IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v135y2020ics0960077920301570.html
   My bibliography  Save this article

Influence of sampling length on estimated fractal dimension of surface profile

Author

Listed:
  • Zuo, Xue
  • Tang, Xiang
  • Zhou, Yuankai

Abstract

To study the influence of sampling length on estimated fractal dimension of surface profile, a series of profiles with same sampling interval and different lengths are generated by the Weierstrass-Mandelbrot function. The influence of sampling length on the estimated fractal dimension and the width of scaling region of both theoretical and real measured profiles are analyzed. The computing results show that the fractal dimension cannot be accurately calculated because of the fluctuation and narrow scaling region in the case of insufficient data points. This fluctuation tends to be weakened, and the linearity of the scaling region is improved with the increase of sampling length. The estimated fractal dimension increases with the sampling length, and eventually maintains at its theoretical value. Therefore, the sampling length should be more than the minimum length where the stable value can be achieved. Moreover, the sampling length should be appropriately increased for the smooth surface. This study provides basis for choosing sampling length appropriately to meet the requirements of computing accuracy and efficiency.

Suggested Citation

  • Zuo, Xue & Tang, Xiang & Zhou, Yuankai, 2020. "Influence of sampling length on estimated fractal dimension of surface profile," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    • Handle: RePEc:eee:chsofr:v:135:y:2020:i:c:s0960077920301570
    DOI: 10.1016/j.chaos.2020.109755
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920301570
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109755?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chamorro-Posada, Pedro, 2016. "A simple method for estimating the fractal dimension from digital images: The compression dimension," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 562-572.
    2. Liu, Yao & Wang, Yashun & Chen, Xun & Zhang, Chunhua & Tan, Yuanyuan, 2017. "Two-stage method for fractal dimension calculation of the mechanical equipment rough surface profile based on fractal theory," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 495-502.
    3. Panigrahy, Chinmaya & Seal, Ayan & Mahato, Nihar Kumar & Bhattacharjee, Debotosh, 2019. "Differential box counting methods for estimating fractal dimension of gray-scale images: A survey," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 178-202.
    4. Chen, Zhiying & Liu, Yong & Zhou, Ping, 2018. "A comparative study of fractal dimension calculation methods for rough surface profiles," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 24-30.
    5. Spodarev, Evgeny & Straka, Peter & Winter, Steffen, 2015. "Estimation of fractal dimension and fractal curvatures from digital images," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 134-152.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Zhiwei & Wang, Jianjian & Yuan, Meng & Wang, Zhongyu & Feng, Pingfa & Feng, Feng, 2022. "An indicator to quantify the complexity of signals and surfaces based on scaling behaviors transcending fractal," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Feng Feng & Meng Yuan & Yousheng Xia & Haoming Xu & Pingfa Feng & Xinghui Li, 2022. "Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    3. García-Miguel, Carmen & San Martín, Jesús, 2021. "Covering fractals with constant radius tiles: Distribution functions and their implications for resource management," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Jiang, Kai & Liu, Zhifeng & Tian, Yang & Zhang, Tao & Yang, Congbin, 2022. "An estimation method of fractal parameters on rough surfaces based on the exact spectral moment using artificial neural network," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jiang, Kai & Liu, Zhifeng & Tian, Yang & Zhang, Tao & Yang, Congbin, 2022. "An estimation method of fractal parameters on rough surfaces based on the exact spectral moment using artificial neural network," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Martsepp, Merike & Laas, Tõnu & Laas, Katrin & Priimets, Jaanis & Tõkke, Siim & Mikli, Valdek, 2022. "Dependence of multifractal analysis parameters on the darkness of a processed image," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Chen, Zhiying & Liu, Yong & Zhou, Ping, 2018. "A comparative study of fractal dimension calculation methods for rough surface profiles," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 24-30.
    4. Arce, Walker & Pierce, James & Velcsov, Mihaela Teodora, 2021. "A single-scale fractal feature for classification of color images: A virus case study," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    5. Chamorro-Posada, Pedro, 2016. "A simple method for estimating the fractal dimension from digital images: The compression dimension," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 562-572.
    6. Huzak, Renato & Vlah, Domagoj & Žubrinić, Darko & Županović, Vesna, 2023. "Fractal analysis of degenerate spiral trajectories of a class of ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    7. Bruno Rafael de Almeida Moreira & Ronaldo da Silva Viana & Victor Hugo Cruz & Paulo Renato Matos Lopes & Celso Tadao Miasaki & Anderson Chagas Magalhães & Paulo Alexandre Monteiro de Figueiredo & Luca, 2020. "Anti-Thermal Shock Binding of Liquid-State Food Waste to Non-Wood Pellets," Energies, MDPI, vol. 13(12), pages 1-26, June.
    8. Lahmiri, Salim, 2016. "Image characterization by fractal descriptors in variational mode decomposition domain: Application to brain magnetic resonance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 235-243.
    9. Roman Kaminskiy & Nataliya Shakhovska & Jana Kajanová & Yurii Kryvenchuk, 2021. "Method of Distinguishing Styles by Fractal and Statistical Indicators of the Text as a Sequence of the Number of Letters in Its Words," Mathematics, MDPI, vol. 9(19), pages 1-16, September.
    10. Li, Zhiwei & Wang, Jianjian & Yuan, Meng & Wang, Zhongyu & Feng, Pingfa & Feng, Feng, 2022. "An indicator to quantify the complexity of signals and surfaces based on scaling behaviors transcending fractal," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    11. Jia, Li & Peng, Shoujian & Wu, Bin & Xu, Jiang & Yan, Fazhi & Chen, Yuexia, 2023. "Exploration on the characteristics of 3D crack network expansion induced by hydraulic fracturing: A hybrid approach combining experiments and algorithms," Energy, Elsevier, vol. 282(C).
    12. Feng Feng & Meng Yuan & Yousheng Xia & Haoming Xu & Pingfa Feng & Xinghui Li, 2022. "Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal," Mathematics, MDPI, vol. 10(7), pages 1-17, March.
    13. Zhang, Shuai & Li, Yingjun & Wang, Guicong & Qi, Zhenguang & Zhou, Yuanqin, 2024. "A novel method for calculating the fractal dimension of three-dimensional surface topography on machined surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    14. Liu, Jingshou & Ding, Wenlong & Dai, Junsheng & Zhao, Gang & Sun, Yaxiong & Yang, Haimeng, 2018. "Unreliable determination of fractal characteristics using the capacity dimension and a new method for computing the information dimension," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 16-24.
    15. Liu, Yao & Wang, Yashun & Chen, Xun & Yu, Huangchao, 2018. "A spherical conformal contact model considering frictional and microscopic factors based on fractal theory," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 96-107.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:135:y:2020:i:c:s0960077920301570. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.