The rapid and accurate identification of three-dimensional (3D) height parameters, specifically skewness and kurtosis , is critical for evaluating the functional performance of manufacturing. Traditional approaches for quantifying these parameters often rely on labor-intensive experimental measurements or computationally expensive numerical simulations, which hinder real-time quality control and process optimization. To address these limitations, this study presents an integrated framework combining the spectral representation method (SRM) with a convolutional neural network (CNN) to automate the identification of and for non-Gaussian rough surfaces. The proposed methodology not only accelerates parameter estimation but also bridges the gap between stochastic surface modeling and data-driven machine learning. The research commenced with the acquisition of high-fidelity surface topography data from three common machining processes: vertical milling, face milling, and flat grinding. A KEYENCE VK-X260K laser confocal microscope was employed to capture 3D surface profiles at a resolution of 0.1 µm, ensuring precise measurement of micro-scale asperities. Statistical analysis of the experimental data revealed that the realistic ranged for skewness and kurtosis in industrial contexts span : -0.7 to 0.7 and : 1.5 to 5.0, respectively. These ranges were subsequently used to guide the generation of a synthetic dataset via the SRM, a stochastic modeling technique that reconstructed non-Gaussian surfaces by modulating spectral density functions and higher-order statistical moments. The dataset comprised over 10 000 synthetic 3D surfaces, with each annotated with ground-truth and values, thereby providing a robust foundation for training and validating deep learning models. A dedicated CNN architecture was engineered to directly process 3D surface height matrices and predict skewness and kurtosis. The network design incorporated multi-scale convolutional layers (3×3, 5×5,7×7, and 9×9 filters) to capture both local roughness features and global texture patterns, while batch normalization reduced the problem of gradient disappearance and accelerated the learning process of the model. In order to optimize the performance, a single factor experimental design was used to systematically evaluate the influence of network depth and filter size on the prediction accuracy. The convolutional neural network model was trained with an Adam optimizer, and the learning rate was set to 0.001. The results show that with the increase of network depth, the network performance gradually increases to the peak, and then decreases. However, the increase of filters in the network degrades the performance of the model. Only when the depth is 50 layers convolution and the filter size is 3×3, the network has the best performance. Compared with the traditional statistical feature calculation method, which calculates the third-order and fourth-order central moments of surface height distribution after generating a rough surface based on the spectral representation model. Experimental results show that for the skewness () and kurtosis () calculated based on the Convolutional Neural Network (CNN), the optimal absolute percentage errors (APEs) reach 8.8% and 1.5% respectively, and their mean absolute percentage error (MAPEs) can be controlled within 12.9% and 3.7% respectively. Notably, the CNN reduces computational time by three orders of magnitude, enabling near-instantaneous parameter estimation compared with the SRM simulations. This study not only advances the understanding of non-Gaussian surface generation and characterization, but also establishes a new paradigm for leveraging deep learning in tribology and precision manufacturing. The proposed methodology holds significant potential for real-time quality control, surface optimization, and functional performance prediction in industrial settings.
Key words
skewness /
kurtosis /
convolutional neural network /
contact surface
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Funding
The National Natural Science Foundation of China (52105135); Hubei Provincial Natural Science Foundation (2020CFB174); Nantong Science and Technology Plan Project (JC2023008)
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