Comparison of two fractal interpolation methods

Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo

doi:10.1016/j.physa.2016.11.120

Cited by 10 publications

(2 citation statements)

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“…interpolation function is a continuous function that is interpolated at these points, and its graph is an attraction of the Iterated Function System (IFS). The specific construction process [13][14][15] is as follow. Let each function in the iteration function system be an affine transformation, written as…”

Section: Brief Introduction Of Data Missing Processing Methodsmentioning

confidence: 99%

Comparative Analysis of Multi-fractal Data Missing Processing Methods

Simin¹

2019

ACM

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Data missing often affects the characteristics of the sequence. Using appropriate methods to process the missing data is the premise and guarantee to obtain high quality information. In this study, a fractal interpolation method is proposed to fill the missing data with self-similar feature sequences. Two sets of binomial multifractal sequences with parameters of 0.25 and 0.35 are taken as the research objects, and the Hurst index value of the sequence after filling processing is calculated by MF-DMA, which verifies the practicability of the fractal interpolation filling method. At the same time, the method is applied to multi-fractal sequences with missing rates of 10%, 15% and 20% respectively, and compared with the filling effects of deletion method and random filling method, then, the applicability of the three methods is obtained. The results show that, for binomial multifractal sequences with different missing ratios, the Hurst index of the sequence processed by fractal interpolation has the highest degree of fitting with the theoretical value, its effect of repairing the fractal sequence is better than the other two methods, and has a good application prospect.

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Section: Brief Introduction Of Data Missing Processing Methodsmentioning

confidence: 99%

Comparative Analysis of Multi-fractal Data Missing Processing Methods

Simin¹

2019

ACM

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“…The power spectrum method is a classical and direct application of fractal calculations, and has been extensively used. As the mechanical performances of the ternary Ni-W-P coatings are hard to make a comparison, the fractal dimension of coating is built based on structure function method [32] (equation ( 1)), which can be expressed as follows:…”

Section: Fractal Surface Calculationsmentioning

confidence: 99%

Investigation on the mechanical performance of the electroless Ni–W–P coating based on fractal theory

Ren

Cheng

Han

et al. 2019

Surf. Topogr.: Metrol. Prop.

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Engineering surface shows fractal characteristics, and mechanical performance of electroless Ni-W-P coating with fractal parameters can avoid the effects of instrument resolution and sampling length. In the present work, the ternary Ni-W-P coatings were deposited on mild steel (1015) polished with various sandpapers. Surface morphology of coating and mechanical property, including matrix roughness, adhesion strength, friction behavior and elastic modulus were investigated by using scanning electron microscopy (SEM) and MFT-4000 multifunctional material surface performance instrument, respectively. The results present that the mechanical property of the electroless Ni-W-P coating is affected by the fractal features. The stress in the direction of matrix surface is considered to decrease due to the rougher matrix. Meanwhile, the elements are prone to be deposited and the adhesion strength between Ni-W-P coating and matrix is seen to increase. The experiments also indicate that the friction coefficient of coating reduces as the fractal dimension of coating increase. However, the regularity of the relationship between fractal dimension and elastic modulus of Ni-W-P coating is inconspicuous while the elastic modulus is mainly affected by its own chemical component. The work provides evidence that the fractal dimension has a significant influence on the mechanical property of the electroless Ni-W-P coating. Nomenclature V deposition rate [mg mm −2 h −1 ]RECEIVED

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Hydrogeological Effects of Fault Geometry for Analysing Groundwater Inflow in a Coal Mine

Wang

Sui

2021

Mine Water Environ

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Comparison of two fractal interpolation methods

Cited by 10 publications

References 50 publications

Comparative Analysis of Multi-fractal Data Missing Processing Methods

Comparative Analysis of Multi-fractal Data Missing Processing Methods

Investigation on the mechanical performance of the electroless Ni–W–P coating based on fractal theory

Hydrogeological Effects of Fault Geometry for Analysing Groundwater Inflow in a Coal Mine

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