A Novel Hybrid Neural Network with Optimized Feature Selection for Spindle Thermal Error Prediction

In modern intelligent manufacturing, spindle thermal errors are critical to machining accuracy. To address this, we propose a two-stage prediction framework. First, for feature selection, an enhanced Red-Billed Magpie Optimization algorithm (RBMO-X) optimizes the parameters of a hybrid convolutional neural network (DLTK). Concurrently, PSO-optimized HDBSCAN clustering combined with Pearson correlation selects optimal temperature-sensitive points. The DLTK network integrates LSTM, deformable convolution, Transformer, and Fourier KAN modules for robust spatiotemporal feature extraction. The experimental results demonstrate significant improvements. The proposed feature selection method improves the Silhouette index by 32.39% and increases BWP by 49.16%. Using the selected points reduces prediction RMSE by 31.89% compared to random selection. The final RBMO-X-DLTK model achieves an RMSE of 0.181 μm, an MAE of 0.128 μm, and an R2 score of 0.9978, outperforming seven benchmark models (e.g., BP, LSTM, CNN-LSTM). In practical validation, the model enabled an average thermal error reduction of 89%. This integrated approach provides a robust and accurate solution for spindle thermal error prediction, demonstrating strong generalization capability.