{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T12:41:09Z","timestamp":1785415269517,"version":"3.56.0"},"reference-count":50,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T00:00:00Z","timestamp":1782518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52505091"],"award-info":[{"award-number":["52505091"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"award":["52505091"],"award-info":[{"award-number":["52505091"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010818","name":"Beijing Information Science & Technology University","doi-asserted-by":"crossref","award":["KF20202223203"],"award-info":[{"award-number":["KF20202223203"]}],"id":[{"id":"10.13039\/501100010818","id-type":"DOI","asserted-by":"crossref"}]},{"award":["KF20202223203"],"award-info":[{"award-number":["KF20202223203"]}],"id":[{"id":"https:\/\/ror.org\/04xnqep60","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Bearing fault diagnosis methods based on single sensors often suffer from reduced accuracy due to limited information. Although multi-sensor systems provide richer vibration information, the high dimensionality and complexity of these signals still pose challenges for effective feature extraction and fusion. In addition, many existing deep learning-based fusion methods rely on a single analysis domain or simple feature concatenation, making it difficult to fully exploit the complementarity among raw temporal signals, time-domain statistical features, and frequency-domain characteristics. To address these issues, this paper proposes a multi-view graph-based fault diagnosis framework with adaptive fusion, termed MDEGCN, for bearing condition identification. Specifically, non-overlapping vibration windows are treated as graph nodes, and three graph views are constructed to capture temporal proximity, time-domain similarity, and frequency-domain correlation, respectively. Each graph view is processed by an enhanced graph neural network branch to learn view-specific representations, and an adaptive, differentiable fusion mechanism is introduced to integrate complementary information from different views for final fault classification. Experiments on the Northeast Forestry University and Politecnico di Torino bearing datasets were conducted under a purged blocked split protocol to reduce potential information leakage between adjacent windows. Additional hard settings with a low training ratio further evaluate the robustness of the proposed framework under limited labelled data. The experimental results demonstrate that MDEGCN achieves competitive diagnostic performance and provides an effective multi-view representation learning strategy for bearing fault diagnosis.<\/jats:p>","DOI":"10.3390\/computation14070148","type":"journal-article","created":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T00:54:42Z","timestamp":1782694482000},"page":"148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Multi-View Graph Learning Framework for Bearing Fault Diagnosis with Adaptive Fusion"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0335-0594","authenticated-orcid":false,"given":"Xueyi","family":"Li","sequence":"first","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chaolun","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5844-9623","authenticated-orcid":false,"given":"Jiannan","family":"Dong","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhilin","family":"Dong","sequence":"additional","affiliation":[{"name":"College of Engineering, Zhejiang Normal University, Jinhua 321004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianyang","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15728","DOI":"10.1109\/TASE.2025.3571516","article-title":"Multi-condition fault diagnosis of dynamic systems: A survey, insights, and prospects","volume":"22","author":"Han","year":"2025","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Seid Ahmed, Y., Abubakar, A.A., Arif, A.F.M., and Al-Badour, F.A. (2025). Advances in fault detection techniques for automated manufacturing systems in industry 4.0. Front. Mech. Eng., 11.","DOI":"10.3389\/fmech.2025.1564846"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s42417-025-01913-7","article-title":"A comprehensive survey of multi-view intelligent fault diagnosis tailored to the sensor, machinery equipment, and industrial system faults","volume":"13","author":"Lin","year":"2025","journal-title":"J. Vib. Eng. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"8543","DOI":"10.1021\/acs.iecr.5c00283","article-title":"Review on graph neural networks for process soft sensor development, fault diagnosis, and process monitoring","volume":"64","author":"Jia","year":"2025","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Duan, H., Chen, G., Yu, Y., Du, C., Bao, Z., and Ma, D. (2025). DyGAT-FTNet: A dynamic graph attention network for multi-sensor fault diagnosis and time\u2013frequency data fusion. Sensors, 25.","DOI":"10.3390\/s25030810"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"110328","DOI":"10.1016\/j.ress.2024.110328","article-title":"Causal intervention graph neural network for fault diagnosis of complex industrial processes","volume":"251","author":"Liu","year":"2024","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"100158","DOI":"10.1016\/j.dche.2024.100158","article-title":"Improved fault detection and diagnosis using graph auto encoder and attention-based graph convolution networks","volume":"11","author":"Brahmbhatt","year":"2024","journal-title":"Digit. Chem. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2716","DOI":"10.1177\/14759217251327760","article-title":"On cross-attention-based graph neural networks for fault diagnosis using multi-sensor measurement","volume":"25","author":"Ren","year":"2025","journal-title":"Struct. Health Monit."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/j.prostr.2026.02.039","article-title":"Prototype-attention domain adaptation for explainable bearing fault diagnosis","volume":"80","author":"Rezazadeh","year":"2026","journal-title":"Procedia Struct. Integr."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"114173","DOI":"10.1016\/j.engappai.2026.114173","article-title":"A novel interpretable dynamic weighted domain adaptation network for cross-domain fault diagnosis of bearings under time-varying speeds","volume":"170","author":"Li","year":"2026","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103776","DOI":"10.1016\/j.aei.2025.103776","article-title":"A fault diagnosis data augmentation method integrating multimodal non-gaussian denoising diffusion generative adversarial network","volume":"68","author":"Li","year":"2025","journal-title":"Adv. Eng. Inform."},{"key":"ref_12","first-page":"64","article-title":"A single-device environment-adaptive mixed reality framework for real-time industrial fault diagnosis","volume":"5","author":"Li","year":"2026","journal-title":"J. Dyn. Monit. Diagn."},{"key":"ref_13","first-page":"207","article-title":"Attribute-driven fuzzy fault tree model for adaptive lubricant failure diagnosis","volume":"3","author":"Wang","year":"2024","journal-title":"J. Dyn. Monit. Diagn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"202","DOI":"10.20517\/ir.2025.11","article-title":"Digital twins to embodied artificial intelligence: Review and perspective","volume":"5","author":"Li","year":"2025","journal-title":"Intell. Robot."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Su, K., Kong, X., Li, X., Wang, T., and Chu, F. (2026). BI-sandwich: A cross-domain model for fault diagnosis of aircraft engine main shaft bearings. Struct. Health Monit., 14759217261426251.","DOI":"10.1177\/14759217261426251"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"108453","DOI":"10.1016\/j.compchemeng.2023.108453","article-title":"Graph attention network with granger causality map for fault detection and root cause diagnosis","volume":"180","author":"Liu","year":"2024","journal-title":"Comput. Chem. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wang, L., You, P., Zhang, X., Jiang, L., and Li, Y. (2025). Adaptive adjustment graph representation learning method for rotating machinery fault diagnosis under noisy signals. Front. Mech. Eng., 20.","DOI":"10.1007\/s11465-024-0818-y"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"045402","DOI":"10.1088\/3050-2454\/ae227a","article-title":"Metric learning-based two-stage imbalanced fault diagnosis model for water injection pump","volume":"1","author":"Yao","year":"2025","journal-title":"J. Reliab. Sci. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, Z., Ma, J., Fan, R., Zhao, Y., Ai, J., and Dong, Y. (2025). Aircraft sensor fault diagnosis based on GraphSage and attention mechanism. Sensors, 25.","DOI":"10.3390\/s25030809"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1186\/s40537-023-00876-4","article-title":"A review of graph neural networks: Concepts, architectures, techniques, challenges, datasets, applications, and future directions","volume":"11","author":"Khemani","year":"2024","journal-title":"J. Big Data"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"108653","DOI":"10.1016\/j.ymssp.2021.108653","article-title":"The emerging graph neural networks for intelligent fault diagnostics and prognostics: A guideline and a benchmark study","volume":"168","author":"Li","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","unstructured":"Su, K., Ran, G., Li, X., Wang, T., Yang, Y., Chu, F., and Kong, X. (2026). Harmonising convolutional networks and transformer for transfer learning in bearing fault diagnosis. Nondestruct. Test. Eval., 1\u201325.","DOI":"10.1080\/10589759.2025.2606949"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"110609","DOI":"10.1016\/j.ymssp.2023.110609","article-title":"A graph-guided collaborative convolutional neural network for fault diagnosis of electromechanical systems","volume":"200","author":"Xu","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"112025","DOI":"10.1016\/j.ymssp.2024.112025","article-title":"Noise-robust multi-view graph neural network for fault diagnosis of rotating machinery","volume":"224","author":"Li","year":"2025","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"106927","DOI":"10.1016\/j.engappai.2023.106927","article-title":"Graph attention U-net to fuse multi-sensor signals for long-tailed distribution fault diagnosis","volume":"126","author":"Yang","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_27","unstructured":"Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, \u0141., and Polosukhin, I. (2017). Attention Is All You Need; Advances in neural information processing systems, Curran Associates Inc."},{"key":"ref_28","unstructured":"Kipf, T.N. (2016). Semi-supervised classification with graph convolutional networks. arXiv."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.ymssp.2018.05.050","article-title":"Deep learning and its applications to machine health monitoring","volume":"115","author":"Zhao","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","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_31","doi-asserted-by":"crossref","unstructured":"Zhang, W., Peng, G., Li, C., Chen, Y., and Zhang, Z. (2017). A new deep learning model for fault diagnosis with good anti-noise and domain adaptation ability on raw vibration signals. Sensors, 17.","DOI":"10.20944\/preprints201701.0132.v1"},{"key":"ref_32","first-page":"1","article-title":"Fault diagnosis of linear guide rails based on SSTG combined with CA-DenseNet","volume":"3","author":"Wu","year":"2024","journal-title":"J. Dyn. Monit. Diagn."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"143","DOI":"10.20517\/ir.2025.09","article-title":"An overview of industrial image segmentation using deep learning models","volume":"5","author":"Wang","year":"2025","journal-title":"Intell. Robot."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"105003","DOI":"10.1016\/j.ijnonlinmec.2024.105003","article-title":"ML-based bevel gearbox fault diagnosis: An extensive time domain feature extraction approach with limited data","volume":"170","author":"Kumar","year":"2025","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.measurement.2019.06.022","article-title":"Compound faults diagnosis based on customized balanced multiwavelets and adaptive maximum correlated kurtosis deconvolution","volume":"146","author":"Hong","year":"2019","journal-title":"Measurement"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5835","DOI":"10.1007\/s12206-025-0920-z","article-title":"A fault feature extraction method for a reciprocating compressor based on optimized SVMD and CMFBSIE","volume":"39","author":"Huang","year":"2025","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"8628","DOI":"10.1109\/TII.2024.3366993","article-title":"Transparent operator network: A fully interpretable network incorporating learnable wavelet operator for intelligent fault diagnosis","volume":"20","author":"Li","year":"2024","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Khan, A., Junaid, A., and Siddique, M.F. (2026). Smart predictive maintenance: A TCN-based system for early fault detection in industrial machinery. Machines, 14.","DOI":"10.3390\/machines14020164"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"229","DOI":"10.20517\/ir.2026.12","article-title":"Fixed-time prescribed performance formation control of heterogeneous UAV-USV systems under actuator faults","volume":"6","author":"Liang","year":"2026","journal-title":"Intell. Robot."},{"key":"ref_40","unstructured":"Veysi, P., Adeli, M., Naziri, N.P., and Adeli, E. (2024). A gentle approach to multi-sensor fusion data using linear kalman filter. arXiv."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2441","DOI":"10.1007\/s10845-023-02165-6","article-title":"Fault diagnosis and self-healing for smart manufacturing: A review","volume":"35","author":"Aldrini","year":"2024","journal-title":"J. Intell. Manuf."},{"key":"ref_42","unstructured":"Gilmer, J., Schoenholz, S.S., Riley, P.F., Vinyals, O., and Dahl, G.E. (2017). Neural message passing for quantum chemistry. Proceedings of the International Conference on Machine Learning, PMLR."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"035301","DOI":"10.1088\/3050-2454\/ae064d","article-title":"A neuro-fuzzy approach with hypergraph convolution for fault diagnosis in industrial devices","volume":"1","author":"Zhuang","year":"2025","journal-title":"J. Reliab. Sci. Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"6015","DOI":"10.1109\/TNNLS.2021.3132376","article-title":"Interaction-aware graph neural networks for fault diagnosis of complex industrial processes","volume":"34","author":"Chen","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"106267","DOI":"10.1016\/j.mechmachtheory.2025.106267","article-title":"A fault diagnosis method for bearings based on multiscale graph convolutional network under non-stationary speed conditions","volume":"217","author":"Li","year":"2025","journal-title":"Mech. Mach. Theory"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"100141","DOI":"10.1016\/j.cjme.2025.100141","article-title":"Knowledge extraction and retrieval-augmented generation for intelligent maintenance of wind power equipment based on graph attention networks","volume":"39","author":"Li","year":"2025","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"45104","DOI":"10.1109\/ACCESS.2026.3675976","article-title":"Advanced fault diagnosis in rotary machines using optimized transfer learning","volume":"14","author":"Zaman","year":"2026","journal-title":"IEEE Access"},{"key":"ref_48","unstructured":"Pham, H., Guan, M., Zoph, B., Le, Q., and Dean, J. (2018). Efficient neural architecture search via parameters sharing. Proceedings of the International Conference on Machine Learning, PMLR."},{"key":"ref_49","unstructured":"Xu, Y., Xie, L., Zhang, X., Chen, X., Qi, G.-J., Tian, Q., and Xiong, H. (2019). Pc-darts: Partial channel connections for memory-efficient architecture search. arXiv."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"He, C., Ye, H., Shen, L., and Zhang, T. (2020, January 16\u201318). Milenas: Efficient neural architecture search via mixed-level reformulation. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.01201"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/14\/7\/148\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T04:45:55Z","timestamp":1782967555000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/14\/7\/148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,27]]},"references-count":50,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["computation14070148"],"URL":"https:\/\/doi.org\/10.3390\/computation14070148","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,27]]}}}