{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T17:02:30Z","timestamp":1774544550178,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2022,10,14]],"date-time":"2022-10-14T00:00:00Z","timestamp":1665705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science and Technology Research Project of Jiangxi Education Department","award":["GJJ212504"],"award-info":[{"award-number":["GJJ212504"]}]},{"name":"Science and Technology Research Project of Jiangxi Education Department","award":["61973262"],"award-info":[{"award-number":["61973262"]}]},{"name":"Science and Technology Research Project of Jiangxi Education Department","award":["E2019203146"],"award-info":[{"award-number":["E2019203146"]}]},{"name":"Science and Technology Research Project of Jiangxi Education Department","award":["E2020203128"],"award-info":[{"award-number":["E2020203128"]}]},{"name":"Science and Technology Research Project of Jiangxi Education Department","award":["ZD2021106"],"award-info":[{"award-number":["ZD2021106"]}]},{"name":"Science and Technology Research Project of Jiangxi Education Department","award":["NGYJZX-2021-04"],"award-info":[{"award-number":["NGYJZX-2021-04"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["GJJ212504"],"award-info":[{"award-number":["GJJ212504"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61973262"],"award-info":[{"award-number":["61973262"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["E2019203146"],"award-info":[{"award-number":["E2019203146"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["E2020203128"],"award-info":[{"award-number":["E2020203128"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ZD2021106"],"award-info":[{"award-number":["ZD2021106"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NGYJZX-2021-04"],"award-info":[{"award-number":["NGYJZX-2021-04"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Hebei Province","award":["GJJ212504"],"award-info":[{"award-number":["GJJ212504"]}]},{"name":"Natural Science Foundation of Hebei Province","award":["61973262"],"award-info":[{"award-number":["61973262"]}]},{"name":"Natural Science Foundation of Hebei Province","award":["E2019203146"],"award-info":[{"award-number":["E2019203146"]}]},{"name":"Natural Science Foundation of Hebei Province","award":["E2020203128"],"award-info":[{"award-number":["E2020203128"]}]},{"name":"Natural Science Foundation of Hebei Province","award":["ZD2021106"],"award-info":[{"award-number":["ZD2021106"]}]},{"name":"Natural Science Foundation of Hebei Province","award":["NGYJZX-2021-04"],"award-info":[{"award-number":["NGYJZX-2021-04"]}]},{"name":"Science and Technology program of Colleges of Hebei Education Department","award":["GJJ212504"],"award-info":[{"award-number":["GJJ212504"]}]},{"name":"Science and Technology program of Colleges of Hebei Education Department","award":["61973262"],"award-info":[{"award-number":["61973262"]}]},{"name":"Science and Technology program of Colleges of Hebei Education Department","award":["E2019203146"],"award-info":[{"award-number":["E2019203146"]}]},{"name":"Science and Technology program of Colleges of Hebei Education Department","award":["E2020203128"],"award-info":[{"award-number":["E2020203128"]}]},{"name":"Science and Technology program of Colleges of Hebei Education Department","award":["ZD2021106"],"award-info":[{"award-number":["ZD2021106"]}]},{"name":"Science and Technology program of Colleges of Hebei Education Department","award":["NGYJZX-2021-04"],"award-info":[{"award-number":["NGYJZX-2021-04"]}]},{"name":"Nonlinear Dynamics and Application Research Center of Nanchang Institute of Science and Technology","award":["GJJ212504"],"award-info":[{"award-number":["GJJ212504"]}]},{"name":"Nonlinear Dynamics and Application Research Center of Nanchang Institute of Science and Technology","award":["61973262"],"award-info":[{"award-number":["61973262"]}]},{"name":"Nonlinear Dynamics and Application Research Center of Nanchang Institute of Science and Technology","award":["E2019203146"],"award-info":[{"award-number":["E2019203146"]}]},{"name":"Nonlinear Dynamics and Application Research Center of Nanchang Institute of Science and Technology","award":["E2020203128"],"award-info":[{"award-number":["E2020203128"]}]},{"name":"Nonlinear Dynamics and Application Research Center of Nanchang Institute of Science and Technology","award":["ZD2021106"],"award-info":[{"award-number":["ZD2021106"]}]},{"name":"Nonlinear Dynamics and Application Research Center of Nanchang Institute of Science and Technology","award":["NGYJZX-2021-04"],"award-info":[{"award-number":["NGYJZX-2021-04"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Given the complexity of the operating conditions of rolling bearings in the actual rolling process of a hot mill and the difficulty in collecting data pertinent to fault bearings comprehensively, this paper proposes an approach that diagnoses the faults of a rolling mill bearing by employing the improved sparrow search algorithm deep belief network (ISAA-DBN) with limited data samples. First, the fast spectral kurtosis approach is adopted to convert the non-stationary original vibration signals collected by the acceleration sensors installed at the axial and radial ends of the rolling mill bearings into two-dimensional (2D) spectral kurtosis time\u2013frequency images with higher feature recognition, and the principal component analysis (PCA) technique is used to decrease the dimension of the data in order to achieve a high diagnosis rate with a limited number of samples. Subsequently, the sparrow search algorithm (SSA) is used to realize the intelligent optimized self-adaptive function of a deep belief network (DBN). Furthermore, the firefly disturbance algorithm is employed to improve the spatial search capability and robustness of SSA-DBN in order to achieve better performance of the ISSA-DBN method. Finally, the proposed approach is experimentally compared to other approaches used for diagnosis. The results show that the proposed approach not only retains the useful features of the data through dimension reduction but also improves the efficiency of the diagnosis and achieves the highest diagnosis accuracy with limited data samples. In addition, the optimal position of the sensor for diagnosing rolling mill roll faults is identified.<\/jats:p>","DOI":"10.3390\/s22207815","type":"journal-article","created":{"date-parts":[[2022,10,17]],"date-time":"2022-10-17T03:43:58Z","timestamp":1665978238000},"page":"7815","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Bearing Fault Diagnosis of Hot-Rolling Mill Utilizing Intelligent Optimized Self-Adaptive Deep Belief Network with Limited Samples"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7144-896X","authenticated-orcid":false,"given":"Rongrong","family":"Peng","sequence":"first","affiliation":[{"name":"Nonlinear Dynamics and Application Research Center, Nanchang Institute of Science and Technology, Nanchang 330108, China"},{"name":"National Engineering Research Center for Equipment and Technology of Cold Rolled Strip, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingzhong","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Engineering Research Center for Equipment and Technology of Cold Rolled Strip, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peiming","family":"Shi","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Yanshan University, Qinhuangdao 006004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"77","DOI":"10.2355\/isijinternational.43.77","article-title":"Analysis of chatter in tandem cold rolling mills","volume":"43","author":"Yukio","year":"2003","journal-title":"ISIJ Int."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"108466","DOI":"10.1016\/j.knosys.2022.108466","article-title":"A multi-source information transfer learning method with subdomain adaptation for cross-domain fault diagnosis","volume":"243","author":"Tian","year":"2022","journal-title":"Knowl.-Based. Syst."},{"key":"ref_3","first-page":"35","article-title":"Dynamics of rolling mills-mathematical models and experimental results","volume":"54","author":"Monaco","year":"1977","journal-title":"Iron. Steel. Eng."},{"key":"ref_4","first-page":"41","article-title":"Four-h mill-stand chatter of the fifth-octave mode","volume":"55","author":"Roberts","year":"1978","journal-title":"Iron. Steel. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.2355\/isijinternational1966.18.1","article-title":"An analysis of chattering in cold rolling for ultrathin gauge steel strip","volume":"18","author":"Yarita","year":"1978","journal-title":"Trans. ISIJ."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.jmatprotec.2014.10.002","article-title":"High-speed rolling by the hybrid-lubrication system in tandem cold rolling mills","volume":"216","author":"Kimura","year":"2015","journal-title":"J. Mater. Process. Tech."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1410","DOI":"10.1007\/BF02915964","article-title":"Fault diagnosis of roll shape under the speed variation in hot rolling mill","volume":"20","author":"Lee","year":"2006","journal-title":"J. Mech. Sci. Tech."},{"key":"ref_8","first-page":"351","article-title":"Study on the chatter vibration of a steel plate mill based on second order cyclic autocorrelation demodulation","volume":"4","author":"He","year":"2011","journal-title":"Int. J. Des. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2075","DOI":"10.1007\/s12206-014-0106-6","article-title":"Characteristic recognition of chatter mark vibration in a rolling mill based on the non-dimensional parameters of the vibration signal","volume":"28","author":"Shao","year":"2014","journal-title":"J. Mech. Sci. Tech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.jprocont.2015.08.010","article-title":"A brief review and the first application of time-frequency-based analysis methods for monitoring of strip rolling mills","volume":"35","author":"Rothera","year":"2015","journal-title":"J. Process. Contr."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.ymssp.2015.07.022","article-title":"Customized maximal-overlap multiwavelet denoising with data-driven group threshold for condition monitoring of rolling mill drivetrain","volume":"68","author":"Chen","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2801","DOI":"10.1007\/s11431-009-0253-7","article-title":"Gearbox fault diagnosis of rolling mills using multiwavelet sliding window neighboring coefficient denoising and optimal blind deconvolution","volume":"52","author":"Yuan","year":"2009","journal-title":"Sci. China. Ser. E Technol. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1126\/science.1127647","article-title":"Reducing the dimensionality of data with neural networks","volume":"313","author":"Hinton","year":"2006","journal-title":"Science"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.compind.2018.08.008","article-title":"Interactive data visualization of chatter conditions in a cold rolling mill","volume":"103","author":"Perez","year":"2018","journal-title":"Comput. Ind."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/s00170-010-2946-2","article-title":"Multivariable data analysis of a cold rolling control system to minimize defects","volume":"54","author":"Takami","year":"2011","journal-title":"Int. J. Adv. Manuf. Tech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1016\/j.conengprac.2012.03.007","article-title":"Neural networks for modeling and fault detection of the inter-stand strip tension of a cold tandem mill","volume":"20","author":"Arinton","year":"2012","journal-title":"Control Eng. Pract."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.ins.2013.06.045","article-title":"Residual-based fault detection using soft computing techniques for condition monitoring at rolling mills","volume":"259","author":"Serdio","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/TIM.2019.2902003","article-title":"Online fault diagnosis method based on transfer convolutional neural networks","volume":"69","author":"Xu","year":"2020","journal-title":"IEEE. Trans. Instrum. Meas."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhao, C., Sun, J.L., Liu, S.L., and Peng, Y. (2021). Fault diagnosis method for rolling mill multi-row bearing based on AMVMD-MC1DCNN under unbalanced dataset. Sensors, 21.","DOI":"10.3390\/s21165494"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"108903","DOI":"10.1016\/j.ymssp.2022.108903","article-title":"A novel multi-source sensing data fusion driven method for detecting rolling mill health states under imbalanced and limited datasets","volume":"171","author":"Shi","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"106990","DOI":"10.1016\/j.ymssp.2020.106990","article-title":"Autocorrelated envelops for early fault detection of rolling bearings","volume":"146","author":"Xu","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"108374","DOI":"10.1016\/j.measurement.2020.108374","article-title":"A novel mechanical fault signal feature extraction method based on unsaturated piecewise tri-stable stochastic resonance","volume":"168","author":"Zhao","year":"2021","journal-title":"Measurement"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.ymssp.2005.12.002","article-title":"Fast computation of the kurtogram for the detection of transient faults","volume":"21","author":"Antoni","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_24","first-page":"1100","article-title":"A tutorial on principal component analysis","volume":"52","author":"Shlens","year":"2014","journal-title":"Int. J. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.ymssp.2009.06.015","article-title":"Enhancement of signal denoising and multiple fault signatures detecting in rotating machinery using dual-tree complex wavelet transform","volume":"24","author":"Wang","year":"2010","journal-title":"Mech. Syst. Signal. Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"10773","DOI":"10.1007\/s00521-019-04612-z","article-title":"Intelligent bearing fault diagnosis using PCA-DBN framework","volume":"32","author":"Zhu","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1080\/21642583.2019.1708830","article-title":"A novel swarm intelligence optimization approach: Sparrow search algorithm","volume":"8","author":"Xue","year":"2020","journal-title":"Syst. Sci. Control Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.patcog.2013.05.025","article-title":"Training restricted Boltzmann machines: An introduction","volume":"47","author":"Fishier","year":"2014","journal-title":"Pattern Recogn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1162\/089976602760128018","article-title":"Training products of experts by minimizing contrastive divergence","volume":"14","author":"Hinton","year":"2002","journal-title":"Neural Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5091","DOI":"10.1007\/s00500-016-2104-3","article-title":"Firefly algorithm with adaptive control parameters","volume":"21","author":"Wang","year":"2017","journal-title":"Soft Comput."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/20\/7815\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:54:24Z","timestamp":1760144064000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/20\/7815"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,14]]},"references-count":30,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["s22207815"],"URL":"https:\/\/doi.org\/10.3390\/s22207815","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,14]]}}}