{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T05:45:48Z","timestamp":1788587148234,"version":"build-2803163510"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,12,28]],"date-time":"2024-12-28T00:00:00Z","timestamp":1735344000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2024,12,28]],"date-time":"2024-12-28T00:00:00Z","timestamp":1735344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"name":"The paper is supported by the by the Key Science and Technology Research Project of the Henan Province","award":["(No. 242102220025)"],"award-info":[{"award-number":["(No. 242102220025)"]}]},{"name":"by the Science and Technology Innovation Project of China Tobacco Industry Co., Ltd","award":["(AW2023024)"],"award-info":[{"award-number":["(AW2023024)"]}]},{"name":"by the Key R&D Projects in Henan Province","award":["No. 231111221100"],"award-info":[{"award-number":["No. 231111221100"]}]},{"name":"by the Key R&D Projects in Henan Province","award":["No. 241111222400"],"award-info":[{"award-number":["No. 241111222400"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-024-82452-1","type":"journal-article","created":{"date-parts":[[2024,12,28]],"date-time":"2024-12-28T04:44:48Z","timestamp":1735361088000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Reliability evaluation of rolling bearings based on generative adversarial network sample enhancement and maximum entropy method"],"prefix":"10.1038","volume":"14","author":[{"given":"Fannian","family":"Meng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liujie","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenliao","family":"Du","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoyun","family":"Gong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changjun","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuangqiang","family":"Luo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,12,28]]},"reference":[{"issue":"6","key":"82452_CR1","doi-asserted-by":"publisher","first-page":"1636","DOI":"10.21595\/jve.2019.20092","volume":"21","author":"F Gougam","year":"2019","unstructured":"Gougam, F. et al. Bearing fault diagnosis based on feature extraction of empirical wavelet transform (EWT) and fuzzy logic system (FLS) under variable operating conditions. J. Vibroeng. 21(6), 1636\u20131650 (2019).","journal-title":"J. Vibroeng."},{"key":"82452_CR2","doi-asserted-by":"publisher","first-page":"63584","DOI":"10.1109\/ACCESS.2018.2877447","volume":"6","author":"J Xie","year":"2018","unstructured":"Xie, J. et al. An end-to-end model based on improved adaptive deep belief network and its application to bearing fault diagnosis. IEEE Access 6, 63584\u201363596 (2018).","journal-title":"IEEE Access"},{"issue":"2","key":"82452_CR3","doi-asserted-by":"publisher","DOI":"10.1098\/rsos.181488","volume":"6","author":"J Li","year":"2019","unstructured":"Li, J. et al. Research on rolling bearing fault diagnosis based on multi-dimensional feature extraction and evidence fusion theory. Roy. Soc. Open Sci. 6(2), 181488 (2019).","journal-title":"Roy. Soc. Open Sci."},{"issue":"2","key":"82452_CR4","first-page":"280","volume":"32","author":"X Zhang","year":"2010","unstructured":"Zhang, X. et al. FEM numerical simulation onto the contact status of hollow roller in rock-bit\u2019s roller bearing system. J. Mech. Strength 32(2), 280\u2013285 (2010).","journal-title":"J. Mech. Strength"},{"issue":"11","key":"82452_CR5","first-page":"50","volume":"29","author":"L Liu","year":"2012","unstructured":"Liu, L. et al. Simulation analysis of sensitive bearing friction torque based on ADAMS. J. Mach. Des. 29(11), 50\u201352 (2012).","journal-title":"J. Mach. Des."},{"key":"82452_CR6","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.triboint.2012.04.016","volume":"53","author":"NM Ene","year":"2012","unstructured":"Ene, N. M. & Dimofte, F. Effect of fluid film wave bearings on attenuation of gear mesh noise and vibration. Tribol. Int. 53, 108\u2013114 (2012).","journal-title":"Tribol. Int."},{"issue":"15","key":"82452_CR7","first-page":"203","volume":"32","author":"L Zhang","year":"2013","unstructured":"Zhang, L. & Wang, Y. Influence of vibration and shock on transient thermal elastohydrodynamic lubrication of seawater-lubricated plastic bearings. J. Vib. Shock 32(15), 203\u2013208 (2013).","journal-title":"J. Vib. Shock"},{"key":"82452_CR8","first-page":"150","volume":"56","author":"JB Ali","year":"2015","unstructured":"Ali, J. B. et al. Accurate bearing remaining useful life prediction based on Weibull distribution and artificial neural network. Mech. Syst. Signal Process. 56, 150\u2013172 (2015).","journal-title":"Mech. Syst. Signal Process."},{"issue":"3","key":"82452_CR9","first-page":"481","volume":"28","author":"XIA Xin-tao","year":"2013","unstructured":"Xin-tao, X. I. A. et al. Assessment of optimum confidence interval of reliability with three-parameter Weibull distribution using bootstrap weighted-norm method. J. Aerosp. Power 28(3), 481\u2013488 (2013).","journal-title":"J. Aerosp. Power"},{"issue":"5","key":"82452_CR10","first-page":"78","volume":"34","author":"R Zheng","year":"2015","unstructured":"Zheng, R. Parameter estimation of three-parameter Weibull distribution and its application in reliability analysis. J. Vib. Shock 34(5), 78\u201381 (2015).","journal-title":"J. Vib. Shock"},{"issue":"1","key":"82452_CR11","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1002\/1520-6416(20010115)134:1<36::AID-EEJ5>3.0.CO;2-L","volume":"134","author":"S Utsumi","year":"2001","unstructured":"Utsumi, S. et al. Use of wavelet transform and fuzzy system theory to distinguish wear particles in lubricating oil for bearing diagnosis. Electr. Eng. Japan 134(1), 36\u201344 (2001).","journal-title":"Electr. Eng. Japan"},{"key":"82452_CR12","doi-asserted-by":"crossref","unstructured":"Verma, A. K., Srividya, A. & Bhatkar, M. V. A reliability based analysis of generation\/transmission system incorporating TCSC using fuzzy set theory. In 2006 IEEE International Conference on Industrial Technology 2779\u20132784. (IEEE, 2006).","DOI":"10.1109\/ICIT.2006.372655"},{"issue":"5","key":"82452_CR13","first-page":"810","volume":"40","author":"J Yang","year":"2006","unstructured":"Yang, J., Hu, D. & Wu, Z. Bayesian uncertainty inverse analysis method based on pome. J. Zhejiang Univ. Eng. Sci. 40(5), 810 (2006).","journal-title":"J. Zhejiang Univ. Eng. Sci."},{"issue":"17","key":"82452_CR14","first-page":"2273","volume":"25","author":"X Xia","year":"2014","unstructured":"Xia, X., Qin, Y. & Qiu, M. Adjustment for the machining errors of machine tool based on grey bootstrap maximum entropy method. China Mech. Eng. 25(17), 2273\u20132277 (2014).","journal-title":"China Mech. Eng."},{"key":"82452_CR15","first-page":"663","volume":"43","author":"DB Zhang","year":"2012","unstructured":"Zhang, D. B. et al. Structural reliability analysis of tunnel lining based on maximal entropy principle and optimization method. J. Cent. South Univ. (Sci. Technol.) 43, 663\u2013668 (2012).","journal-title":"J. Cent. South Univ. (Sci. Technol.)"},{"key":"82452_CR16","unstructured":"Dong, X. F., Li, H. L. & Yu, H. J. Degradation analysis of machine tool spindle based on maximum entropy and discrimination information. J. Vib. Shock 32(5) (2013)."},{"key":"82452_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2020.107043","volume":"146","author":"K Yu","year":"2021","unstructured":"Yu, K. et al. A multi-stage semi-supervised learning approach for intelligent fault diagnosis of rolling bearing using data augmentation and metric learning. Mech. Syst. Signal Process. 146, 107043 (2021).","journal-title":"Mech. Syst. Signal Process."},{"issue":"2","key":"82452_CR18","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6501\/ad076c","volume":"35","author":"Z Yuyan","year":"2023","unstructured":"Yuyan, Z. et al. Semi-supervised diagnosis method for coupling faults of key rotating components based on EEMD-KPCA under cross working conditions. Meas. Sci. Technol. 35(2), 025014 (2023).","journal-title":"Meas. Sci. Technol."},{"key":"82452_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.measurement.2019.107393","volume":"152","author":"H Zhiyi","year":"2020","unstructured":"Zhiyi, H. et al. Transfer fault diagnosis of bearing installed in different machines using enhanced deep auto-encoder. Measurement 152, 107393 (2020).","journal-title":"Measurement"},{"issue":"7","key":"82452_CR20","doi-asserted-by":"publisher","first-page":"4961","DOI":"10.1109\/TII.2020.2968370","volume":"16","author":"Y Gao","year":"2020","unstructured":"Gao, Y., Liu, X. & Xiang, J. FEM simulation-based generative adversarial networks to detect bearing faults. IEEE Trans. Ind. Inf. 16(7), 4961\u20134971 (2020).","journal-title":"IEEE Trans. Ind. Inf."},{"issue":"04","key":"82452_CR21","first-page":"208","volume":"8","author":"F Hua","year":"2019","unstructured":"Hua, F. Rolling bearing anomaly detection based on generative adversarial networks. Artif. Intell. Robot. Res. 8(04), 208\u2013218 (2019).","journal-title":"Artif. Intell. Robot. Res."},{"key":"82452_CR22","unstructured":"Arjovsky, M., Chintala, S. & Bottou, L. Wasserstein generative adversarial networks. In International Conference on Machine Learning. PMLR 214\u2013223 (2017)."},{"key":"82452_CR23","unstructured":"Goodfellow, I., Pouget-Abadie, J., Mirza, M, et al. Generative adversarial nets. Adv. Neural Inf. Process. Syst. 27 (2014)."},{"issue":"1","key":"82452_CR24","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1109\/TR.2018.2882682","volume":"69","author":"B Wang","year":"2018","unstructured":"Wang, B. et al. A hybrid prognostics approach for estimating remaining useful life of rolling element bearings. IEEE Trans. Reliab. 69(1), 401\u2013412 (2018).","journal-title":"IEEE Trans. Reliab."},{"issue":"16","key":"82452_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3901\/JME.2019.16.001","volume":"55","author":"LEI Yaguo","year":"2019","unstructured":"Yaguo, L. E. I. et al. XJTU-SY rolling element bearing accelerated life test datasets: A tutorial. J. Mech. Eng. 55(16), 1\u20136 (2019).","journal-title":"J. Mech. Eng."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-82452-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-82452-1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-82452-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,28]],"date-time":"2024-12-28T19:03:51Z","timestamp":1735412631000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-82452-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,28]]},"references-count":25,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["82452"],"URL":"https:\/\/doi.org\/10.1038\/s41598-024-82452-1","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,28]]},"assertion":[{"value":"19 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 December 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 December 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"31185"}}