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Timely and accurate diagnosis of rotating machinery faults is crucial for ensuring production safety, reducing economic losses, and improving efficiency. Traditional deep learning methods can only extract features from the vertices of the input data, thereby overlooking the information contained in the relationships between vertices. This paper proposes a Legendre graph convolutional network (LGCN) integrated with a self-attention graph pooling method, which is applied to fault diagnosis of rotating machinery. The SA-LGCN model converts vibration signals from Euclidean space into graph signals in non-Euclidean space, employing a fast local spectral filter based on Legendre polynomials and a self-attention graph pooling method, significantly improving the model\u2019s stability and computational efficiency. By applying the proposed method to 10 different planetary gearbox fault tasks, we verify that it offers significant advantages in fault diagnosis accuracy and load adaptability under various working conditions.<\/jats:p>","DOI":"10.3390\/s24175475","type":"journal-article","created":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T12:58:07Z","timestamp":1724417887000},"page":"5475","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Self-Attention Legendre Graph Convolution Network for Rotating Machinery Fault Diagnosis"],"prefix":"10.3390","volume":"24","author":[{"given":"Jiancheng","family":"Ma","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinying","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, North University of China, Taiyuan 030051, China"},{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Siyuan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1123-4537","authenticated-orcid":false,"given":"Jia","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Licheng","family":"Jing","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106587","DOI":"10.1016\/j.ymssp.2019.106587","article-title":"Applications of machine learning to machine fault diagnosis: A review and roadmap","volume":"138","author":"Lei","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1007\/s11465-018-0472-3","article-title":"Basic research on machinery fault diagnostics: Past, present, and future trends","volume":"13","author":"Chen","year":"2018","journal-title":"Front. Mech. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.neucom.2017.07.032","article-title":"A neural network constructed by deep learning technique and its application to intelligent fault diagnosis of machines","volume":"272","author":"Jia","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106272","DOI":"10.1016\/j.ymssp.2019.106272","article-title":"Mechanical fault diagnosis using convolutional neural networks and extreme learning machine","volume":"133","author":"Chen","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/j.neucom.2022.05.056","article-title":"A clustered blueprint separable convolutional neural network with high precision for high-speed train bogie fault diagnosis","volume":"500","author":"Jia","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"108774","DOI":"10.1016\/j.measurement.2020.108774","article-title":"Fault diagnosis of rotating machinery based on recurrent neural networks","volume":"171","author":"Zhang","year":"2021","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"111616","DOI":"10.1016\/j.measurement.2022.111616","article-title":"A novel multiscale feature adversarial fusion network for unsupervised cross-domain fault diagnosis","volume":"200","author":"Shi","year":"2022","journal-title":"Measurement"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"111189","DOI":"10.1016\/j.ymssp.2024.111189","article-title":"Mining knowledge from unlabeled data for fault diagnosis: A multi-task self-supervised approach","volume":"211","author":"Kong","year":"2024","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"110309","DOI":"10.1016\/j.ymssp.2023.110309","article-title":"Class-incremental continual learning model for plunger pump faults based on weight space meta-representation","volume":"196","author":"Liu","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"109884","DOI":"10.1016\/j.ymssp.2022.109884","article-title":"Deep discriminative transfer learning network for cross-machine fault diagnosis","volume":"186","author":"Qian","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_11","unstructured":"Chen, Z., Xu, J., Alippi, C., Ding, S.X., Shardt, Y., Peng, T., and Yang, C. (2021). Graph neural network-based fault diagnosis: A review. arXiv."},{"key":"ref_12","unstructured":"Kipf, T.N., and Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv."},{"key":"ref_13","first-page":"1025","article-title":"Inductive representation learning on large graphs","volume":"30","author":"Hamilton","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_14","first-page":"10-48550","article-title":"Graph attention networks","volume":"1050","author":"Velickovic","year":"2017","journal-title":"Stat"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Xie, G.S., Liu, J., Xiong, H., and Shao, L. (2021, January 20\u201325). Scale-aware graph neural network for few-shot semantic segmentation. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA.","DOI":"10.1109\/CVPR46437.2021.00543"},{"key":"ref_16","unstructured":"Phu, M.T., and Nguyen, T.H. (2021, January 6\u201311). Graph convolutional networks for event causality identification with rich document-level structures. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Virtual."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ramnath, K., Sari, L., Hasegawa-Johnson, M., and Yoo, C. (2021, January 6\u201311). Worldly wise (WoW)-cross-lingual knowledge fusion for fact-based visual spoken-question answering. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Virtual.","DOI":"10.18653\/v1\/2021.naacl-main.153"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"12739","DOI":"10.1109\/TIE.2020.3040669","article-title":"Multireceptive field graph convolutional networks for machine fault diagnosis","volume":"68","author":"Li","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"9157","DOI":"10.1109\/TCYB.2021.3059002","article-title":"Graph convolutional network-based method for fault diagnosis using a hybrid of measurement and prior knowledge","volume":"52","author":"Chen","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1109\/TII.2022.3161674","article-title":"Multiscale deep graph convolutional networks for intelligent fault diagnosis of rotor-bearing system under fluctuating working conditions","volume":"19","author":"Zhao","year":"2022","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4186","DOI":"10.1109\/TIE.2022.3176280","article-title":"Compound fault diagnosis of harmonic drives using deep capsule graph convolutional network","volume":"70","author":"Yang","year":"2022","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4167","DOI":"10.1109\/TIE.2021.3075871","article-title":"SuperGraph: Spatial-temporal graph-based feature extraction for rotating machinery diagnosis","volume":"69","author":"Yang","year":"2021","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"111618","DOI":"10.1016\/j.knosys.2024.111618","article-title":"Node classification oriented Adaptive Multichannel Heterogeneous Graph Neural Network","volume":"292","author":"Li","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"111861","DOI":"10.1016\/j.knosys.2024.111861","article-title":"Neighborhood convolutional graph neural network","volume":"295","author":"Chen","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"110891","DOI":"10.1016\/j.knosys.2023.110891","article-title":"Attention-aware temporal\u2013spatial graph neural network with multi-sensor information fusion for fault diagnosis","volume":"278","author":"Wang","year":"2023","journal-title":"Knowl.-Based Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"122827","DOI":"10.1016\/j.eswa.2023.122827","article-title":"Graph neural network-based bearing fault diagnosis using Granger causality test","volume":"242","author":"Zhang","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"13140","DOI":"10.1109\/JSEN.2023.3269445","article-title":"A novel spiking graph attention network for intelligent fault diagnosis of planetary gearboxes","volume":"23","author":"Cao","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"106518","DOI":"10.1016\/j.neunet.2024.106518","article-title":"A two-stage importance-aware subgraph convolutional network based on multi-source sensors for cross-domain fault diagnosis","volume":"179","author":"Yu","year":"2024","journal-title":"Neural Netw."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3076","DOI":"10.1109\/TMECH.2023.3247172","article-title":"Hierarchical graph convolutional networks with latent structure learning for mechanical fault diagnosis","volume":"28","author":"Zhong","year":"2023","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_30","first-page":"3844","article-title":"Convolutional neural networks on graphs with fast localized spectral filtering","volume":"29","author":"Defferrard","year":"2016","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_31","unstructured":"Ying, Z., You, J., Morris, C., Ren, X., Hamilton, W., and Leskovec, J. (2018). Hierarchical graph representation learning with differentiable pooling. Adv. Neural Inf. Process. Syst., 31."},{"key":"ref_32","unstructured":"Gao, H., and Ji, S. (2019, January 9\u201315). Graph u-nets. Proceedings of the International Conference on Machine Learning, Long Beach, CA, USA."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5475\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:42:28Z","timestamp":1760110948000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/17\/5475"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,23]]},"references-count":32,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["s24175475"],"URL":"https:\/\/doi.org\/10.3390\/s24175475","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,23]]}}}