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

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.