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<p>The thermal error of machine tools is one of the most critical factors affecting machining accuracy. Compared to conventional temperature sensor-based acquisition methods, thermographic imaging enables comprehensive characterization of the global temperature field within the measurement space, thereby preventing the inherent data loss associated with discrete point-based sampling. Existing image processing models are predominantly developed for discrete prediction tasks such as classification, while thermal error modeling fundamentally constitutes a continuous regression problem. This study proposes a novel multistage thermal error prediction framework with a collaborative architecture. Thermal images are first processed through the classification mode to generate category numbers. Based on the category number, the corresponding regression prediction model is selected to enter the precision prediction mode with using multi-source heterogeneous information as input. During the training phase, each category-specific regression model is trained independently and finally all regression models trained for different categories are integrated together to achieve invoking trained submodules selectively based on real-time classification feedback. The thermal image dataset labeled according to thermal error values is constructed to train a ConvNeXt-based classification model. The ConvNeXt-based classification model achieves an average Z-axis classification accuracy of 44.22% on three test datasets, which is 67.82% and 36.61% higher than those of the ViT (Vision Transformer) and CNN models, and the average Y-axis classification accuracy is 42.78%, with improvements of 69.55% and 67.24%. Gradient-weighted Class Activation Mapping (Grad-CAM) is adopted to conduct visualization analysis on the deep features of thermal images of different categories in network layers. In addition, a feature engineering method combining feature selection and feature extraction is proposed, and the feature dimension after processing is reduced by 72.46% compared with the original feature dimension. Meanwhile, an enhanced multi-parameter weighted ensemble Support Vector Regression (SVR) model is developed. Compared with multiple baseline models, the average root mean square error (RMSE) of the Z-axis prediction results on three test datasets is 0.3013&#xa0;μm, with an improvement of more than 65.70%, and the average RMSE of the Y-axis prediction results is 0.4679&#xa0;μm, with an improvement of more than 51.46%.</p>

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Precision thermal error modeling for CNC machine tool spindle based on thermographic classification and segmented regression with multi-source heterogeneous information fusion

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Hongqi Liu,
  • Yixing He,
  • Xinyong Mao,
  • Bin Li,
  • Fangyu Peng,
  • Songping He

摘要

The thermal error of machine tools is one of the most critical factors affecting machining accuracy. Compared to conventional temperature sensor-based acquisition methods, thermographic imaging enables comprehensive characterization of the global temperature field within the measurement space, thereby preventing the inherent data loss associated with discrete point-based sampling. Existing image processing models are predominantly developed for discrete prediction tasks such as classification, while thermal error modeling fundamentally constitutes a continuous regression problem. This study proposes a novel multistage thermal error prediction framework with a collaborative architecture. Thermal images are first processed through the classification mode to generate category numbers. Based on the category number, the corresponding regression prediction model is selected to enter the precision prediction mode with using multi-source heterogeneous information as input. During the training phase, each category-specific regression model is trained independently and finally all regression models trained for different categories are integrated together to achieve invoking trained submodules selectively based on real-time classification feedback. The thermal image dataset labeled according to thermal error values is constructed to train a ConvNeXt-based classification model. The ConvNeXt-based classification model achieves an average Z-axis classification accuracy of 44.22% on three test datasets, which is 67.82% and 36.61% higher than those of the ViT (Vision Transformer) and CNN models, and the average Y-axis classification accuracy is 42.78%, with improvements of 69.55% and 67.24%. Gradient-weighted Class Activation Mapping (Grad-CAM) is adopted to conduct visualization analysis on the deep features of thermal images of different categories in network layers. In addition, a feature engineering method combining feature selection and feature extraction is proposed, and the feature dimension after processing is reduced by 72.46% compared with the original feature dimension. Meanwhile, an enhanced multi-parameter weighted ensemble Support Vector Regression (SVR) model is developed. Compared with multiple baseline models, the average root mean square error (RMSE) of the Z-axis prediction results on three test datasets is 0.3013 μm, with an improvement of more than 65.70%, and the average RMSE of the Y-axis prediction results is 0.4679 μm, with an improvement of more than 51.46%.