{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T03:31:06Z","timestamp":1771903866029,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,6,14]],"date-time":"2022-06-14T00:00:00Z","timestamp":1655164800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["51705053"],"award-info":[{"award-number":["51705053"]}]},{"name":"National Natural Science Foundation of China","award":["CQYC201903230"],"award-info":[{"award-number":["CQYC201903230"]}]},{"name":"National Natural Science Foundation of China","award":["cstc2021ycjh-bgzxm0346"],"award-info":[{"award-number":["cstc2021ycjh-bgzxm0346"]}]},{"name":"National Natural Science Foundation of China","award":["cstc2019jcyj-msxmX0720"],"award-info":[{"award-number":["cstc2019jcyj-msxmX0720"]}]},{"name":"National Natural Science Foundation of China","award":["KJZD-K201901503"],"award-info":[{"award-number":["KJZD-K201901503"]}]},{"name":"Chongqing Talents Program Innovation and Entrepreneurship Demonstration Team","award":["51705053"],"award-info":[{"award-number":["51705053"]}]},{"name":"Chongqing Talents Program Innovation and Entrepreneurship Demonstration Team","award":["CQYC201903230"],"award-info":[{"award-number":["CQYC201903230"]}]},{"name":"Chongqing Talents Program Innovation and Entrepreneurship Demonstration Team","award":["cstc2021ycjh-bgzxm0346"],"award-info":[{"award-number":["cstc2021ycjh-bgzxm0346"]}]},{"name":"Chongqing Talents Program Innovation and Entrepreneurship Demonstration Team","award":["cstc2019jcyj-msxmX0720"],"award-info":[{"award-number":["cstc2019jcyj-msxmX0720"]}]},{"name":"Chongqing Talents Program Innovation and Entrepreneurship Demonstration Team","award":["KJZD-K201901503"],"award-info":[{"award-number":["KJZD-K201901503"]}]},{"DOI":"10.13039\/501100013223","name":"Chongqing Research Program of Basic Research and Frontier Technology","doi-asserted-by":"publisher","award":["51705053"],"award-info":[{"award-number":["51705053"]}],"id":[{"id":"10.13039\/501100013223","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013223","name":"Chongqing Research Program of Basic Research and Frontier Technology","doi-asserted-by":"publisher","award":["CQYC201903230"],"award-info":[{"award-number":["CQYC201903230"]}],"id":[{"id":"10.13039\/501100013223","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013223","name":"Chongqing Research Program of Basic Research and Frontier Technology","doi-asserted-by":"publisher","award":["cstc2021ycjh-bgzxm0346"],"award-info":[{"award-number":["cstc2021ycjh-bgzxm0346"]}],"id":[{"id":"10.13039\/501100013223","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013223","name":"Chongqing Research Program of Basic Research and Frontier Technology","doi-asserted-by":"publisher","award":["cstc2019jcyj-msxmX0720"],"award-info":[{"award-number":["cstc2019jcyj-msxmX0720"]}],"id":[{"id":"10.13039\/501100013223","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013223","name":"Chongqing Research Program of Basic Research and Frontier Technology","doi-asserted-by":"publisher","award":["KJZD-K201901503"],"award-info":[{"award-number":["KJZD-K201901503"]}],"id":[{"id":"10.13039\/501100013223","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Research Program of Chongqing Municipal Education Commission","award":["51705053"],"award-info":[{"award-number":["51705053"]}]},{"name":"Science and Technology Research Program of Chongqing Municipal Education Commission","award":["CQYC201903230"],"award-info":[{"award-number":["CQYC201903230"]}]},{"name":"Science and Technology Research Program of Chongqing Municipal Education Commission","award":["cstc2021ycjh-bgzxm0346"],"award-info":[{"award-number":["cstc2021ycjh-bgzxm0346"]}]},{"name":"Science and Technology Research Program of Chongqing Municipal Education Commission","award":["cstc2019jcyj-msxmX0720"],"award-info":[{"award-number":["cstc2019jcyj-msxmX0720"]}]},{"name":"Science and Technology Research Program of Chongqing Municipal Education Commission","award":["KJZD-K201901503"],"award-info":[{"award-number":["KJZD-K201901503"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The working environment of rotating machines is complex, and their key components are prone to failure. The early fault diagnosis of rolling bearings is of great significance; however, extracting the single scale fault feature of the early weak fault of rolling bearings is not enough to fully characterize the fault feature information of a weak signal. Therefore, aiming at the problem that the early fault feature information of rolling bearings in a complex environment is weak and the important parameters of Variational Modal Decomposition (VMD) depend on engineering experience, a fault feature extraction method based on the combination of Adaptive Variational Modal Decomposition (AVMD) and optimized Multiscale Fuzzy Entropy (MFE) is proposed in this study. Firstly, the correlation coefficient is used to calculate the correlation between the modal components decomposed by VMD and the original signal, and the threshold of the correlation coefficient is set to optimize the selection of the modal number K. Secondly, taking Skewness (Ske) as the objective function, the parameters of MFE embedding dimension M, scale factor S and time delay T are optimized by the Particle Swarm Optimization (PSO) algorithm. Using optimized MFE to calculate the modal components obtained by AVMD, the MFE feature vector of each frequency band is obtained, and the MFE feature set is constructed. Finally, the simulation signals are used to verify the effectiveness of the Adaptive Variational Modal Decomposition, and the Drivetrain Dynamics Simulator (DDS) are used to complete the comparison test between the proposed method and the traditional method. The experimental results show that this method can effectively extract the fault features of rolling bearings in multiple frequency bands, characterize more weak fault information, and has higher fault diagnosis accuracy.<\/jats:p>","DOI":"10.3390\/s22124504","type":"journal-article","created":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T01:39:54Z","timestamp":1655257194000},"page":"4504","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Weak Fault Feature Extraction of Rolling Bearings Based on Adaptive Variational Modal Decomposition and Multiscale Fuzzy Entropy"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2702-8471","authenticated-orcid":false,"given":"Zhongliang","family":"Lv","sequence":"first","affiliation":[{"name":"College of Mechanical and Power Engineering, Chongqing University of Science and Technology, Chongqing 401331, China"}]},{"given":"Senping","family":"Han","sequence":"additional","affiliation":[{"name":"College of Mechanical and Power Engineering, Chongqing University of Science and Technology, Chongqing 401331, China"}]},{"given":"Linhao","family":"Peng","sequence":"additional","affiliation":[{"name":"College of Mechanical and Power Engineering, Chongqing University of Science and Technology, Chongqing 401331, China"}]},{"given":"Lin","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Mechanical and Power Engineering, Chongqing University of Science and Technology, Chongqing 401331, China"}]},{"given":"Yujiang","family":"Cao","sequence":"additional","affiliation":[{"name":"College of Mechanical and Power Engineering, Chongqing University of Science and Technology, Chongqing 401331, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.measurement.2016.08.003","article-title":"Feature selection for machine fault diagnosis using clustering of non-negation matrix factorization","volume":"94","author":"Liang","year":"2016","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.isatra.2019.09.020","article-title":"Incipient winding fault detection and diagnosis for squirrel-cage induction motors equipped on CRH trains","volume":"99","author":"Wu","year":"2020","journal-title":"ISA Trans."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1109\/TIA.2010.2049623","article-title":"Diagnosis of Bearing Faults in Induction Machines by Vibration or Current Signals: A Critical Comparison","volume":"46","author":"Immovilli","year":"2010","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/MIAS.2017.2740463","article-title":"Bearing Health Diagnosed with a Mobile Phone: Acoustic Signal Measurements Can be Used to Test for Structural Faults in Motors","volume":"24","author":"Rzeszucinski","year":"2018","journal-title":"IEEE Ind. Appl. Mag."},{"key":"ref_5","first-page":"1846","article-title":"Induction Machine Bearing Fault Detection by Means of Statistical Processing of the Stray Flux Measurement","volume":"62","author":"Frosini","year":"2015","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bustos, A., Rubio, H., Castejon, C., and Garcia-Prada, J.C. (2018). EMD-Based Methodology for the Identification of a High-Speed Train Running in a Gear Operating State. Sensors, 18.","DOI":"10.3390\/s18030793"},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble Empirical Mode Decomposition: A Noise-Assisted Data Analysis Method","volume":"1","author":"Wu","year":"2009","journal-title":"Adv Adapt. Data Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1098\/rsif.2005.0058","article-title":"The local mean decomposition and its application to EEG perception dat","volume":"2","author":"Smith","year":"2005","journal-title":"J. R. Soc. Interface"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational Mode Decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","first-page":"219","article-title":"Rolling Bearing Fault Feature Extraction Based on Variational Mode Decomposition Optimized by Information Entropy","volume":"5","author":"Li","year":"2018","journal-title":"Shock Vib."},{"key":"ref_13","first-page":"22","article-title":"Rolling Bearing Fault Diagnosis Based on Variational Mode Decomposition and Permutation Entropy","volume":"4","author":"Zheng","year":"2017","journal-title":"Shock Vib."},{"key":"ref_14","first-page":"78","article-title":"Weak fault feature extraction of rolling bearings based on MCKD and VMD","volume":"36","author":"Xia","year":"2017","journal-title":"Shock Vib."},{"key":"ref_15","first-page":"484","article-title":"Feature extraction and classification of EEG sleep stages based on fuzzy entropy","volume":"25","author":"Liu","year":"2010","journal-title":"J. Data Acq Proces"},{"key":"ref_16","first-page":"145","article-title":"Multiscale fuzzy entropy and its application in fault diagnosis of rolling bearings","volume":"27","author":"Zhen","year":"2014","journal-title":"J Vib. Eng. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00994018","article-title":"Support-vector networks","volume":"20","author":"Cortes","year":"1995","journal-title":"Mach. Learn."},{"key":"ref_18","first-page":"928","article-title":"Gear fault diagnosis method based on ASTFA and PMMFE","volume":"29","author":"Li","year":"2016","journal-title":"J. Vib. Eng. Technol."},{"key":"ref_19","first-page":"163","article-title":"Gear fault diagnosis based on EEMD multi-scale fuzzy entropy","volume":"34","author":"Yang","year":"2015","journal-title":"Shock Vib."},{"key":"ref_20","first-page":"68","article-title":"Armored vehicle recognition based on VMD multi-scale entropy and ABC-SVM","volume":"32","author":"Fan","year":"2018","journal-title":"J. Armored Forces"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2404","DOI":"10.1007\/s11771-019-4183-7","article-title":"Rolling bearing fault diagnosis based on fine composite multi-scale fuzzy entropy and particle swarm optimization support vector machine","volume":"26","author":"Xu","year":"2019","journal-title":"J. Cent. South Univ."},{"key":"ref_22","first-page":"169","article-title":"Fault diagnosis algorithm of rolling bearing based on LMD-MFE and DHMM","volume":"38","author":"Ding","year":"2018","journal-title":"Noise Vib. Control"},{"key":"ref_23","unstructured":"Kennedy, J., and Eberhart, R. (1995, January 1). Particle Swarm Optimization. Proceedings of the ICNN\u201995\u2014International Conference on Neural Networks, Perth, WA, Australia."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/12\/4504\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:31:16Z","timestamp":1760139076000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/12\/4504"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,14]]},"references-count":23,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["s22124504"],"URL":"https:\/\/doi.org\/10.3390\/s22124504","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,14]]}}}