Abstract
The thermal error reduces the machining accuracy of machine tools, and should be effectively controlled. But the accurate prediction of the thermal error is challenging because of the complex and dynamic running conditions. In previous studies, the temporal feature of the thermal error is considered, and the spatial feature of the thermal error is not considered. However, the thermal error has temporal-spatial (TS) behaviors, and then it is not sufficient to consider the temporal feature only, leading to a low prediction accuracy and poor robustness. Furthermore, most studies on the TS modeling ignore the complexity of the spatial feature, resulting in the spatial feature of the thermal error not being comprehensively captured. When building a TS model, many studies simply connect the spatial model with the temporal model in series. However, the spatial feature changes with the running time, and the series model cannot truly reflect the TS features. To address these challenges, a new dynamic TS memory graph convolutional network (DTSMGCN) model is proposed to learn the dynamic TS features of the thermal error in this study. The generation mechanism of the thermal error is demonstrated by solving the heat conduction equation, and the dynamic TS behaviors are revealed by the Laplace transform. The designed DTSMGCN cell consists of the marginal unit, joint unit, and hybrid adjacency matrix, and can capture the temporal feature of each variable and the TS features among variables. Moreover, to expedite the training process and improve the executing efficiency, an industrial-oriented machine learning big data framework (IOMLBDF) is designed. The proposed DTSMGCN model is embedded into the designed IOMLBDF. The results show that the DTSMGCN model outperforms other machine learning models, and the designed IOMLBDF can improve the training efficiency when increasing the number of virtual machine nodes and achieve the real-time control of the thermal error.
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Abbreviations
- L :
-
Laplace matrix
- \(W_{0}\) :
-
Weight parameter of the first layer
- X :
-
Feature sequence
- \(\delta\) :
-
Threshold
- \(A\) :
-
Adjacency matrix
- \(A^{g}_{i,j}\) :
-
Geographical edge weigh between of node \(i\) and node \(j\)
- IOMLBDF:
-
Industrial-oriented machine learning big data framework
- MLR:
-
Multiple linear regression
- GCN:
-
Graph convolutional network
- HDFS:
-
Hadoop distributed file system
- EC:
-
Edge computing
- TS:
-
Temporal-spatial
- CNN:
-
Convolutional neural network
- \(D\) :
-
Degree matrix
- \(\sigma\) :
-
Activation function
- k :
-
Dimension of the variables
- \(d^{i,j}\) :
-
Distance between the node \(i\) and node \(j\)
- \(I\) :
-
Identity matrix
- \(A^{s}_{i,j}\) :
-
Semantic edge weight between of the node \(i\) and node \(j\)
- DTSMGCN:
-
Dynamic temporal-spatial memory graph convolutional network
- LSTMN:
-
Long short-term memory network
- GRU:
-
Gated recurrent unit
- CC:
-
Cloud computing
- PC:
-
Personal computer
- RNN:
-
Recurrent neural network
- FC:
-
Fog computing
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (52275474, 51905057), the Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission (cstc2019jcyj-msxmX0050), the Fundamental Research Funds for the Central Universities (2020CDJQY-A036), the Venture & Innovation Support Program for Chongqing Overseas Returnees (cx2019054), the State Key Laboratory for Manufacturing Systems Engineering (sklms2020016), the Postgraduate Research and Innovation Project of Chongqing (CYS22012), and the Postgraduate Research and Innovation Project of Chongqing (CYS22013).
Funding
Funding was provided by the National Natural Science Foundation of China (52275474, 51905057), the Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission (cstc2019jcyj-msxmX0050), the Fundamental Research Funds for the Central Universities (2020CDJQY-A036), the Venture & Innovation Support Program for Chongqing Overseas Returnees (cx2019054), the State Key Laboratory for Manufacturing Systems Engineering (sklms2020016), the Postgraduate Research and Innovation Project of Chongqing (CYS22012), and the Postgraduate Research and Innovation Project of Chongqing (CYS22013).
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Gui, H., Liu, J., Ma, C. et al. Industrial-oriented machine learning big data framework for temporal-spatial error prediction and control with DTSMGCN model. J Intell Manuf 35, 1173–1196 (2024). https://doi.org/10.1007/s10845-023-02095-3
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DOI: https://doi.org/10.1007/s10845-023-02095-3