scholarly journals Surface Evaluation by Estimation of Fractal Dimension and Statistical Tools

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Vlastimil Hotar ◽  
Petr Salac
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Complex Surface ◽  
Complete Analysis ◽  
Complex Data ◽  
Statistical Tools ◽  
Statistical Tool ◽  
Industrial Practice ◽  
Structured Surfaces ◽  
Analyse Data

Structured and complex data can be found in many applications in research and development, and also in industrial practice. We developed a methodology for describing the structured data complexity and applied it in development and industrial practice. The methodology uses fractal dimension together with statistical tools and with software modification is able to analyse data in a form of sequence (signals, surface roughness), 2D images, and dividing lines. The methodology had not been tested for a relatively large collection of data. For this reason, samples with structured surfaces produced with different technologies and properties were measured and evaluated with many types of parameters. The paper intends to analyse data measured by a surface roughness tester. The methodology shown compares standard and nonstandard parameters, searches the optimal parameters for a complete analysis, and specifies the sensitivity to directionality of samples for these types of surfaces. The text presents application of fractal geometry (fractal dimension) for complex surface analysis in combination with standard roughness parameters (statistical tool).

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

scholarly journals Effect of tillage, slope, and rainfall on soil surface microtopography quantified by geostatistical and fractal indices during sheet erosion

2020 ◽  
Vol 12 (1) ◽  
pp. 232-241
Author(s):  
Na Ta ◽  
Chutian Zhang ◽  
Hongru Ding ◽  
Qingfeng Zhang
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Soil Surface ◽  
Rainfall Events ◽  
Tillage Practices ◽  
Surface Microtopography ◽  
Artificial Rainfall ◽  
Soil Surface Roughness ◽  
The Difference ◽  
Sheet Erosion

AbstractTillage and slope will influence soil surface roughness that changes during rainfall events. This study tests this effect under controlled conditions quantified by geostatistical and fractal indices. When four commonly adopted tillage practices, namely, artificial backhoe (AB), artificial digging (AD), contour tillage (CT), and linear slope (CK), were prepared on soil surfaces at 2 × 1 × 0.5 m soil pans at 5°, 10°, or 20° slope gradients, artificial rainfall with an intensity of 60 or 90 mm h−1 was applied to it. Measurements of the difference in elevation points of the surface profiles were taken before rainfall and after rainfall events for sheet erosion. Tillage practices had a relationship with fractal indices that the surface treated with CT exhibited the biggest fractal dimension D value, followed by the surfaces AD, AB, and CK. Surfaces under a stronger rainfall tended to have a greater D value. Tillage treatments affected anisotropy differently and the surface CT had the strongest effect on anisotropy, followed by the surfaces AD, AB, and CK. A steeper surface would have less effect on anisotropy. Since the surface CT had the strongest effect on spatial variability or the weakest spatial autocorrelation, it had the smallest effect on runoff and sediment yield. Therefore, tillage CT could make a better tillage practice of conserving water and soil. Simultaneously, changes in semivariogram and fractal parameters for surface roughness were examined and evaluated. Fractal parameter – crossover length l – is more sensitive than fractal dimension D to rainfall action to describe vertical differences in soil surface roughness evolution.

scholarly journals Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1054
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
Isfarita Ismail ◽  
Mohammad Izat Emir Zulkifly
Keyword(s):  
Complex Surface ◽  
Complex Data ◽  
Fuzzy Data ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Surface Data ◽  
Model Complex

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

scholarly journals A Stochastic Model for the Fractal Dimension Estimation of Asphaltenes Aggregation

2019 ◽  
Vol 8 (6) ◽  
pp. 1992-1995
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Stochastic Model ◽  
Production Systems ◽  
Experimental Results ◽  
Crude Oils ◽  
Dimension Estimation ◽  
Maximum Value ◽  
Solids Deposition

Some of the problems associated with the transportation of crude oils are due to the presence of heavy compounds as asphaltene molecules. This work developed a stochastic model that predicts the fractal dimension of the asphaltene aggregates. It was found that the maximum value of the fractal dimension is 1.71, which corresponds to the reported experimental results. The model can be applied as a universal growing behavior for the analysis of surface roughness when solids deposition is observed in the production systems involving crude oils

scholarly journals An Exploration of Fractal Based Prognostic Model and Comparative Analysis for Second Wave of COVID-19 Diffusion

2021 ◽  
Author(s):  
Easwaramoorthy D. ◽  
Gowrisankar A. ◽  
Manimaran A. ◽  
Nandhini S. ◽  
Santo Banerjee ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Death Rate ◽  
Transmission Rate ◽  
The United States ◽  
Fractal Interpolation ◽  
Interpolation Function ◽  
Statistical Tool ◽  
Dimension Estimate ◽  
Fractal Interpolation Function ◽  
Second Wave

Abstract The coronavirus disease 2019 (COVID-19) pandemic has fatalized 216 countries across the world and has claimed the lives of millions of people globally. Researches are being carried out worldwide by scientists to understand the nature of this catastrophic virus and find a potential vaccine for it. The most possible efforts have been taken to present this paper as a form of contribution to the understanding of this lethal virus in the first and second wave. This paper presents a unique technique for the methodical comparison of disastrous virus dissemination in two waves amid five most infested countries and the death rate of the virus in order to attain a clear view on the behaviour of the spread of the disease. For this study, the dataset of the number of deaths per day and the number of infected cases per day of the most affected countries, The United States of America, Brazil, Russia, India, and The United Kingdom have been considered in first and second wave. The correlation fractal dimension has been estimated for the prescribed datasets of COVID-19 and the rate of death has been compared based on the correlation fractal dimension estimate curve. The statistical tool, analysis of variance has also been used to support the performance of the proposed method. Further, the prediction of the daily death rate has been demonstrated through the autoregressive moving average model. In addition, this study also emphasis a feasible reconstruction of the death rate based on the fractal interpolation function. Subsequently, the normal probability plot is portrayed for the original data and the predicted data, derived through the fractal interpolation function to estimate the accuracy of the prediction. Finally, this paper neatly summarized with the comparison and prediction of epidemic curve of the first and second waves of COVID-19 pandemic to picturize the transmission rate in the both times.

Properties of Large Eden Clusters in the Plane

1994 ◽  
Vol 3 (4) ◽  
pp. 471-505 ◽  
Author(s):  
J. M. Hammersley ◽  
G. Mazzarino
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Computer Simulations ◽  
Statistical Data ◽  
Higher Dimensions ◽  
Central Cluster ◽  
Circular Shape ◽  
Angular Direction ◽  
Edge Method ◽  
Macroscopic Shape

Whereas the cylindrical version of an Eden cluster in the plane has a surface roughness with a fractal dimension predicted by theory, the central version has hitherto seemed to conflict with theory. However, a fresh way of analysing computer simulations of the central version shows that this anomaly is more apparent than real, and the central version can thereby be reconciled with theory. As a by-product, we obtain statistical data on the properties of the central version in the plane. The macroscopic shape of a central cluster is not circular, and microscopic roughness depends weakly upon the angular direction of portions of the surface. Rather surprisingly, the edge method of construction gives a more nearly circular shape than the external and internal methods. For higher dimensions than the plane, the corresponding treatment is more difficult, and there the situation remains obscure. Higher dimensions and certain other clusters (e.g.Richardson clusters) are treated briefly in Section 6. The theory of surface roughness uses a spatial generalization of martingales, called a serial harness: this is also described in Section 6.

Approaches to Quantitative Data Analysis and Evaluation

2016 ◽  
Author(s):  
Stephen Rae ◽  
Ahmed Salhin ◽  
Babak Taheri ◽  
Catherine Porter ◽  
Christian König ◽  
...  
Keyword(s):  
Big Data ◽  
Data Analysis ◽  
Quantitative Data ◽  
Statistical Techniques ◽  
Statistical Tools ◽  
Analysis And Evaluation ◽  
Quantitative Data Analysis ◽  
Analyse Data

To understand data and present findings appropriately, researchers need awareness of statistical techniques. This chapter discusses the statistical tools used to analyse data collected. It focuses on two sets of the most widely used statistical tools, as shown in the ‘Deductive’ section in the data analysis area of the Methods Map (see Chapter 4): (1) exploring relationships and (2) comparing groups. In addition, we briefly explain ‘Big Data’.

scholarly journals Application of Multivariate-Rank-Based Techniques in Clustering of Big Data

2018 ◽  
Vol 43 (4) ◽  
pp. 179-190
Author(s):  
Pritha Guha
Keyword(s):  
Big Data ◽  
Dna Analysis ◽  
Retail Banking ◽  
Data Sets ◽  
Complex Data ◽  
Data Handling ◽  
Credit Risk Management ◽  
Statistical Tools ◽  
Executive Summary ◽  
Complex Data Sets

Executive Summary Very large or complex data sets, which are difficult to process or analyse using traditional data handling techniques, are usually referred to as big data. The idea of big data is characterized by the three ‘v’s which are volume, velocity, and variety ( Liu, McGree, Ge, & Xie, 2015 ) referring respectively to the volume of data, the velocity at which the data are processed and the wide varieties in which big data are available. Every single day, different sectors such as credit risk management, healthcare, media, retail, retail banking, climate prediction, DNA analysis and, sports generate petabytes of data (1 petabyte = 250 bytes). Even basic handling of big data, therefore, poses significant challenges, one of them being organizing the data in such a way that it can give better insights into analysing and decision-making. With the explosion of data in our life, it has become very important to use statistical tools to analyse them.

A Digital Near Net Shape Manufacturing Propeller with Complex Surface

2011 ◽  
Vol 201-203 ◽  
pp. 117-120
Author(s):  
Zhong Fei Jiao ◽  
Shan Yao ◽  
Shu Ming Zhao ◽  
Feng Zeng ◽  
Di Wu
Keyword(s):  
Surface Roughness ◽  
Rapid Prototyping ◽  
Dimensional Accuracy ◽  
Casting Process ◽  
Complex Surface ◽  
High Accuracy ◽  
Parametric Modeling ◽  
Marine Propeller ◽  
3D Cad ◽  
Near Net Shape

An integrated digital routine is applied in the near net shape manufacturing of marine propeller. Firstly, the 3D CAD file of propeller is created by parametric modeling. Secondly, the propeller casting process is simulated using CAE software, through which an optimized casting scheme is obtained. Thirdly, fabricates the mold using laser rapid prototyping and cast the metal propeller. Finally, evaluate the casting precision performance. CAD, CAE and CAM are integrated in this process. The dimensional accuracy of the final piece is controlled within 1mm and its surface roughness achieves Ra 6.3μm. The result shows that the pattern-less casting of propeller can be achieved by this method, reducing cost and performing high accuracy.

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