RECOGNITION OF 3D SURFACE FRACTAL DIMENSION BASED ON CONVOLUTIONAL NEURAL NETWORK

Liuqun Wang, Sheng Lei and Zijie Wang
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Liuqun Wang: School of Computer Science, South-Central Minzu University, Wuhan 430074, P. R. China
Sheng Lei: School of Computer Science, South-Central Minzu University, Wuhan 430074, P. R. China
Zijie Wang: School of Computer Science, South-Central Minzu University, Wuhan 430074, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-13

Abstract: Fractal dimension (FD), as an important parameter for the surface morphology of mechanical machining, can be used to analyze the friction characteristics of contacting surfaces. The accurate and rapid measurement of the FD is of significant importance. To this end, this paper presents a novel approach based on a convolutional neural network (3D-CNN) for the recognition of three-dimensional FDs on machined surfaces. We construct a dataset of anisotropic rough surfaces with different FDs using the Weierstrass–Mandelbrot (WM) fractal function and use a one-factor experimental design to analyze the influence of network parameters (network depth, filter size, filter quantity) on the accuracy of FD identification, finding the optimal combination of neural network parameters. By comparing our 3D-CNN method with three other methods (differential box-counting (DBC), triangular prism surface area (TPSA), and fractal Brownian motion (FBM)), we validated the effectiveness of our proposed method. The experimental results show that the average absolute percentage error of FD calculated by the 3D-CNN method can be controlled within 2%, and the method exhibits small errors throughout the full dynamic range of FDs. We also apply the proposed method to calculate the FD of the vertical milling surface and compare the results with the TPSA and FBM methods. The results show that the FD obtained by our method is close to the other two methods, and can be used to calculate the FD of three-dimensional surface profiles, thereby providing a new approach for the dynamic modeling and parameter identification of contact surfaces.

Keywords: Fractal Dimension; Convolutional Neural Network; Weierstrass–Mandelbrot Function; Deep Learning; Surface Topography (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501263

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