Semi-supervised modeling and compensation for the thermal error of precision feed axes

  • Mohan Lei
  • Jun YangEmail author
  • Shuai Wang
  • Liang Zhao
  • Ping Xia
  • Gedong Jiang
  • Xuesong Mei


The data-driven modeling of thermal error-temperature relationship is key to achieve ideal compensation effect for precision machine tools. The improvements of the modeling quality are limited only depending on ameliorating the regression algorithm with same training data, and more information must be introduced for further improvements. The thermal error data, in particular for the feed axes, are usually high-cost and scarce, but the temperature data are usually readily available. Here, it is indicated that an extra information, the low-cost unlabeled temperature data which are easily accessible under various operation conditions, can be exploited to enrich the thermal error modeling data for the feed axes. Then the co-training semi-supervised support vector machines for regression (COSVR), which can include the pattern information of the unlabeled data in modeling, is employed to establish the thermal error-temperature model for feed axes. Thermal experiments were conducted on two cases of different axes, and the labeled data of temperature and thermal error and the unlabeled data of only temperature were obtained under different operating speeds. The linear thermal errors were modeled by COSVR using all the data, and by the genetic algorithm SVR (GA-SVR) using only the labeled data, respectively. Comparisons showed that the COSVR model outperformed the GA-SVR model by 11.45% and 34.14% in RMSE on the two axes, respectively, and by 53.03% of maximum thermal error reduction in the compensation.


Precision boring machine Feed axes Co-training Semi-supervised support vector machine Unlabeled data 


Funding information

This work was financially supported by the National Natural Science Foundation of China (51605375), Research Project of State Key Lab of Digital Manufacturing Equipment & Technology DMETKF2019017, Research Project of State Key Laboratory of Mechanical System and Vibration MSV201701, and Natural Science Foundation of Shaanxi (2017JM5081).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Mohan Lei
    • 1
    • 2
  • Jun Yang
    • 1
    • 3
    Email author
  • Shuai Wang
    • 1
    • 2
  • Liang Zhao
    • 1
    • 2
  • Ping Xia
    • 1
  • Gedong Jiang
    • 1
    • 2
  • Xuesong Mei
    • 1
    • 2
  1. 1.State Key Laboratory for Manufacturing Systems EngineeringXi’an Jiaotong UniversityXi’anChina
  2. 2.Shaanxi Key Laboratory of Intelligent RobotsXi’an Jiaotong UniversityXi’anChina
  3. 3.State Key Lab of Digital Manufacturing Equipment & TechnologyHuazhong University of Science and TechnologyWuhanChina

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