Thermal error prediction method of Transformer-GRU composite model for CNC machine tool feeding system based on multi-source information fusion

Abstract One of the key elements influencing machining precision is the thermal inaccuracy of the CNC machine tool feeding mechanism. To improve prediction capability, this article presents a Transformer-gated recurrent unit (GRU) composite model for thermal error prediction, which adopts an information fusion method to consider the combined effects of multiple factors on thermal error. First, an experimental platform is constructed to measure thermal error, temperature and vibration data in the feeding system. Fuzzy C-means and gray relational analysis are adopted to screen out the data of temperature sensitive points, and vibration data are processed by means of empirical mode decomposition with wavelet thresholding, Spearman correlation coefficient and kernel principal component analysis. The temperature and vibration data are then fused using a multi-source information fusion (MSIF) technique. A Transformer-GRU composite model that embeds the GRU into the Transformer architecture is introduced. Finally, the temperature, vibration and displacement data are fused to construct a composite Transformer-GRU model for thermal error prediction of the feeding system. To prove the effectiveness of the presented model, its prediction results are compared and analyzed with Transformer, Transformer-long short-term memory (LSTM) and CNN-GRU models. The performance metrics show that the Transformer–GRU composite model achieves RMSE, MAE, and MSE values of 1.40, 1.15, and 1.97, respectively—representing reductions of 36.9%, 15.4%, and 29.9% relative to the Transformer; 36.9%, 39.1%, and 59.9% relative to the Transformer–LSTM; and 41.4%, 40.4%, and 65.4% relative to the CNN–GRU. The results demonstrate that the Transformer-GRU composite model, which utilizes MSIF, achieves higher prediction accuracy.