• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1995.10a
• /
• pp.161-164
• /
• 1995

Nonlinear analysis of various phenomena has been developed with improvement of computer. The characteristics form nonlinear analysis are available in monitoring and diagnosis state of system. There are many nonlinear property in cutting process, but nonlinear signals have been considered as noise. In this study, nonlinear analysis technique is applied and it will be verified that cutting force is chaos by calculating Lyapunov exponents,fractal dimension and embedding dimension. The relation between characteristic parameter calculated form sensor signal and various cutting condition is investigated.

• Imaging Science in Dentistry
• /
• v.41 no.2
• /
• pp.71-78
• /
• 2011

Purpose : This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Materials and Methods : Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. Results : The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. Conclusion : The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm.

• Imaging Science in Dentistry
• /
• v.36 no.4
• /
• pp.183-188
• /
• 2006

Purpose: The purpose of this research was to study bone changes after bilateral sagittal split osteotomy through fractal analysis and measurement of mandibular cortical thickness. Materials and Methods: This study included twenty-two prognathic patients who underwent bilateral sagittal split osteotomy. Panoramic radiographs of these patients were taken immediately before operation and at 1 month, 6 months, and 12 months postoperatively. The fractal dimension was measured by the box-counting method in the region of interest centered on both the basal and interdental bones between the first and second mandibular molars. Measurements of mandibular cortical thickness were taken both in the area between the first and second mandibular molars and at the osteotomy site. Changes of fractal dimension and cortical thickness over four stages were statistically analyzed. Results: The fractal dimension of the mandibular basal bone before surgery and after 1 month, 6 months and 12 months were $1.4099{\pm}0.0657,\;1.382{\pm}0.0595,\;1.2995{\pm}0.0949,\;and\;1.4166{\pm}0.0676$, respectively (Repeated-measures ANOVA, P<0.001). However, no statistically significant differences were noted in interdental fractal dimensions among the four stages. Mandibular cortical thickness between the first and second mandibular molars before operation and after 1 month, 6 months and 12 months was $3.74{\pm}0.48mm,\;3.63{\pm}0.47mm,\;3.41{\pm}0.61mm\;and\;3.55{\pm}0.66mm$ (P<0.01), respectively. Mandibular cortical thickness at the osteotomy site at each of the four stages was $3.22{\pm}0.44mm,\;2.87{\pm}0.59mm,\;2.37{\pm}0.61mm\;and\;2.64{\pm}0.62mm$, respectively (P<0.001). Conclusion: This study suggests that the mandibular tissue continued decreasing for 6 months postoperatively and then increased over the subsequent 6 months.

• Journal of Educational Research in Mathematics
• /
• v.19 no.2
• /
• pp.341-354
• /
• 2009

The purpose of this study is to show the Fractals activities for mathematically gifted students, and to analyze the constructions on Fractals of the mathematically gifted. The subjects of this study were 5 mathematically gifted students in the Gifted Education Institut and also 6th graders at elementary schools. These activities on Fractals focused on constructing Fractals with the students' rules and were performed three ways; Fractal cards, colouring rules, Fractal curves. Analysis of collected data revealed in as follows: First, the constructions on Fractals transformed the ratios of lines and were changed using oblique lines or curves. Second, to make colouring rules on Fractals, students presented the sensitivities of initial and fractal dimensions on Fractals. In conclusion, this study suggested the importance of communication and mathematical approaches in the mathematics classrooms for the mathematically gifted.

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

• Transactions of the Society of Information Storage Systems
• /
• v.2 no.1
• /
• pp.43-49
• /
• 2006

Fractal/angle multiplexing is a $LiNBO_3$ crystal using a X-Y Galvano mirror, and the random access concept in fractal/angle multiplexing are discussed in this paper. First, the brief introduction of the designed holographic digital data storage system is presented. Then, the average access time concept for the storage system is newly defined, and the comparison of the average access time between the holographic storage and a conventional optical disk is performed. Second, the basic simulation and experiment to find the X-Y Galvano mirror dynamics are conducted. From this analysis, we find that the average access time in our HDDS which has 6 degree scan angle is about 5 msec. This result is very high performance when it compared with the average access time of a conventional optical disk. Finally, some recording results using fractal/angle multiplexing are presented, then, the relationship between bit error rate and angle mismatch for the each multiplexing are discussed.

• Geomechanics and Engineering
• /
• v.1 no.4
• /
• pp.323-335
• /
• 2009

Gravels forming part of the base of flexible pavements experience abrasion and crushing as a result of static and dynamic loads. Abrasion takes place when the sharp corners of the particles of gravel are removed as a result of compressive and shear loads. As a result of abrasion, the particles change in shape. Crushing is caused by the fragmentation of the particles into a mixture of many small particles of varying sizes. In this study, the abrasion and crushing of gravels are evaluated experimentally and analytically. The laboratory component of this study involves gravels that were subjected to abrasion and dynamic compression tests. The evaluation of the abrasion and crushing experienced by the gravel was carried out using fractals. In this study, the fractal dimension concept from fractal theory is used to evaluate: (a) the changes in shape, and (b) the crushing (fragmentation) of the original particles of gravel. It was determined that the fractal dimension of the profile of the particles decreased as a result of abrasion. With respect to crushing, the fragmentation fractal dimension was found to increase with the degree of breakage of the gravel. To understand the influence of crushing on the permeability of the gravels, the hydraulic conductivity of the gravels was measured before and after crushing. The hydraulic conductivity of the gravels was found to decrease with an increase in their level of crushing. Also, changes in the angle of friction of the granular materials as a result of abrasion was calculated using the Krumbein's roundness chart. The angle of friction of the granular materials was found to decrease as a result of abrasion.

• Journal of Welding and Joining
• /
• v.16 no.5
• /
• pp.108-118
• /
• 1998

This study proposes th analysis and evaluation method of time series ultrasonic signal using the chaos feature extraction for ultrasonic pattern recognition. Features extracted from time series data using the chaos time series signal analyze quantitatively weld defects. For this purpose, analysis objective in this study is fractal dimension and Lyapunov exponent. Trajectory changes in the strange attractor indicated that even same type of defects carried substantial difference in chaosity resulting from distance shifts such as 0.5 and 1.0 skip distance. Such differences in chaosity enables the evaluation of unique features of defects in the weld zone. In quantitative chaos feature extraction, feature values of 4.511 and 0.091 in the case of side hole and 4.539 and 0.115 in the case of vertical hole were proposed on the basis of fractal dimension and Lyapunov exponent. Proposed chaos feature extraction in this study can enhances ultrasonic pattern recognition results from defect signals of weld zone such as side hole and vertical hole.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.233-236
• /
• 2008

Recently, the development and application of unmaned robots are increasing in various fields including surveillance and reconnaissance, planet exploration and disaster relief. Unmaned robots are usually controlled from distance using radio communications but they should be equipped with autonomous travelling function to cope with unexpected terrains and obstacles. This means that unmanned robots should be able to evaluate terrain's characteristics quantitatively using mounted sensors so as to traverse harsh natural terrains autonomously. For this purpose, this paper presents an algorithm for extracting terrain information from elevation maps as an early step of traversability analysis. Slope and roughness information are extracted from a world terrain map based on least squares method and fractal theory, respectively. The effectiveness of the proposed algorithm is verified on both fractal and real terrain maps.

• Journal of the Korean Society for Precision Engineering
• /
• v.15 no.11
• /
• pp.152-165
• /
• 1998

This study proposes the analysis and evaluation method of time series ultrasonic signal using the chaoral post-process system for precision rate enhancement of ultrasonic pattern recognition. Chaos features extracted from time series data for analysis quantitatively weld defects For this purpose, feature extraction objectives in this study are fractal dimension, Lyapunov exponent, shape of strange attrator. Trajectory changes in the strange attractor indicated that even same type of defects carried substantial difference in chaoticity resulting from distance shifts such as nearby 0.5, 1.0 skip distance. Such difference in chaoticity enables the evaluation of unique features of defects in the weld zone. In quantitative chaos fenture extraction, feature values of 0.835 and 0.823 in the case of slag inclusion and 0.609 and 0.573 in the case of crack were suggested on the basis of fractal dimension and Lyapunov exponent. Proposed chaoral post-process system in this study can enhances precision rate of ultrasonic pattern recognition results from defect signals of weld zone, such as slag inclusion and crack.