped, and $40{\times}40$ pixel square regions of interest were selected near the mandibular canines and 1st molars. After the image processing procedure, the fractal dimension was calculated using the box-counting method. Results: Fractal dimension after orthognathic surgery decreased in a statistically significant manner (P<0.05). The change in fractal dimension on the canine side had greater statistical significance as compared to that seen on the 1st molar side. Conclusion: This study found that bone density decreases after orthognathic surgery due to transient osteopenia related to the regional acceleratory phenomenon. This result can provide a guide to evaluating orthodontic tooth movement after orthognathic surgery.

• 한국생산제조학회지
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• 제7권5호
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• pp.7-14
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• 1998

In this paper, Fractal analysis applied to evaluate machined surface profile. The spectrum method was used to calculate fractal dimension of generated surface profiles by Weierstrass-Mandelbrot fractal function. To avoid estimation errors by low frequency characteristics of FFT, the Maximum Entropy Method (MEM) was examined. We suggest a new criterion to define the MEM order m. MEM power spectrum with our criterion is proved to be advantageous by the comparison with the experimental results.

• 한국지반공학회논문집
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• 제18권6호
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• pp.25-32
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• 2002

전통적인 흙의 입도분포 곡선상에서 흙의 구성 성분에 따른 프랙탈 차원의 변화에 대해서 Wu등(1993)과Bittelli 등(1999)의 연구결과를 중심으로 Buchan 등(1993)의 실험결과를 이용하여 고찰하였다. 자료분석시에는 실트와 모래의 경계값의 변화에 따른 프랙탈 차원의 변화를 알아보기 위하여 20$\mu{m}$, 63$\mu{m}$ 그리고 125$\mu{m}$에 대한 프랙탈 차원을 산정하여 전체 범위에서 구한 프랙탈 차원과 비교하였다. 분석결과에서는 전통적인 입도분포곡선상에서 프랙탈 차원의 산정은 가능한 것으로 나타났으며, 실트와 모래성분의 경계값은 Wu 등(1993)이 제시한 것 보다 Bittelli 등(1999)이 제시한 경계값이 더 적절함을 알 수 있었다. 또한 Bittelli 등(1999)이 제시한 실험식을 이용해서 실트영역의 프랙탈 차원을 비교적 정확하게 산정할 수 있었다.

• 한국해양공학회지
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• 제14권1호
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• pp.29-36
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• 2000

Surface micro-crack grows along intergranular or transgranular region of crystal grains. But if it meets the barrier such as sessile dislocation and precipitates it loses straightness and deflects. Investigators had many difficulties in estimating fatigue life of smooth specimen because of the random distribution growth and coalescence of surface micro-cracks. The path of surface micro-crack has irregularity due to nonhomogeneous microstructure. Euclidian geometry can't quantify the shape of surface micro-crack but fractal geometry can. Therefore in this paper fractal dimension is measured at various stage of cycle ratio and estimated cycle ratio in 2024-T3 aluminium, alloy.