New Novel Graph Neural Network Architecture Integrating Wavelet Transform and Fourier Analysis for Thermal Error Prediction

Introduction: Thermal error in ball screw feed systems critically compromises the machining accuracy and stability of machine tools, necessitating advanced prediction models to address this challenge. Methods: This paper has proposed a love evolution algorithm-optimized wavelet Fourier graph neural network (LEA-WFGN) for thermal error prediction. The model combines Fourier and wavelet transforms to extract complex error characteristics, while a graph structure enables efficient node fusion. The love evolution algorithm dynamically optimizes parameters to improve robustness. Experiments on a CNC machine collected temperature and error data at 16 measurement points under varying conditions. Results: Comparative experiments with multiple state-of-the-art thermal error prediction models (including BP neural networks, SVM, and hybrid deep learning methods) demonstrated the superiority of LEA-WFGN. Key improvements included an 8.97% reduction in MAPE, a 0.0252 decrease in MAE, a 0.0311 lower RMSE, and a 0.001 increase in R² compared to existing benchmarks. Discussion: The results underscored the effectiveness of the proposed model in significantly enhancing prediction accuracy and stability. The dual-domain analysis capability allowed for robust capture of both global and localized thermal deformation patterns, even under dynamic machining conditions. However, the study was limited to specific types of CNC machine tools and measurement configurations; generalizability to other systems may require further validation. Conclusion: The LEA-WFGN model substantially advanced thermal error prediction, achieving a 15.6% overall performance improvement and sub-micron level accuracy (MAE ≤ 0.2 μm). It demonstrated strong potential for industrial application in CNC error compensation, with formal patent protection currently in progress.