Subspace Metric-Based Transfer Learning for Spindle Thermal Error Prediction Under Time-Varying Conditions

Restricted by the scarcity of labeled samples, the transfer domain adaptation has been applied to thermal error prediction of machine tools under complex industrial practices. However, extant studies largely rest on the assumption that the target distribution is given and invariant, which violates the fact that the working conditions may change over time in the real production. To this end, this article presents a novel subspace metric-based dynamic domain adaptation (SMDDA) scheme for real-time prediction of thermal error. First, a practical thermal feature extractor is constructed to capture both local and global features of temperature sequences. Then, the domain adaptation of thermal features is achieved by aligning each source–target domain pair and the outputs of each regressor. In particular, instead of directly aligning the original thermal features, we align their angles and scales in a specific subspace generated by the pseudo-inverse Gram matrix of the two domains to improve the characterization of feature correlations. To fit real-time temperature streams with dynamic conditions, a model updating strategy with buffered weighted incremental time windows (BWITWs) is proposed, which achieves the dynamic prediction of thermal errors via pseudo-values generated by the target network and its asynchronous update with the online network. Extensive evaluations and comparisons with the state-of-the-art methods under exhaustive experiments covering seven different spindle thermal error transfer tasks show that the proposed SMDDA performs quite competitively in terms of both prediction accuracy and stability.