A novel meta-learning-based spatio-temporal modeling approach for thermal error prediction of multiple machine tools with few labeled data

Thermal errors have a significant effect on the machining accuracy of high-precision machine tools. Developing a high precision and robust thermal error prediction model plays an important role in compensating thermal error and improving machining accuracy. Due to the inherent discrepancies between the machine tools, there exists certain differences in the distribution of thermal error data among different machine tools. Therefore, the thermal error prediction model developed for one machine tool may not be directly applicable to others. To address the aforementioned issue, a novel spatio-temporal thermal error prediction method based on meta-learning is proposed in this paper. This method aims to enhance the robustness of the model under varying operating conditions of a single machine tool, and improve generalization across multiple machine tools. Firstly, a small amount of operational data is collected from each machine tool for subsequent modeling and training purposes. Subsequently, a novel spatio-temporal modeling approach called Stacked Graph Attention Network (SGAT)-Transformer is employed for thermal error modeling. In this framework, the SGAT is responsible for extracting the spatial characteristics of the thermal error, while the Transformer captures the temporal dependencies and time-interaction behaviors associated with these errors. Additionally, to enhance the robustness and generalization ability of the SGAT-Transformer model, this paper introduces a meta-learning approach known as Model-Agnostic Meta-Learning (MAML), which enables rapid adaptation to unknown operating conditions. Finally, two validation cases are designed to further assess the model's robustness and generalization capacity.