A comparative study of fractal dimension calculation methods for rough surface profiles

Chen, Zhiying; Liu, Yong; Zhou, Ping

doi:10.1016/j.chaos.2018.04.027

Cited by 50 publications

(20 citation statements)

References 29 publications

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“…Each packet was analysed by the Variogram method to determine D f . The Variogram method is based on the calculation of the variance of V of the brightness level distribution of a sample surface image (Chen et al, 2018;Bianchi & Bonetto, 2001). In order to obtain the D f , the FERImage software was used (Bianchi & Bonetto, 2001).…”

Section: Morphological Characterization Of Particles and Packetsmentioning

confidence: 99%

“…The D f is important since the separation of flour during the fractionation process depends on the characteristics of the surface and the shape of flour particles (Siliveru et al, 2016). If there are images of the particles, the Variogram method allows obtaining information about D f (Martínez Amezaga et al, 2018;Chen et al, 2018;Benítez et al, 2013). The mentioned method is based on variance (V) calculation of the brightness level distribution of the sample surface image (Chen et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

“…If there are images of the particles, the Variogram method allows obtaining information about D f (Martínez Amezaga et al, 2018;Chen et al, 2018;Benítez et al, 2013). The mentioned method is based on variance (V) calculation of the brightness level distribution of the sample surface image (Chen et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

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Impact of sorghum grain processing on morphological characteristics of particles of wholegrain sorghum flour

et al. 2022

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This work studies the physical characteristics of sorghum whole flour particles produced with grains reduced in tannins by hydrothermal treatment. Flours ground with two types of mills: a roll mill and a blade mill were used; grains were hydrated with a moisture content of 25%. For this moisture the maximum yield was obtained. The effect of the grain moisture during the grinding was evaluated regarding the morphological characteristics, the granulometry and fractal dimension (D f ) of particles. In all the analysed samples, bimodal size distribution curves were obtained. The treated samples showed medium size particles bigger than the samples without treatment. The samples without hydrothermal treatment presented particles with lower damage than the treated samples for both mills. The difference in D f between samples indicated more roughness for the samples with treatment. The proposed treatment could contribute to the development of sorghum whole flour with different properties for the development of gluten-free food.

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Section: Morphological Characterization Of Particles and Packetsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Impact of sorghum grain processing on morphological characteristics of particles of wholegrain sorghum flour

et al. 2022

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“…However, the statistical contact models all simplified the characterizations of the surface topography to various degrees, which consequently caused a large error between the calculated and the actual results. Engineering surfaces are found to have fractal characteristics [29,30]. When fractal parameters instead of statistic parameters are adopted to characterize rough surfaces, there is no need to make too many assumptions about the surface topography, and the fractal characteristics of rough surfaces can be preserved [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

A Fractal Contact Model for Rough Surfaces considering the Variation of Critical Asperity Levels

Liu

Guo

Chen

et al. 2022

Advances in Materials Science and Engineering

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A contact model for rough surfaces based on the fractal theory is proposed in the present work. Firstly, the deformation of the material is divided into four stages: elastic deformation, the first elastoplastic deformation, the second elastoplastic deformation, and full plastic deformation. And the variation of material hardness is considered when analyzing the contact characteristics of a single asperity within the first and second elastoplastic deformation stages. Secondly, the size distribution function of contact spots at different frequency levels is derived. And the expressions of asperity critical frequency levels are rederived. Lastly, the feasibility and credibility of the proposed model are verified by comparison with other contact models and experimental data. The results show that when the variation of the material hardness is considered, the contact area of a single asperity in the first elastoplastic deformation stage becomes larger, while the contact area of a single asperity in the second elastoplastic deformation stage becomes smaller. Moreover, the critical asperity frequency levels of the rough surface are not constant, but the variables are related to the total real contact area of the rough surface and decrease as the real contact area increases. The proposed model is a modification and improvement of the existing fractal contact models, which can lead to a more accurate relationship between the contact load and the total real contact area of the rough surface.

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“…After that, Franceschetti, Jaggard and Sun proposed a one-dimensional and two-dimensional fractal rough sea surface model based on the fractal function of the band Weierstrass. At the same time, Chen et al [16] introduced the PM spectra into the band-limited Weierstrass function to simulate random rough sea surface. Neumann and Pierson proposed the sea wave equation method after fully studying the linear solution of Lagrange on the moving sea surface.…”

Section: Introductionmentioning

confidence: 99%

A Semi-Empirical Model Of Sea Clutter Based On Zero Memory Nonlinearity

Fan

Zhang

et al. 2019

IEEE Access

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Based on the computer simulation technology of zero memory nonlinearity (ZMNL), this paper combines with the backscattering features of sea clutter and conducts simulation for four typical backscattering coefficient empirical models of sea clutter, namely, Technology Service Corporation, Georgia Institutes of Technology, Hybrid Sea Clutter Model, and Naval Research Laboratory. According to the results, the signals of sea clutter simulated by zero memory nonlinearity are able to well satisfy the requirements of spectrum characteristics and amplitude distribution according to experiments on the fitting characteristics of simulated signals. After that, the above-mentioned sea clutter scattering coefficient fitting characteristics are applied to the finite difference time domain (FDTD) electromagnetic scattering equation of the numerical method, and the optimal recursive solution to the backward scattering area fitted by the above four semi-empirical models is proposed for the first time. Then, the method of discretizing the power spectrum equation of the differential form is combined with the FDTD discrete form. The numerical results of discrete simulation take the form of the random phase ω between 0 and 2π and then are converted into a basic iteration of one-dimensional rough length, thus realizing time domain power spectrum inversion. Finally, combined with the above conclusions, this paper proposes a new statistical model based on sea surface backscatter coefficient to invert the two-dimensional sea surface, that is, the three-parameter statistical model. At the same time, this paper further deduces the backscattering function of sea clutter based on random distribution and points out that the incident frequency and the rubbing angle are the main factors affecting the sea clutter scattering model. Based on this conclusion, this paper combines the sea clutter estimation model and the directional function model to simulate a two-dimensional random rough sea surface satisfying the physical laws of the ocean.INDEX TERMS Zero memory nonlinearity, empirical models, finite difference time domain, twodimensional sea surface.

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A comparative study of fractal dimension calculation methods for rough surface profiles

Cited by 50 publications

References 29 publications

Impact of sorghum grain processing on morphological characteristics of particles of wholegrain sorghum flour

Impact of sorghum grain processing on morphological characteristics of particles of wholegrain sorghum flour

A Fractal Contact Model for Rough Surfaces considering the Variation of Critical Asperity Levels

A Semi-Empirical Model Of Sea Clutter Based On Zero Memory Nonlinearity

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