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Thermally induced errors critically limit precision in machine tools (MT), affecting dimensional accuracy in high-precision manufacturing. Physics-based models offer a sustainable solution and can do without training measurements, unlike data-driven models, but are often unsuitable for real-time thermal error compensation due to computational demands and boundary condition uncertainties. This paper presents an enhanced ensemble Kalman filter approach to accurately and efficiently reconstruct the thermal state from limited sensor data. Utilizing a reduced finite element model generated via Krylov modal subspace techniques, the proposed method integrates real-time sensor measurements with an ensemble of perturbed models to robustly estimate thermal states and mechanical deformations. Validation experiments on a thermal test bench with 10 out of 40 temperature sensors observed demonstrate significant improvements in accuracy achieving an RMSE of \(1.5\,^{\circ }\) C. The computational speed is over 45 \(\times \) faster than real-time allowing the implementation of the digital twin for any MT. The reduction of the volumetric thermal error by consistently more than 70% confirm the potential of this digital twin-based approach for real-time thermal error compensation in precision manufacturing.

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Overcoming Uncertainty With an Ensemble of Physical Models and Real-Time Measurements: Thermal Error Compensation Using Kalman Filters In a Digital Twin

  • 会议论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年

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  • Sebastian Lang,
  • Marco Schneider,
  • Lenny Rhiner,
  • Markus Bambach

摘要

Thermally induced errors critically limit precision in machine tools (MT), affecting dimensional accuracy in high-precision manufacturing. Physics-based models offer a sustainable solution and can do without training measurements, unlike data-driven models, but are often unsuitable for real-time thermal error compensation due to computational demands and boundary condition uncertainties. This paper presents an enhanced ensemble Kalman filter approach to accurately and efficiently reconstruct the thermal state from limited sensor data. Utilizing a reduced finite element model generated via Krylov modal subspace techniques, the proposed method integrates real-time sensor measurements with an ensemble of perturbed models to robustly estimate thermal states and mechanical deformations. Validation experiments on a thermal test bench with 10 out of 40 temperature sensors observed demonstrate significant improvements in accuracy achieving an RMSE of \(1.5\,^{\circ }\) C. The computational speed is over 45 \(\times \) faster than real-time allowing the implementation of the digital twin for any MT. The reduction of the volumetric thermal error by consistently more than 70% confirm the potential of this digital twin-based approach for real-time thermal error compensation in precision manufacturing.