Self-optimizing thermal error compensation models with adaptive inputs using Group-LASSO for ARX-models

Thermal errors have a significant impact on the machining accuracy of five-axis machine tools. The thermal adaptive learning control (TALC), which combines adaptable data-based models and on-machine measurements, realizes a precise and robust long-term reduction of thermal errors of machine tools. To further improve the precision and the robustness of data-based models for thermal error compensation, this publication introduces a new method to realize adaptive model inputs. This method combines the Group-LASSO (least absolute shrinkage and selection operator) for autoregressive models with exogenous inputs (ARX) and the particle swarm optimization to realize a simultaneous estimation of the optimal inputs, the model structure, and the model parameters. Additionally, the self-optimization ability of thermal error compensation models, based on the TALC, is increased by introducing error-specific action control limits to define the frequency of model updates. The newly developed methods are applied to compensate the thermal errors of a swiveling and a rotary axis of a five-axis machine tool during a long-term test series of 350 h. Randomly generated speed profiles of the linear and rotary axes as well as the spindle and changing ambient conditions ensure a high variety of thermal load cases within in the analyzed long-term test series. The results show that the prediction accuracy measured as peak-to-peak values and the robustness of the thermal error compensation models are improved by up to 36% and 58% respectively when adaptive instead of static model inputs are used. Furthermore, the compensation results of the new method outperform the previously used sequential input selection method regarding prediction accuracy and repeatability. The average peak-to-peak value of the compensated translational thermal errors is reduced by 23% and the repeatability of the corresponding compensation results is increased by 57%. Consequently, the consideration of the resulting model structure during the selection of the optimal model inputs significantly enhances the performance of the resulting data-based thermal error compensation models.