Condition-adaptive spindle thermal error prediction and compensation using Temporal Kolmogorov–Arnold Networks with hybrid feature selection

Thermal error in spindle systems of machine tools presents a fundamental limitation to high-precision manufacturing. However, conventional thermal error models often fail to accommodate the distinct thermal dynamics of cold start and hot start conditions. This study introduces a condition-adaptive framework to address this limitation. The framework integrates two core components: a novel hybrid feature selection algorithm, Extreme Randomized Trees Recursive Feature Elimination (ERFE), which identifies optimal condition-specific Temperature Sensitive Points (TSPs), and a Temporal Kolmogorov-Arnold Network (TKAN) that employs a temporal encoder and interpretable spline-based activation functions for high-fidelity error prediction. Experimental validation on a motorized spindle confirmed the efficacy of this framework. The ERFE algorithm identified distinct, minimal 3-sensor TSP sets for cold and hot starts, reducing sensor dependency by 70% compared to a baseline 10-sensor array. Using these optimized inputs, the ERFE-TKAN model achieved superior predictive performance, with R 2 values consistently exceeding 0.97 and root mean square error (RMSE) below 1.1 μ m. These results surpassed deep learning benchmarks, including CNN-LSTM and GRU models, even when the benchmarks utilized the full sensor set. Real-time compensation experiments further validated the practical utility of the framework, constraining residual thermal errors within 2 μ m. The proposed ERFE-TKAN framework thus establishes a robust and data-efficient solution for thermal error mitigation under diverse operating conditions, demonstrating the potential of condition-adaptive modeling to advance smart manufacturing.