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<p>To improve the positioning accuracy of CNC machine tool feed systems and reduce the impact of thermal errors on machining precision, this study proposes a thermal error prediction approach based on a Kalman-filter-enhanced CNN-LSTM model. Temperature field and thermal error data of the feed system are collected using temperature sensors and a laser interferometer. To improve input feature quality, K-means + + clustering is first applied to group temperature measurement points, followed by mutual information analysis and local sensitivity analysis to select three representative temperature-sensitive points from seven candidates. In the modeling stage, a convolutional neural network (CNN) is employed to extract local spatial features from temperature data, while a long short-term memory (LSTM) network is used to capture temporal evolution characteristics of thermal errors. A Kalman filter is further introduced to recursively refine model outputs and improve prediction stability and noise robustness. Experiments are conducted on a four-axis machining center. Support vector regression (SVR) and BP neural networks are used as baseline models, and a walk-forward validation strategy is adopted to evaluate time-series generalization performance. Results show that the proposed CNN-LSTM-KF model achieves superior performance compared with all benchmark models, reaching an R² of 0.9959, MAE of 0.7496&#xa0;μm, and RMSE of 0.9724&#xa0;μm. The results demonstrate the effectiveness of the proposed method for accurate and stable thermal error prediction in CNC machine tools.</p>

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Thermal error modeling of linear feed axis based on a Kalman filter-optimized CNN-LSTM model

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Caiqiang Zhang,
  • Xingwei Sun,
  • Hongxun Zhao,
  • Yin Liu,
  • Shibo Mu,
  • Sheng Qu,
  • Liya Jin

摘要

To improve the positioning accuracy of CNC machine tool feed systems and reduce the impact of thermal errors on machining precision, this study proposes a thermal error prediction approach based on a Kalman-filter-enhanced CNN-LSTM model. Temperature field and thermal error data of the feed system are collected using temperature sensors and a laser interferometer. To improve input feature quality, K-means + + clustering is first applied to group temperature measurement points, followed by mutual information analysis and local sensitivity analysis to select three representative temperature-sensitive points from seven candidates. In the modeling stage, a convolutional neural network (CNN) is employed to extract local spatial features from temperature data, while a long short-term memory (LSTM) network is used to capture temporal evolution characteristics of thermal errors. A Kalman filter is further introduced to recursively refine model outputs and improve prediction stability and noise robustness. Experiments are conducted on a four-axis machining center. Support vector regression (SVR) and BP neural networks are used as baseline models, and a walk-forward validation strategy is adopted to evaluate time-series generalization performance. Results show that the proposed CNN-LSTM-KF model achieves superior performance compared with all benchmark models, reaching an R² of 0.9959, MAE of 0.7496 μm, and RMSE of 0.9724 μm. The results demonstrate the effectiveness of the proposed method for accurate and stable thermal error prediction in CNC machine tools.