Thermal error modeling and compensation based on Gaussian process regression for CNC machine tools

Thermal errors are one of the main factors affecting the accuracy of high-precision computer numerical control machine tools. Modeling and compensation are the most common approaches for reducing the influence of thermal error on machine tool accuracy. Accuracy and robustness are the key indicators of machine tool thermal error prediction models, especially under different working conditions. Existing thermal error modeling algorithms provide only point predictions of the thermal error; however, interval predictions of the thermal error are important for understanding the stochastic nature of the thermal error prediction and analysis of reliable risk. To address these challenges, this study proposes a novel thermal error modeling method based on Gaussian process regression (GPR) that provides interval predictions of thermal error and achieves high prediction accuracy and robustness. First, multiple batches of experimental data are used to establish the GPR thermal error model to ensure sufficient modeling information. Second, while existing methods select temperature-sensitive points (TSPs) before modeling, the GPR algorithm can adaptively select TSPs during training of the thermal error GPR prediction model. Third, the proposed model provides interval predictions of thermal errors for evaluating the thermal error prediction reliability. The prediction effects of the GPR model are compared with those of existing thermal error models. The experimental results indicate that the proposed model has the highest prediction accuracy and robustness under different working conditions of the tested compensation models. Furthermore, thermal error compensation experiments are conducted to verify the effectiveness of the proposed model.