Improved box-counting methods to directly estimate the fractal dimension of a rough surface

Wu, Mingyang; Wang, Wensong; Shi, Di; Li, Minghui; Luo, Yafei

doi:10.1016/j.measurement.2021.109303

Cited by 55 publications

(23 citation statements)

References 35 publications

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“…7 shows the correlation between Ds and Sa. An obvious negative correlation can be observed, which is consistent with the conclusions in previous literature [22] . Therefore, a good surface quality means a small surface roughness and a big fractal dimension value.…”

Section: Effects Of Machining Parameters On 3-d Fractal Dimensionsupporting

confidence: 93%

“…Therefore, the 3-D fractal dimension Ds is employed to characterize the machined surface from the perspective of the surface structure. Among the 3-D fractal dimension calculation methods for the mechanical machining surface, the box-counting method has the best accuracy [22] . So, it is adopted as one of the key objectives of optimization.…”

Section: -D Surface Fractal Dimensionmentioning

confidence: 99%

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Optimization of the process parameters for micro-milling thin-walled micro-parts using advanced algorithms

Wang

Bai

Cheng

et al. 2022

Int J Adv Manuf Technol

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The surface integrity and machining accuracy of thin-walled micro parts are significantly affected by micro-milling parameters mostly because of their weak stiffness. Furthermore, there is still a lack of studies focusing on parameters optimization for the fabrication of thin-walled microscale parts. In this paper, an innovative approach is proposed for the optimization of machining parameters with the objectives of surface quality and dimension accuracy, which integrates the Taguchi method, principal component analysis method (PCA) and the Non-dominated sorting genetic algorithm (NSGA-II). In the study, surface arithmetic average height Sa, surface root mean square height Sq, and 3-D fractal dimension Ds are selected to evaluate surface quality. Then micro-milling experiments are conducted based on the Taguchi method. According to the experimental results, the significance of machining parameters can be determined by range analysis. Besides, regression models for the responses are developed comparatively, and the PCA method is employed for dimension reduction of the optimization objective space. Finally, two combinations of machining parameters with the highest satisfaction are obtained through NSGA-II, and verification experiments are carried out. The results show that the surface quality and dimension accuracy of the thin-walled microscale parts can be simultaneously improved by using the proposed approach.

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Section: Effects Of Machining Parameters On 3-d Fractal Dimensionsupporting

confidence: 93%

Section: -D Surface Fractal Dimensionmentioning

confidence: 99%

Optimization of the process parameters for micro-milling thin-walled micro-parts using advanced algorithms

Wang

Bai

Cheng

et al. 2022

Int J Adv Manuf Technol

View full text Add to dashboard Cite

show abstract

“…In recent years, it has been widely used in soil research. The results showed that soil has good self-similarity [27][28][29][30][31] . Therefore, the fractal theory was used to describe the fracture characteristics of the tailings pond.…”

Section: Test Results and Analysismentioning

confidence: 99%

Study on fracture development and progressive failure characteristics of downstream dam-type expansion tailings reservoir

Zhang

Jin

Xu³

2022

Sci Rep

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With the economic development and industrialization, the increasingly accumulated tailings ponds in China have become a great risk. Due to the difficulty of selecting proper site for a new reservoir in Yunnan, a sub-dam was built at the downstream original reservoir. This study explored the fracture development and progressive failure characteristics of the tailings reservoir area after capacity expansion based on a similarity experiment and the numerical simulation. The results showed that the primary cracks in the reservoir area were more than those at the top of the sub-dam. With the increase of the upper load, the primary cracks further developed and penetrated the whole sub-dam top, and the sub-cracks were then produced under the concentrate stress of the primary cracks. After the further development of the sub-cracks, the secondary cracks parallel to the primary cracks were formed on the outer slope of the sub-dam. The progressive failure of a tailings dam can be summarized as: the maximum shear stress was firstly generated at the toe of the slope or the top of the dam which then extended to the top of the sub-dam in the form of a curve and finally formed the failure surface by connecting with the primary fracture of the tensile plastic zone at the top of the dam. The study also found that in the process of tailings accumulation in the new reservoir area, tailings would form "back pressure slope protection" at the initial dam of the original reservoir, which not only effectively delayed the occurrence of shear failure, but also inhibited the generation and penetration of tensile plastic zone.

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“…It is a graph, phenomenon or physical process with self-similar characteristics that can be described by the fractal dimension. There are many methods to calculate the fractal dimension [ 31 , 32 , 33 , 34 ], such as Hausdorff dimension, similarity dimension, box-counting dimension and capacity dimension. In this study, the Hausdorff dimension and box-counting dimension were mainly used for description.…”

Section: Theory and Methodsmentioning

confidence: 99%

Study on Multiple Fractal Analysis and Response Characteristics of Acoustic Emission Signals from Goaf Rock Bodies

Xie

Guo

2022

Sensors

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Based on the actual monitoring data of the acoustic emission (AE) ground pressure monitoring and positioning system, this paper introduces fractal theory and the multifractal detrended fluctuation analysis (MF-DFA) method to estimate the waveform multifractal spectrum of goaf rock acoustic emission signals and investigate multifractal time-varying response characteristics. The research results show that the wavelet hard thresholding method has the best noise reduction effect on the original signal, and the box counting dimension has a strong waveform identification effect. Before deformation damage occurs, fractal spectral width Δα shows an increase and then decrease and the fluctuation scale factor Δf(α) decreases and then increases. When damage occurs, fractal spectral width Δα decreases and then stabilizes and concentrates. Simultaneously, the fluctuation scale factor Δf(α) keeps decreasing until the lowest point, and then shows an increasing trend until it reaches a stable state. This study is of great significance to the stability evaluation and disaster early warning of mine goaf.

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Improved box-counting methods to directly estimate the fractal dimension of a rough surface

Cited by 55 publications

References 35 publications

Optimization of the process parameters for micro-milling thin-walled micro-parts using advanced algorithms

Optimization of the process parameters for micro-milling thin-walled micro-parts using advanced algorithms

Study on fracture development and progressive failure characteristics of downstream dam-type expansion tailings reservoir

Study on Multiple Fractal Analysis and Response Characteristics of Acoustic Emission Signals from Goaf Rock Bodies

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