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两种基于三维分形的地形特征描述方法:理查森拼接法与Sdr法

Two 3D Fractal-Based Approaches for Topographical Characterization: Richardson Patchwork versus Sdr.

作者信息

Berkmans François, Lemesle Julie, Guibert Robin, Wieczorowski Michał, Brown Christopher, Bigerelle Maxence

机构信息

CNRS, UMR 8201-LAMIH-Laboratoire d'Automatique de Mécanique et d'Informatique Industrielles et Humaines, University Polytechnique Hauts-de-France, F-59313 Valenciennes, France.

Institute of Mechanical Technology, Poznan University of Technology, Plac Marii Sklodowskiej-Curie 5, 60-965 Poznan, Poland.

出版信息

Materials (Basel). 2024 May 16;17(10):2386. doi: 10.3390/ma17102386.

DOI:10.3390/ma17102386
PMID:38793452
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11122945/
Abstract

Various methods exist for multiscale characterization of surface topographies, each offering unique insights and applications. The study focuses on fractal-based approaches, distinguishing themselves by leveraging fractals to analyze surface complexity. Specifically, the Richardson Patchwork method, used in the ASME B46.1 and ISO 25178 standards, is compared to the Sdr parameter derived from ISO 25178-2, with a low-pass Gaussian filter for multiscale characterization. The comparison is performed from the relative area calculated on topographies of TA6V samples grit blasted with different pressures and blasting materials (media). The surfaces obtained by grit blasting have fractal-like characteristics over the scales studied, enabling the analysis of area development at multiple levels based on pressure and media. The relative area is similar for both methods, regardless of the complexity of the topographies. The relevance scale for each calculation method that significantly represents the effect of grit blasting pressure on the increased value of the relative area is a tiling of 7657.64 µm² of triangle area for the Patchwork method and a 124.6 µm cut-off for the low-pass Gaussian filter of the Sdr method. These results could facilitate a standard, friendly, new fractal method for multiscale characterization of the relative area.

摘要

存在多种用于表面形貌多尺度表征的方法,每种方法都提供独特的见解和应用。该研究聚焦于基于分形的方法,这些方法通过利用分形来分析表面复杂性而独具特色。具体而言,将ASME B46.1和ISO 25178标准中使用的理查森拼接法与源自ISO 25178 - 2的Sdr参数进行比较,采用低通高斯滤波器进行多尺度表征。比较是基于在不同压力和喷砂材料(介质)下进行喷砂处理的TA6V样品表面形貌所计算出的相对面积来进行的。通过喷砂处理获得的表面在所研究的尺度上具有类分形特征,从而能够基于压力和介质对多个层面的面积发展进行分析。无论表面形貌的复杂性如何,两种方法的相对面积都相似。对于每种计算方法,能够显著体现喷砂压力对相对面积增加值影响的相关尺度,对于拼接法而言是三角形面积为7657.64 µm²的平铺,对于Sdr方法的低通高斯滤波器而言是124.6 µm的截止值。这些结果有助于形成一种标准、友好的用于多尺度表征相对面积的新分形方法。

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