CALCULATION OF FRACTAL DIMENSION BASED ON ARTIFICIAL NEURAL NETWORK AND ITS APPLICATION FOR MACHINED SURFACES

Guo Zhou, Xiaohao Wang, Feng Feng, Pingfa Feng and Min Zhang
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Guo Zhou: Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, Shenzhen 518055, China
Xiaohao Wang: Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, Shenzhen 518055, China†Division of Advanced Manufacturing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
Feng Feng: ��Division of Advanced Manufacturing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
Pingfa Feng: ��Division of Advanced Manufacturing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China‡Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
Min Zhang: ��Division of Advanced Manufacturing, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China

FRACTALS (fractals), 2021, vol. 29, issue 06, 1-19

Abstract: Fractal dimension (D) is a widely used quantity to represent the irregularity of surfaces or profiles, e.g. it is often applied together with surface roughness to evaluate the quality of machined surfaces objectively and precisely. There are some conventional algorithms to calculate D values through the morphological images of measured surfaces. However, the accuracies or efficiencies of these algorithms sometimes might be insufficient to satisfy the requirement of high-precision machining technology. In this paper, an artificial neural network (ANN) model is proposed to evaluate the D value based on a single morphological image. First, the artificial fractal surfaces with preset ideal D values are generated via Weierstrass–Mandelbrot (W–M) function. Then these surfaces are divided into a training dataset and a test dataset, which are used to train the ANN model and compare the model against the conventional algorithms (including box counting, power spectral density, autocorrelation function, structural function, and roughness scaling extraction with flatten order of 1), respectively. The accuracy and efficiency of D calculation by using the trained ANN model are much superior. The mean relative error of ANN model is just 0.25%, while those of conventional algorithms are in the range of 2.22–9.33%. The average time cost for D calculation of ANN model is 1.87ms, while those of conventional algorithms are in the range of 46ms–8s. Based on the advantages verified above, the trained ANN model is utilized to calculate the D values of machined surfaces and investigate the influences of different cutting parameters. It is found that the D values of machined surfaces could be influenced significantly by the feed rate, while the cutting speed and depth are relatively irrelevant.

Keywords: Fractal Dimension; Neural Network; Weierstrass–Mandelbrot Function; Machined Surface; Surface Roughness (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501292

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