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

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  • Chen, Zhiying
  • Liu, Yong
  • Zhou, Ping

Abstract

Fractal dimension is the most important parameter for surface characterization. In this paper, four methods used to estimate the fractal dimensions of surface profiles and their applications in machined surfaces are studied. These methods are first evaluated using surface profiles created by Weierstrass–Mandelbrot function from the three aspects of fitting accuracy, calculation accuracy and calculation stability, and then applied to the machined rough surfaces. By comparing the results of the four methods, it is found that none of the methods is particularly prominent in all of the three aspects. However, the three point sinuosity method is found to be relatively the most suitable and reliable method among the four tested methods for extracting fractal dimensions of both generated and measured rough surface profiles.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:112:y:2018:i:c:p:24-30
    DOI: 10.1016/j.chaos.2018.04.027
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    References listed on IDEAS

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    1. Epstein, Marcelo & Śniatycki, Jędrzej, 2008. "The Koch curve as a smooth manifold," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 334-338.
    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.
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    Cited by:

    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. 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).
    3. 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.
    4. 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).

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