A novel stacking-based ensemble learning framework for thermal error prediction of machine tool feed systems

Xiaoxuan Li, Qinghua Song, Xiaohui Fang, Liguo Zhang, Jin Zheng, Yukui Cai, Zhanqiang Liu, Jiakun Huang, Liquan Liu,
A novel stacking-based ensemble learning framework for thermal error prediction of machine tool feed systems,
Journal of Manufacturing Processes,
Volume 155,
2025,
Pages 655-680,
ISSN 1526-6125,
https://doi.org/10.1016/j.jmapro.2025.10.033.
(https://www.sciencedirect.com/science/article/pii/S1526612525011156)
Abstract: Thermal error is a key factor limiting the machining accuracy of machine tools, and high-precision thermal error modeling is crucial for improving the quality of machined parts and ensuring machining process stability. Nonlinear and time-varying thermal errors caused by complex and nonuniform heat sources in machine tools place higher demands on the modeling accuracy and generalization of thermal error prediction systems. Traditional models, constrained by a single structure, struggle to capture the complex nonlinear relationship between temperature features and thermal errors. To address it, a stacking-based ensemble learning framework that integrates feature enhancement and parameter co-optimization is proposed in this paper. Specifically, interaction features among temperature variables are constructed, and feature identification is performed based on a random forest. A Monte Carlo random search is then employed for the co-optimization of feature combinations and model parameters, resulting in the optimal feature-parameter matching scheme. The first prediction layer integrates multiple heterogeneous base learners to deeply exploit multivariate features. The second prediction layer incorporates a meta-learner to relearn and aggregate base learner outputs, fully leveraging the complementary advantages among models. Additionally, the effect of base learner combinations on prediction performance is investigated, and based on SHAP interpretability analysis, the contribution and underlying mechanisms of each base learner to the final predicted result are revealed. Experimental results show that the stacking model achieves superior prediction accuracy and generalization ability across different testing samples and varying sample sizes, with the average RMSE and MAE reduced by 22.45 % and 21.33 %, respectively, and the average R2 increased by 1.30 %, compared to the optimal single base models. Moreover, after offline training, the response time for obtaining the final thermal error output is within 60 milliseconds. This method provides an ensemble strategy that integrates heterogeneous learners into a strong predictor, with model diversity enhancing the representation of the complex mapping between temperature and thermal errors from multiple perspectives. Moreover, incorporating interaction features improves the utilization of temperature information, enabling accurate modeling with fewer sensors and thus reducing system deployment costs.
Keywords: CNC machine tool; Thermal error modeling; Stacking ensemble learning; Feature interaction; Feature-hyperparameter co-optimization; Heterogeneous base learner