Bayesian-optimized hybrid CNN–RNN framework for high-fidelity prediction of spindle thermal deformation in CNC machine tools

Thermal drift is a major source of dimensional inaccuracy in CNC machine tools. This study presents an integrated framework that combines finite element (FE) thermal validation, synchronized multi-sensor temperature and displacement measurements, and Bayesian optimization of hybrid deep learning architectures for axis-wise thermal error prediction. Long short-term memory (LSTM), gated recurrent unit (GRU), CNN LSTM, and CNN-GRU autoencoder variants are systematically trained and evaluated at 5000 and 10,000 rpm spindle speeds using fivefold cross-validation, residual diagnostics, and Diebold Mariano statistical tests. CNN-enhanced architectures consistently outperform standalone recurrent baselines, achieving the lowest RMSE = 0.049 mm on the X -axis at 5000 rpm. Uncertainty quantification via bootstrap confidence intervals confirms the robustness of hybrid models, although predictive accuracy degrades at 10,000 rpm due to stronger thermo-mechanical nonlinearities. Benchmarking against deep learning and hybrid deep learning models demonstrates statistically significant gains due to the increased complexity of hybrid model structures. While results indicate promising potential for integration into real-time thermal compensation, further validation under cutting loads, diverse operating conditions, and multiple machine platforms is required.