scholarly journals Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Youping Fan ◽  
Dai Zhang ◽  
Jingjiao Li
Keyword(s):  
Fractal Dimension ◽  
Tree Growth ◽  
Fractal Dimensions ◽  
Moisture Level ◽  
Growth Time ◽  
Counting Method ◽  
Box Counting ◽  
Electrical Trees ◽  
Box Counting Method ◽  
Electrical Treeing

The paper aims to understand how the fractal dimension and growth time of electrical trees change with temperature and moisture. The fractal dimension of final electrical trees was estimated using 2-D box-counting method. Four groups of electrical trees were grown at variable moisture and temperature. The relation between growth time and fractal dimension of electrical trees were summarized. The results indicate the final electrical trees can have similar fractal dimensions via similar tree growth time at different combinations of moisture level and temperature conditions.

A Modified Box-Counting Method to Estimate the Fractal Dimensions

2011 ◽  
Vol 58-60 ◽  
pp. 1756-1761 ◽  
Author(s):  
Jie Xu ◽  
Giusepe Lacidogna
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
The Self ◽  
Whole Body ◽  
Counting Method ◽  
Border Effect ◽  
Self Similarity ◽  
Box Counting ◽  
Self Similar ◽  
Box Counting Method

A fractal is a property of self-similarity, each small part of the fractal object is similar to the whole body. The traditional box-counting method (TBCM) to estimate fractal dimension can not reflect the self-similar property of the fractal and leads to two major problems, the border effect and noninteger values of box size. The modified box-counting method (MBCM), proposed in this study, not only eliminate the shortcomings of the TBCM, but also reflects the physical meaning about the self-similar of the fractal. The applications of MBCM shows a good estimation compared with the theoretical ones, which the biggest difference is smaller than 5%.

GOODNESS OF FIT ON A MODIFIED RICHARDSON PLOT BY RESIDUAL ANALYSIS

Fractals ◽  
2000 ◽  
Vol 08 (03) ◽  
pp. 261-265
Author(s):  
IAN H. PARKINSON ◽  
NIC L. FAZZALARI
Keyword(s):  
Fractal Dimension ◽  
Standard Deviation ◽  
Trabecular Bone ◽  
Serial Correlation ◽  
Goodness Of Fit ◽  
Fractal Dimensions ◽  
Accurate Estimation ◽  
Counting Method ◽  
Box Counting ◽  
Box Counting Method

Modified Richardson plots obtained by a box counting method on outlines of trabecular bone were tested for linearity. The degree of deviation from true linearity was quantified. The results showed that although there was evidence of nonlinearity or serial correlation in the Richardson plots, the magnitude of deviation from true linearity was less than 0.3% for the residuals and less than 4% for the standard deviation of the residuals. This study shows that the modified box counting method for estimating overall fractal dimension or sectional fractal dimensions of trabecular bone is efficacious. The low magnitude of deviation from linearity confirms that over a defined range of scale the Richardson plot provides an accurate estimation of the fractal dimension of trabecular bone.

On the Fractal Characters of Seawater Temperature in the Kuroshio

2011 ◽  
Vol 403-408 ◽  
pp. 2931-2935
Author(s):  
Yan Xia Zhou ◽  
Mei Han ◽  
Liang Long Da
Keyword(s):  
Fractal Dimension ◽  
Seawater Temperature ◽  
Sound Field ◽  
Fractal Dimensions ◽  
Three Dimension ◽  
Counting Method ◽  
Acoustic Environment ◽  
Box Counting ◽  
Box Counting Method ◽  
The Kuroshio

The Kurshio can affect sonar detection notably. The software named Gis ArcView is used to identify the Kuroshio area by analyzing underwater acoustics data. And seawater temperature isolines are drawn based on the temperature data which are distributed at some intervals in terms of latitude and longitude. The box counting method is applied to calculating the fractal dimension of the Kuroshio seawater temperature isolines in different seasons at the depth of 60m and 150m.The results indicate that the fractal dimension at 150m deep is bigger than that at 60m, but the former fluctuates less than the latter.It is conformed to the facts about the Kuroshio. Acoustic wave is the best medium through which acoustic information can be well transmitted. In the Kurshio area where underwater acoustic environment is rather complex, many singular areas are formed in the three-dimension sound field, in which sonar detection and tracking will be affected to a great extent. However, with the development of remote sensing technologies, it is possible to observe and forecast such mid-scale phenomena as the Kurshio, ocean fronts and interwaves. Therefore, how to effectively extract and analyze the main characters of these phenomena is quite important for Navies. Some people still get used to judging Kurshio’s existence and even intensity as well by simple criteria for a long time. For example, when the exchange of seawater temperature is exceeds 0.1°C/n mile, it will be considered that an ocean front exists. This criterion in fact is so ambiguous not only in this regard, but also in describing the Kurshio’s intensity[1]. In vies of this, the author operates the software, GIS ArcView, to extract and analyze the Kurshio, and take the box counting method[2] to calculate out the fractal dimensions in the area between 20º~30º N and 120 º~130ºE respectively at the depths of 60m and 150m.

scholarly journals PENDETEKSIAN CITRA DAUN TANAMAN MENGGUNAKAN METODE BOX COUNTING

2020 ◽  
Vol 20 (1) ◽  
pp. 35
Author(s):  
Novita Anggraini Juwitarty ◽  
Kosala Dwidja Purnomo ◽  
Kiswara Agung Santoso
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Plant Leaves ◽  
Counting Method ◽  
Image Detection ◽  
Box Counting ◽  
Irregular Shapes ◽  
Different Types ◽  
Box Counting Method ◽  
Leaf Part

Different types of plants make identification difficult. Therefore, we need a system that can identify the similarity of the leaves based on a reference leaf. Extraction can be done by taking one part of the plant and the most easily obtained part is the leaf part. Natural objects such as leaves have irregular shapes and are difficult to measure, but this can be overcome by using fractal dimensions. In this research, image detection of plant leaves will be carried out using the box counting method. The box counting method is a method of calculating fractal dimensions by dividing images into small boxes in various sizes. Image detection using fractal dimension values, we know which leaves the match with the reference. In this study,10 species of leave were tested, with each species 10 samples of plant leaves. Image testing of plant leaves uses a variety of r box size, namely 1/2 ,1/4 , 1/8 , 1/16 ,1/32 , 1/64 , 128which obtain an average match accuracy of 44%. Keywords: Box Counting, Fractal dimension

Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

2021 ◽  
Author(s):  
Nicholas Dudu ◽  
Arturo Rodriguez ◽  
Gael Moran ◽  
Jose Terrazas ◽  
Richard Adansi ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Atmospheric Turbulence ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Counting Method ◽  
Data Set ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Self Similar ◽  
Box Counting Method

Abstract Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.

scholarly journals FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY

2011 ◽  
Vol 19 (1) ◽  
pp. 45 ◽  
Author(s):  
Ian Parkinson ◽  
Nick Fazzalari
Keyword(s):  
Fractal Dimension ◽  
Trabecular Bone ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Box Counting ◽  
Cell Tissue ◽  
Image Analyser ◽  
Model Independent ◽  
Box Counting Method ◽  
Image Orientation

A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge). The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.

scholarly journals A BOX-COUNTING METHOD TO CHARACTERIZE DEGREES OF FOLIAGE CLUMPING USING AIRBORNE AND SIMULATED LIDAR DATA

2015 ◽  
Vol XL-7/W3 ◽  
pp. 1325-1331
Author(s):  
M. van Leeuwen ◽  
J. A. N. van Aardt ◽  
T. Kampe ◽  
K. Krause
Keyword(s):  
Fractal Dimension ◽  
Leaf Area ◽  
Optical Methods ◽  
Lidar Data ◽  
Counting Method ◽  
Area Index ◽  
Cloud Data ◽  
Box Counting ◽  
Box Counting Method ◽  
Foliage Clumping

Monitoring forest productivity and health is key to sustainable ecosystem management and informed decision making. A key parameter used in monitoring forest resources is the leaf area index (LAI), which is defined as the one-sided leaf area per unit ground area and is used to describe the canopy radiation regime, among other forest biophysical dynamics. Traditional optics-based methods to estimate LAI rely on the measurement of canopy transmission and foliage clumping. Extending optical methods to LiDAR data has been challenging and studies have reported effective LAI assessments, with no further quantification of foliage clumping. This study investigates the use of the box-counting method to assess the fractal dimension of point cloud data for contrasting forest types and along a gradient of foliage dispersal. We demonstrate the box-counting method on simulated ‘range-to-hit’, as well as acquired airborne discrete LiDAR data. Coherent results obtained from the different test cases hint at the potential of the box-counting fractal dimension to characterize foliage clumping and bode well for the use of clumping assessments in support of airborne, wall-to-wall estimates of LAI.

scholarly journals Fractal Characterization of Earthquake occurrences in Nigeria

2019 ◽  
Vol 1 ◽  
pp. 281-287
Author(s):  
N N Abdulsalam ◽  
O Ologe
Keyword(s):  
Fractal Dimension ◽  
Active Zone ◽  
Hazard Analysis ◽  
B Value ◽  
Google Earth ◽  
Counting Method ◽  
Microsoft Word ◽  
Box Counting ◽  
Box Counting Method

Fractal characterization of Earthquake occurrences in Nigeria was carried out in order to know the b-value of tremor occurrences in the country. This will help in hazard analysis and research in the geological and geophysical structures of Nigeria. The method used in determining the b-value is the box counting method, but for simplicity, we used circle. The areas that are tremor prone were posted on a digitized Nigeria map using Google earth and Surfer 7.0 software. The computation with the box counting method was performed with picked radius of the circle from 50km - 350km and the average number of points that falls within each circle were recorded. The graph of log r (the logarithms of radius of circle or scale) against log <N> (logarithms of average number of points) was plotted using grapher and excels Microsoft word and the slope of the graph was determined. The determined slope gave the fractal dimension and the b-value was thus calculated. In this work, a b-value of 0.6 was obtained indicating that Nigeria falls within seismically less active zone.

scholarly journals Binarization methods and investigation of their influence on the fractal dimension of functional coatings

2020 ◽  
pp. 30-42
Author(s):  
Anna Zhurba ◽  
Michail Gasik
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Quantitative Characteristic ◽  
Image Binarization ◽  
Counting Method ◽  
Functional Coatings ◽  
Binary Images ◽  
Box Counting ◽  
Box Counting Method ◽  
Binarization Threshold

An essential element of fractal analysis of functional coatings is the fractal dimension, which is an important quantitative characteristic. Typically, coating images are represented as colored or halftone, and most fractal dimension algorithms are for binary images. Therefore, an important step in fractal analysis is binarization, which is a threshold separation operation and the result of which is a binary image.The purpose of the study is to study and program the methods of image binarization and to study the influence of these methods on the value of fractal dimension of functional coatings.As a result of the binarization threshold, the image is split into two regions, one containing all pixels with values below a certain threshold and the other containing all pixels with values above that threshold. Of great importance is the determination of the binarization threshold.The study analyzed a number of functional coating images, determined the fractal dimension of the image by the Box Counting method at different binarization thresholds and when applying different binarization methods (binarization with lower and upper threshold, with double restriction, and the average method for determining the optimal binarization threshold) images. The Box Counting method is used to depict any structure on a plane. This method allows us to determine the fractal dimension of not strictly self-similar objects. Each image binarization method is used for different types of images and for solving different problems.As a result, the methods of image binarization were developed and implemented, the fractal dimension of binary images was calculated, and the influence of these methods on the value of fractal dimension of functional coatings was investigated.The surfaces of composite steel structure, metallic porous materials, and natural cave structures are analyzed.

Sign in / Sign up

Export Citation Format

Share Document