Generation of Non-Gaussian Rough Surfaces Using a PSD-Amplitude-Constrained Phase C-VAE

The non-Gaussian height distribution and power spectral density (PSD) characteristics of rough surfaces have significant effects on the real contact area, local pressure distribution, oil-film formation, and friction and wear behavior of lubricated contact interfaces in mechanical components. Conventional methods for generating non-Gaussian rough surfaces commonly rely on iterative correction under explicit statistical constraints, which limits their computational efficiency in large-scale sample generation. To address this issue, this study proposes a PSD-amplitude-constrained phase conditional variational autoencoder (phase C-VAE) for generating non-Gaussian rough surfaces. Unlike conventional constructive methods that repeatedly correct surface samples under explicit statistical constraints, the proposed method learns the conditional distribution of the Fourier phase, while the spectral amplitude used for reconstruction is directly determined from the prescribed PSD. By taking the target skewness, kurtosis, and PSD as conditional inputs, the proposed method achieves joint control of higher-order statistical characteristics and spectral characteristics within a unified generative framework. Under target conditions derived from measured surfaces, the generated non-Gaussian rough surface samples achieved mean absolute relative errors of 0.056% and 0.044% for skewness and kurtosis, respectively, with a generation time of 24.62s. These results indicate that the proposed method can effectively match the target skewness and kurtosis while maintaining good consistency between the generated surfaces and the target PSD. The proposed method alleviates the efficiency limitation of conventional constructive methods in the large-scale generation of non-Gaussian rough surface samples and provides an effective machine-learning-based generative approach for rapid batch modeling of rough surfaces in lubrication, friction, and contact analyses.