What question did this study set out to answer?

To develop a robust prediction model for spindle thermal errors using optimized feature selection and advanced neural networks.

February 8, 2026Open Access

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

Key Points

To develop a robust prediction model for spindle thermal errors using optimized feature selection and advanced neural networks.
Implemented a two-stage prediction framework combining feature selection and thermal error prediction.
Utilized an enhanced Red-Billed Magpie Optimization algorithm for optimizing neural network parameters.
Applied PSO-optimized HDBSCAN clustering and Pearson correlation for selecting temperature-sensitive features.
Integrated LSTM, deformable convolution, Transformer, and Fourier KAN for feature extraction.
Improved Silhouette index by 32.39% and BWP by 49.16% with the proposed feature selection method.
Reduced prediction RMSE by 31.89% compared to random point selection.
Achieved an RMSE of 0.181 μm and MAE of 0.128 μm, with an R2 score of 0.9978.
Enabled a thermal error reduction of 89% in practical applications.

Abstract

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.

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