基于卷积神经网络的三维表面分形维数识别

Recognition of 3D Surface Fractal Dimension Based on Convolutional Neural Network

分形维数作为机械加工表面形貌的重要参数,可用于接触表面的摩擦特性分析。然而,现有的分形维数计算方法大多需要选择多组尺度计算相应的测度,这不仅影响分形维数的计算速度和精度,也增加了计算的复杂度。针对机加工表面的三维分形维数测量问题,提出一种基于卷积神经网络的分形维数的识别方法。采用Weierstrass-Mandelbrot分形函数构建一个包含不同分形维数的三维粗糙表面数据集,利用单因素实验法分析网络参数(网络深度、滤波器大小、滤波器数量)对三维分形维数识别精度的影响,以找到最优的神经网络参数组合。通过与差分盒维数法、三角棱镜表面积法和分形布朗运动法3种方法进行对比,验证卷积神经网络法识别三维分形维数的有效性。实验结果表明:基于卷积神经网络方法计算的分形维数平均绝对百分比误差可控制在1.5%以下;该方法在分形维数全动态范围内都表现出较小的误差,可用于计算三维表面轮廓分形维数。

Fractal dimension,as an important parameter for the surface morphology of mechanical machining,can be used to analyze the friction characteristics of contacting surfaces.However,most existing methods for calculating fractal dimensions require selecting multiple scales to compute the corresponding measures,which not only affects the calculation speed and accuracy of fractal dimensions but also increases the complexity of computation.A recognition method of fractal dimension based on convolutional neural network(CNN)was proposed for the measurement of three-dimensional(3D)fractal dimension of machined surface.A 3D rough surface dataset containing different fractal dimensions was constructed using the Weierstrass-Mandelbrot fractal function.The single factor experiment method was used to analyze the influence of the network parameters(network depth,filter size,filter number)on the recognition accuracy of 3D fractal dimension,in order to find the optimal combination of neural network parameters.By comparing with the three methods of differential box dimension method,triangular prism surface area method and fractal Brownian motion method,the effectiveness of convolutional neural network method in identifying 3D fractal dimension was verified.The experimental results show that the average absolute percentage error of the fractal dimension calculated by the convolutional neural network method can be controlled below 1.5%.The proposed method exhibits small errors across the entire dynamic range of fractal dimensions and can be used to calculate the fractal dimension of 3D surface profiles.