{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T12:14:49Z","timestamp":1777637689111,"version":"3.51.4"},"reference-count":52,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,20]],"date-time":"2024-12-20T00:00:00Z","timestamp":1734652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12393783"],"award-info":[{"award-number":["12393783"]}]},{"name":"National Natural Science Foundation of China","award":["12072207"],"award-info":[{"award-number":["12072207"]}]},{"name":"National Natural Science Foundation of China","award":["52205571"],"award-info":[{"award-number":["52205571"]}]},{"name":"National Natural Science Foundation of China","award":["KJ-202305"],"award-info":[{"award-number":["KJ-202305"]}]},{"name":"National Natural Science Foundation of China","award":["12393783"],"award-info":[{"award-number":["12393783"]}]},{"name":"National Natural Science Foundation of China","award":["12072207"],"award-info":[{"award-number":["12072207"]}]},{"name":"National Natural Science Foundation of China","award":["52205571"],"award-info":[{"award-number":["52205571"]}]},{"name":"National Natural Science Foundation of China","award":["KJ-202305"],"award-info":[{"award-number":["KJ-202305"]}]},{"name":"National Natural Science Foundation of China under Grant","award":["12393783"],"award-info":[{"award-number":["12393783"]}]},{"name":"National Natural Science Foundation of China under Grant","award":["12072207"],"award-info":[{"award-number":["12072207"]}]},{"name":"National Natural Science Foundation of China under Grant","award":["52205571"],"award-info":[{"award-number":["52205571"]}]},{"name":"National Natural Science Foundation of China under Grant","award":["KJ-202305"],"award-info":[{"award-number":["KJ-202305"]}]},{"name":"Student Science Research Project of Hebei Jiaotong Vocational and Technical College","award":["12393783"],"award-info":[{"award-number":["12393783"]}]},{"name":"Student Science Research Project of Hebei Jiaotong Vocational and Technical College","award":["12072207"],"award-info":[{"award-number":["12072207"]}]},{"name":"Student Science Research Project of Hebei Jiaotong Vocational and Technical College","award":["52205571"],"award-info":[{"award-number":["52205571"]}]},{"name":"Student Science Research Project of Hebei Jiaotong Vocational and Technical College","award":["KJ-202305"],"award-info":[{"award-number":["KJ-202305"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Diagnosing faults in wheelset bearings is critical for train safety. The main challenge is that only a limited amount of fault sample data can be obtained during high-speed train operations. This scarcity of samples impacts the training and accuracy of deep learning models for wheelset bearing fault diagnosis. Studies show that the Auxiliary Classifier Generative Adversarial Network (ACGAN) demonstrates promising performance in addressing this issue. However, existing ACGAN models have drawbacks such as complexity, high computational expenses, mode collapse, and vanishing gradients. Aiming to address these issues, this paper presents the Transformer and Auxiliary Classifier Generative Adversarial Network (TACGAN), which increases the diversity, complexity and entropy of generated samples, and maximizes the entropy of the generated samples. The transformer network replaces traditional convolutional neural networks (CNNs), avoiding iterative and convolutional structures, thereby reducing computational expenses. Moreover, an independent classifier is integrated to prevent the coupling problem, where the discriminator is simultaneously identified and classified in the ACGAN. Finally, the Wasserstein distance is employed in the loss function to mitigate mode collapse and vanishing gradients. Experimental results using the train wheelset bearing datasets demonstrate the accuracy and effectiveness of the TACGAN.<\/jats:p>","DOI":"10.3390\/e26121113","type":"journal-article","created":{"date-parts":[[2024,12,20]],"date-time":"2024-12-20T04:07:40Z","timestamp":1734667660000},"page":"1113","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sample Augmentation Using Enhanced Auxiliary Classifier Generative Adversarial Network by Transformer for Railway Freight Train Wheelset Bearing Fault Diagnosis"],"prefix":"10.3390","volume":"26","author":[{"given":"Jing","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"},{"name":"Hebei Province University Road Traffic Perception and Intelligent Application Technology Research and Development Center, Hebei Jiaotong Vocational and Technical College, Shijiazhuang 050011, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junfeng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science, South China Business College Guangdong University of Foreign Studies, Guangzhou 510545, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zonghao","family":"Yuan","sequence":"additional","affiliation":[{"name":"College of Career Technology, Hebei Normal University, Shijiazhuang 050043, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianming","family":"Mu","sequence":"additional","affiliation":[{"name":"State Grid Shijiazhuang Electric Power Supply Company, Shijiazhuang 050021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zengqiang","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronic Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"},{"name":"Hebei Provincial Collaborative Innovation Center of Transportation Power Grid Intelligent Integration Technology and Equipment, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suyan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronic Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"065108","DOI":"10.1088\/1361-6501\/acb609","article-title":"A recursive multi-head graph attention residual network for high-speed train wheelset bearing fault diagnosis","volume":"34","author":"Yuan","year":"2023","journal-title":"Meas. Sci. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"045005","DOI":"10.1088\/1361-6501\/acabdb","article-title":"Rolling bearing fault diagnosis based on 2D time-frequency images and data augmentation technique","volume":"34","author":"Fu","year":"2023","journal-title":"Meas. Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"7285","DOI":"10.1109\/TII.2021.3136144","article-title":"Fault diagnosis of wheelset bearings in high-speed trains using logarithmic short-time continuous wavelet transformand modified self-calibrated residual network","volume":"18","author":"Xin","year":"2021","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106914","DOI":"10.1016\/j.ymssp.2020.106914","article-title":"A general multi-objective optimized wavelet filter and its applications in fault diagnosis of wheelset bearings","volume":"145","author":"Yang","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/j.isatra.2021.09.009","article-title":"A promising new tool for fault diagnosis of railway wheelset bearings: SSO-based Kurtogram","volume":"128","author":"Yi","year":"2022","journal-title":"ISA Trans."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.measurement.2016.01.023","article-title":"Wheel-bearing fault diagnosis of trains using empirical wavelet transform","volume":"82","author":"Cao","year":"2016","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"109986","DOI":"10.1016\/j.measurement.2021.109986","article-title":"Research on test bench bearing fault diagnosis of improved EEMD based on improved adaptive resonance technology","volume":"185","author":"Li","year":"2021","journal-title":"Measurement"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1016\/j.ymssp.2016.09.010","article-title":"Rolling bearing fault detection and diagnosis based on composite multiscale fuzzy entropy and ensemble support vector machines","volume":"85","author":"Zheng","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1922","DOI":"10.1109\/TASE.2019.2915286","article-title":"Online fault diagnosis for industrial processes with Bayesian network-based probabilistic ensemble learning strategy","volume":"16","author":"Yu","year":"2019","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.ress.2018.02.010","article-title":"Hierarchical discriminating sparse coding for weak fault feature extraction of rolling bearings","volume":"184","author":"Jiao","year":"2019","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1007\/s11265-019-01461-w","article-title":"Application of multiscale learning neural network based on CNN in bearing fault diagnosis","volume":"91","author":"Wang","year":"2019","journal-title":"J. Signal Process. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.isatra.2019.11.010","article-title":"A novel bearing intelligent fault diagnosis framework under time-varying working conditions using recurrent neural network","volume":"100","author":"An","year":"2020","journal-title":"ISA Trans."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s12206-022-0102-1","article-title":"Application of recurrent neural network to mechanical fault diagnosis: A review","volume":"36","author":"Zhu","year":"2022","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_14","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_15","doi-asserted-by":"crossref","first-page":"78056","DOI":"10.1109\/ACCESS.2022.3193244","article-title":"Rolling bearing fault diagnosis based on improved GAN and 2-D representation of acoustic emission signals","volume":"10","author":"Pham","year":"2022","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"102027","DOI":"10.1016\/j.aei.2023.102027","article-title":"Adaptive variational autoencoding generative adversarial networks for rolling bearing fault diagnosis","volume":"56","author":"Wang","year":"2023","journal-title":"Adv. Eng. Inform."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12044","DOI":"10.1109\/JSEN.2022.3173446","article-title":"Rolling bearing fault diagnosis method base on periodic sparse attention and LSTM","volume":"22","author":"An","year":"2022","journal-title":"IEEE Sens. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"125050","DOI":"10.1088\/1361-6501\/acf598","article-title":"Bearing fault diagnosis based on CNN-BiLSTM and residual module","volume":"34","author":"Fu","year":"2023","journal-title":"Meas. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5081","DOI":"10.1109\/TIE.2019.2931255","article-title":"Broad convolutional neural network based industrial process fault diagnosis with incremental learning capability","volume":"67","author":"Yu","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105834","DOI":"10.1016\/j.asoc.2019.105834","article-title":"Automatic determination of digital modulation types with different noises using convolutional neural network based on time\u2013frequency information","volume":"86","author":"Daldal","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3525712","DOI":"10.1109\/TIM.2021.3119135","article-title":"Conditional GAN and 2-D CNN for bearing fault diagnosis with small samples","volume":"70","author":"Yang","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"108018","DOI":"10.1016\/j.ymssp.2021.108018","article-title":"Bearing fault diagnosis method based on adaptive maximum cyclostationarity blind deconvolution","volume":"162","author":"Wang","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"18338","DOI":"10.1109\/JSEN.2023.3264870","article-title":"A bearing Fault Diagnosis Method Based on Improved Mutual Dimensionless and Deep Learning","volume":"23","author":"Xiong","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4041","DOI":"10.1007\/s12652-021-03177-x","article-title":"A bearing fault diagnosis model based on CNN with wide convolution kernels","volume":"13","author":"Song","year":"2021","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3197","DOI":"10.1109\/TAES.2020.2969579","article-title":"Motion classification using kinematically sifted acgan-synthesized radar micro-doppler signatures","volume":"56","author":"Erol","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"101552","DOI":"10.1016\/j.aei.2022.101552","article-title":"Multi-mode data augmentation and fault diagnosis of rotating machinery using modified ACGAN designed with new framework","volume":"52","author":"Li","year":"2022","journal-title":"Adv. Eng. Inform."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"045107","DOI":"10.1088\/1361-6501\/acb0e9","article-title":"Remaining useful life prediction of bearings based on self-attention mechanism, multi-scale dilated causal convolution, and temporal convolution network","volume":"34","author":"Wei","year":"2023","journal-title":"Meas. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zou, L., Zhang, H., and Wang, C. (2020). MW-ACGAN: Generating multiscale high-resolution SAR images for ship detection. Sensors, 20.","DOI":"10.3390\/s20226673"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3506412","DOI":"10.1109\/TIM.2023.3238032","article-title":"CFFsBD: A candidate fault frequencies-based blind deconvolution for rolling element bearings fault feature enhancement","volume":"72","author":"Cheng","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.isatra.2024.03.033","article-title":"TRA-ACGAN: A motor bearing fault diagnosis model based on an auxiliary classifier generative adversarial network and transformer network","volume":"149","author":"Fu","year":"2024","journal-title":"ISA Trans."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3517811","DOI":"10.1109\/TIM.2021.3082264","article-title":"Intelligent fault diagnosis of rotary machines: Conditional auxiliary classifier GAN coupled with meta learning using limited data","volume":"70","author":"Dixit","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"110545","DOI":"10.1016\/j.measurement.2021.110545","article-title":"Fault diagnosis based on SPBO-SDAE and transformer neural network for rotating machinery","volume":"188","author":"Du","year":"2022","journal-title":"Measurement"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"108616","DOI":"10.1016\/j.ymssp.2021.108616","article-title":"A novel time\u2013frequency Transformer based on self\u2013attention mechanism and its application in fault diagnosis of rolling bearings","volume":"168","author":"Ding","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Liu, W., Zhang, Z., and Zhang, J. (2023). A novel fault diagnosis method of rolling bearings combining convolutional neural network and transformer. Electronics, 12.","DOI":"10.3390\/electronics12081838"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.jmsy.2023.02.018","article-title":"A transformer-based approach for novel fault detection and fault classification\/diagnosis in manufacturing: A rotary system application","volume":"67","author":"Wu","year":"2023","journal-title":"J. Manuf. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/j.neucom.2022.04.111","article-title":"A time series transformer based method for the rotating machinery fault diagnosis","volume":"494","author":"Jin","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"107969","DOI":"10.1016\/j.epsr.2022.107969","article-title":"Transformer fault diagnosis based on improved deep coupled dense convolutional neural network","volume":"209","author":"Li","year":"2022","journal-title":"Electr. Power Syst. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"106507","DOI":"10.1016\/j.engappai.2023.106507","article-title":"Diagnosisformer: An efficient rolling bearing fault diagnosis method based on improved Transformer","volume":"124","author":"Hou","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"9649","DOI":"10.1109\/JSEN.2023.3260469","article-title":"A lightweight transformer with strong robustness application in portable bearing fault diagnosis","volume":"23","author":"Fang","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3515114","DOI":"10.1109\/TIM.2023.3271729","article-title":"ICoT-GAN: Integrated convolutional transformer GAN for rolling bearings fault diagnosis under limited data condition","volume":"72","author":"Gao","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"30984","DOI":"10.1109\/JSEN.2023.3331696","article-title":"Multirotational Speed Data Augmentation and Data Repair of High-speed Train Wheelset Bearings using Graph Speed Classifier GAN","volume":"23","author":"Ma","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"86824","DOI":"10.1109\/ACCESS.2023.3305261","article-title":"An Auxiliary Classifier Generative Adversarial Network based Fault Diagnosis for Analog Circuit","volume":"11","author":"Zheng","year":"2023","journal-title":"IEEE Access"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1049\/elp2.12147","article-title":"A novel method for transformer fault diagnosis based on refined deep residual shrinkage network","volume":"16","author":"Hu","year":"2022","journal-title":"IET Electr. Power Appl."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"102075","DOI":"10.1016\/j.aei.2023.102075","article-title":"Fault transfer diagnosis of rolling bearings across multiple working conditions via subdomain adaptation and improved vision transformer network","volume":"57","author":"Liang","year":"2023","journal-title":"Adv. Eng. Inform."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Tang, X., Xu, Z., and Wang, Z. (2022). A novel fault diagnosis method of rolling bearing based on integrated vision transformer model. Sensors, 22.","DOI":"10.3390\/s22103878"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1109\/TR.2022.3180273","article-title":"Intelligent diagnosis using continuous wavelet transform and gauss convolutional deep belief network","volume":"72","author":"Zhao","year":"2022","journal-title":"IEEE Trans. Reliab."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"7055","DOI":"10.1109\/TII.2022.3208001","article-title":"Fault diagnosis of wheeled robot based on prior knowledge and spatial-temporal difference graph convolutional network","volume":"19","author":"Miao","year":"2022","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Wang, M., Zhang, W., and Shao, M. (2024). Separation and Extraction of Compound-Fault Signal Based on Multi-Constraint Non-Negative Matrix Factorization. Entropy, 26.","DOI":"10.3390\/e26070583"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Mao, Y., Xin, J., and Zang, L. (2024). Fault Diagnosis Method for Rolling Bearings Based on Grey Relation Degree. Entropy, 26.","DOI":"10.3390\/e26030222"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Lu, L., Wang, W., and Kong, D. (2023). Fault diagnosis of rotating machinery using kernel neighborhood preserving embedding and a modified sparse bayesian classification model. Entropy, 25.","DOI":"10.3390\/e25111549"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Rostaghi, M., Khatibi, M.M., and Ashory, M.R. (2023). Refined composite multiscale fuzzy dispersion entropy and its applications to bearing fault diagnosis. Entropy, 25.","DOI":"10.3390\/e25111494"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"107413","DOI":"10.1016\/j.knosys.2021.107413","article-title":"A novel weak fault diagnosis method for rolling bearings based on LSTM considering quasi-periodicity","volume":"231","author":"Gao","year":"2021","journal-title":"Knowl.-Based Syst."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/12\/1113\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:56:04Z","timestamp":1760115364000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/12\/1113"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,20]]},"references-count":52,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["e26121113"],"URL":"https:\/\/doi.org\/10.3390\/e26121113","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,20]]}}}