• 한국기계가공학회지
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• 제7권4호
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• pp.109-114
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• 2008

The fractal dimension aims to quantitatively define the irregular characteristics of the shape in nature. It can be useful in describing morphological characteristics of various wear particles. This paper was undertaken to diagnose failure condition for sliding members in lubrication using fractal dimension. The experiments were undertaken to analyze the shape of wear particles and to diagnose failure condition for sliding members in lubrication using the image processing and the fractal parameters. It was possible to diagnose wear mechanism, friction, and damage state of machines through analysis of shape characteristics for wear particle in driven condition using fractal parameters.

• 한국공작기계학회논문집
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• 제11권1호
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• pp.77-82
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• 2002

It is known that fractal theory has recently been used as a useful in the characterization of surface texture and the understanding of tribological phenomena such as friction wear and lubrication The fractal based method for describing the rubbed surface texture has aroused great interest In this paper the fractal descriptors was applied to rubbed surface of hydraulic driving material with image processing system in order to describe morphology of the rubbed surface The results showed that the fractal dimension can be determined by sum of intensity difference of surface pixel. The two step size to get fractal dimension is similar to surface roughness Ra. Fractal dimensions of the rubbed surfaces increase with an increase of applied load Morphology of the rubbed surface driving in lubricant can be effectively obtained by fractal dimensions.

• Structural Engineering and Mechanics
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• 제57권3호
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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.

• 국제학술발표논문집
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• The 6th International Conference on Construction Engineering and Project Management
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• pp.463-467
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• 2015

Mega-shock means a sporadic event such as the earning shock, which occurred by sudden market changes, and it can cause serious problems of profit loss of international construction projects. Therefore, the early response and prevention by analyzing and predicting the Mega-shock is critical for successful project delivery. This research is preliminary study to develop a prediction model that supports market condition analysis and Mega-shock forecasting. To avoid disadvantages of classic statistical approaches that assume the market factors are linear and independent and thus have limitations to explain complex interrelationship among a range of international market factors, the research team explored the Fractal Theory that can explain self-similarity and recursiveness of construction market changes. The research first found out correlation of the major market factors by statistically analyzing time-series data. The research then conducted a base of the Fractal analysis to distinguish features of fractal from data. The outcome will have potential to contribute to building up a foundation of the early shock warning system for the strategic international project management.

• 한국지역지리학회지
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• 제11권6호
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• pp.530-542
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• 2005

본 연구에서는 지형이 위치별로 자기 상사성을 가진다는 전제하에 프랙탈 차원을 이용한 지형의 복잡성을 표현해 보고자 한다. 특히 수치지도 분석기법에서 표면적요소를 산정하여 프랙탈 차원을 산정하도록 한다. 또한 프랙탈 차원과 지형 형상요소들과의 관계를 규명하고, 프랙탈 차원의 통계적 대표치로서의 기능에 대해 고찰해 보려한다. 본 연구에서는 GIS기법을 적용하여 지형의 프랙탈 특성을 구하였다. 길이를 이용하여 하천이나 해안선의 1차원적 프랙탈 특성을 구하는 것에서 벗어나 면적의 개념 즉, 투영면적과 표면적을 이용하여 지형의 2차원적 프랙탈 특성을 구해보았다. 그리고 프랙탈 차원과 평균경사도와의 상관관계를 검토해 보았다. 연구결과 다음과 같은 결론을 얻게 되었다. 1) 프랙탈 차원을 구하기 위한 척도로서 표면적을 사용한 경우에서도 일반적 프랙탈 차원의 특성과 같이 지형의 복잡성과 비례관계의 성질을 나타내었다. 2) 본 연구에서 제안한 표면적을 이용한 프랙탈 차원은 영천지역에서는 $2.10{\sim}2.24$이고 의성지역은 $2.02{\sim}2.15$으로 나타났다. 이 값들은 통상 알려진 지형의 프랙탈 차원인 $2.10{\sim}2.20$의 범위에 든다. 3) 평균 경사도와 프랙탈 차원의 상관관계는 평균경사도가 $25^{\circ}$ 이상인 지역에서 결정계수 $R^2$값이 $25^{\circ}$ 이하인 지역에 비해 30% 정도 작아진다. 그러므로 모든 지형의 거침도를 표현하기 위해선 프랙탈 차원이 알맞을 것으로 본다. 본 연구결과를 통해 투영면적과 표면적을 이용한 프랙탈 차원 산정공식이 유효함을 확인하였다. 그러나 본 기법이 충분히 타당성을 인정받기 위해선 연구대상지역의 확대를 통하여 경사도와 표면적, 프랙탈 차원과의 상관관계를 더욱 명확히 할 필요가 있다. 향후 연구에선 지형의 복원에 적용 할 수 있을 것이며 fBm모델을 이용하여 교통류 해석에도 적용이 가능할 것이다.

• 물과 미래
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• 제28권5호
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• pp.117-127
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• 1995

해상도를 고려하는 GIUH 모형에 대한 적용과 분석을 평창강 유역의 소유역인 이목정유역에 대하여 수행하였다. 모형의 적용과 Fractal 분석을 위해 1:25,000, 1:50,000 그리고 1:100,000 축척의 지도를 이용하였다. 따라서 축척간의 비율이 일정한 값을 갖는다. 링크의 길이는 해상도 1mm의 구장기를 이용하였고 Fractal 차원은 Richardson 방법을 사용하였다. 지도의 축척에 따라 매개변수들의 현저한 변화를 발견하였으며 이러한 경향은 매개변수의 물리적 의미를 상실하게 한다. 그런데 Fractal 변환과 의 Melton지형법칙은 이러한 규모문제를 효과적으로 조정해주는 역할을 할 수 있다. 그리고 이 방법은 하도망과 유역간의 연관성을 모형에 반영할 수 있는 장점이 있다. 이 연구에서 제안한 GIUH의 적용성을 검증하기 위해 지수형 GIUH 모형과 비교하였다. 그 결과 제안된 2모수 gamma GIUH 모형이 좋은 재현성을 보였다. 따라서 Fractal 이론을 도입한 2모수 gamma GIUH 모형은 축척을 고려하는 IUH를 유도하는데 있어서 적절하다고 할 수 있다.

• Imaging Science in Dentistry
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• 제40권3호
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• pp.123-129
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• 2010

Purpose : To evaluate the effect of surgical treatment of ligature-induced peri-implantitis in dogs using fractal analysis. Also, the capabilities of fractal analysis as bone analysis techniques were compared with those of histomorphometric analysis. Materials and Methods : A total of 24 implants were inserted in 6 dogs. After a 3-months, experimental periimplantitis characterized by a bone loss of about 3 mm was established by inducing with wires. Surgical treatment involving flap procedure, debridement of implants surface with chlorhexidine and saline (group 1), guided bone regeneration (GBR) with absorbable collagen membrane and mineralized bone graft (group 2), and $CO_2$ laser application with GBR (group 3) were performed. After animals were sacrificed in 8 and 16 weeks respectively, bone sections including implants were made. Fractal dimensions were calculated by box-counting method on the skeletonized images, made from each region of interest, including five screws at medial and distal aspects of implant, were selected. Results : Statistically significant differences in the fractal dimensions between the group 1($0.9340{\pm}0.0126$) and group 3($0.9783{\pm}0.0118$) at 16 weeks were found (P<0.05). The fractal dimension was statistically significant different between 8($0.9395{\pm}0.0283$) and 16 weeks in group 3 (P<0.05). These results were similar with the result of the evaluation of new bone formation in histomorphometric analysis. Conclusions : Treatment of experimental peri-implantitis by using $CO_2$ laser with GBR is more useful than other treatments in the formation of new bone and also the tendency of fractal dimension to increase relative to healing time may be a useful means of evaluating.

• Geomechanics and Engineering
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• 제4권3호
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• pp.219-227
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• 2012

Pavement management systems require systematic monitoring of pavement surfaces to determine preventive and corrective maintenance. The process involves the accumulation of large amounts of visual data, typically obtained from site visitation. The pavement surface condition is then correlated to a pavement distress index that is based on a scoring system previously established by state or federal agencies. The scoring system determines if the pavement section requires maintenance, overlay or reconstruction. One of the surface distresses forming part of the overall pavement distress index is the Alligator Crack Index (AC Index). The AC Index involves the visual evaluation of the crack severity of a section of a pavement as being low, medium, or high. This evaluation is then integrated into a formula in order to obtain the AC Index. In this study a quantification of the visual evaluation of the severity of alligator cracking is carried out using photographs and the fractal dimension concept from fractal theory. Pavements with low levels of cracking were found to have a fractal dimension equal to 1.051. Pavements with moderate levels of cracking had a fractal dimension equal to 1.1754. Pavements with high degrees of cracking had a fractal dimension that varied between 1.5037 (high) and 1.7111 (very high). Pavements with a level of cracking equal to 1.8976 represented pavements that disintegrated and developed potholes. Thus, the visual evaluation of the state of cracking of a pavement (the AC Index) could be enhanced with the use of the fractal dimension concept from fractal theory.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2009년도 IWAIT
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• pp.655-658
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• 2009

Fractal dimension has been used for texture analysis as it is highly correlated with human perception of surface roughness and applied to quantifying the structures of wide range of objects in biology and medicine. On the other hand, the evaluation of the human skin state is based solely on the subjective assessment of clinicians; this assessment may vary from moment to moment and from rater to rater. Therefore we attempt to analysis of skin texture image using fractal dimension and discuss its application to evaluating human skin state. It can be helpful for extracting human features and also can be useful for detection of many human skin diseases. This paper presents a method to calculate fractal dimension of skin with use of camera lens magnification. We take multiple pictures frequently from skin with different camera lens magnification as a magnification factor of fractal set, and counting the number of objects (cells) in each picture as a number of self similar pieces of fractal set.

• 치과방사선
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• 제28권1호
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• pp.17-26
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• 1998

The purpose of this study was to investigate whether a radiographic estimate of osseous fractal dimension is useful in the characterization of structural changes in bone. Ten specimens of bone were progressively decalcified in fresh 50 ml solutions of 0.1 N hydrochloric acid solution at cummulative timed periods of 5, 10, 20, 30, 60 and 90 minutes, and radiographed from 0 degree projection angle controlled by intraoral parelleling device. The test set of 70 radiographs was digitized and digitally filtered to reduce film -grain noise. I performed one-dimensional variance and fractal analysis of bony profiles or scan lines. Correlation analysis quantified the relationship between variance and fractal dimension. The obtained results were as follow. 1. After the first stage of decalcification variance and fractal dimension of scan line pixel intensities generally decreased with a range of 57.94 to 12.64 and 1.59 to 1.36. 2. Correlation coefficient(r) relating variances to fractal dimensions was consistantly excellent(range r=0.90 to 0.98). 3. Variance and fractal dimension were much alike in ability to discriminate, at leat on a group basis, between control and decalcified specimens.