{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T15:00:37Z","timestamp":1784214037743,"version":"3.55.0"},"reference-count":39,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T00:00:00Z","timestamp":1701043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Natural Science Foundation of Tianjin","award":["20YDTPJC00840"],"award-info":[{"award-number":["20YDTPJC00840"]}]},{"name":"the Natural Science Foundation of Tianjin","award":["JG-ZD-2205"],"award-info":[{"award-number":["JG-ZD-2205"]}]},{"name":"the Natural Science Foundation of Tianjin","award":["2022SKYZ328"],"award-info":[{"award-number":["2022SKYZ328"]}]},{"name":"Tianjin Chengjian University Postgraduate Education Reform","award":["20YDTPJC00840"],"award-info":[{"award-number":["20YDTPJC00840"]}]},{"name":"Tianjin Chengjian University Postgraduate Education Reform","award":["JG-ZD-2205"],"award-info":[{"award-number":["JG-ZD-2205"]}]},{"name":"Tianjin Chengjian University Postgraduate Education Reform","award":["2022SKYZ328"],"award-info":[{"award-number":["2022SKYZ328"]}]},{"DOI":"10.13039\/501100019062","name":"Tianjin Research Innovation Project for Postgraduate Students","doi-asserted-by":"publisher","award":["20YDTPJC00840"],"award-info":[{"award-number":["20YDTPJC00840"]}],"id":[{"id":"10.13039\/501100019062","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100019062","name":"Tianjin Research Innovation Project for Postgraduate Students","doi-asserted-by":"publisher","award":["JG-ZD-2205"],"award-info":[{"award-number":["JG-ZD-2205"]}],"id":[{"id":"10.13039\/501100019062","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100019062","name":"Tianjin Research Innovation Project for Postgraduate Students","doi-asserted-by":"publisher","award":["2022SKYZ328"],"award-info":[{"award-number":["2022SKYZ328"]}],"id":[{"id":"10.13039\/501100019062","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Due to the difficulty in dealing with non-stationary and nonlinear vibration signals using the single decomposition method, it is difficult to extract weak fault features from complex noise; therefore, this paper proposes a fault feature extraction method for rolling bearings based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and variational mode decomposition (VMD) methods. CEEMDAN was used to decompose the signal, and the signal was then screened and reconstructed according to the component envelope kurtosis. Based on the kurtosis of the maximum envelope spectrum as the fitness function, the sparrow search algorithm (SSA) was used to perform adaptive parameter optimization for VMD, which decomposed the reconstructed signal into several IMF components. According to the kurtosis value of the envelope spectrum, the optimal component was selected for an envelope demodulation analysis to realize fault feature extraction for rolling bearings. Finally, by using open data sets and experimental data, the accuracy of envelope kurtosis and envelope spectrum kurtosis as a component selection index was verified, and the superiority of the proposed feature extraction method for rolling bearings was confirmed by comparing it with other methods.<\/jats:p>","DOI":"10.3390\/s23239441","type":"journal-article","created":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T07:56:10Z","timestamp":1701071770000},"page":"9441","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Fault Feature Extraction Method for Rolling Bearings Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Variational Mode Decomposition"],"prefix":"10.3390","volume":"23","author":[{"given":"Lijing","family":"Wang","sequence":"first","affiliation":[{"name":"School of Control and Mechanical Engineering, Tianjin Chengjian University, Tianjin 300384, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongjiang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Control and Mechanical Engineering, Tianjin Chengjian University, Tianjin 300384, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao","family":"Xi","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Tiangong University, Tianjin 300387, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4129-0112","authenticated-orcid":false,"given":"Shichun","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Control and Mechanical Engineering, Tianjin Chengjian University, Tianjin 300384, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1016\/j.measurement.2018.06.047","article-title":"Weak characteristic determination for blade crack of centrifugal compressors based on underdetermined blind source separation","volume":"128","author":"He","year":"2018","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.isatra.2017.08.009","article-title":"An adaptive stochastic resonance method based on grey wolf optimizer algorithm and its application to machinery fault diagnosis","volume":"71","author":"Zhang","year":"2017","journal-title":"ISA Trans."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16878132231197362","DOI":"10.1177\/16878132231197362","article-title":"Research on gearbox compound fault diagnosis method and system development based on entire gearbox health maintenance","volume":"15","author":"Yan","year":"2023","journal-title":"Adv. Mech. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1515\/phys-2018-0095","article-title":"Application of modified culture Kalman filter in bearing fault diagnosis","volume":"16","author":"Hailun","year":"2018","journal-title":"Open Phys."},{"key":"ref_5","first-page":"697","article-title":"Application of complex shifted morlet wavelet in vibration monitoring of spindle bearing of crank shaft grinder","volume":"259","author":"Wang","year":"2003","journal-title":"Key Eng. Mater."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"154777","DOI":"10.1109\/ACCESS.2021.3129061","article-title":"A novel intelligent fault diagnosis method for rolling bearings based on compressed sensing and stacked multi-granularity convolution denoising auto-encoder","volume":"9","author":"Liang","year":"2021","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.ymssp.2018.01.009","article-title":"Hyper-spherical distance discrimination: A novel data description method for aero-engine rolling bearing fault detection","volume":"109","author":"Lin","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.jsv.2016.01.017","article-title":"Nonlocal sparse model with adaptive structural clustering for feature extraction of aero-engine bearings","volume":"368","author":"Zhang","year":"2016","journal-title":"J. Sound. Vib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"109116","DOI":"10.1016\/j.measurement.2021.109116","article-title":"Fault diagnosis of rolling bearing using marine predators algorithm-based support vector machine and topology learning and out-of-sample embedding","volume":"176","author":"Chen","year":"2021","journal-title":"Measurement"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.isatra.2020.12.054","article-title":"Modified multiscale weighted permutation entropy and optimized support vector machine method for rolling bearing fault diagnosis with complex signals","volume":"114","author":"Wang","year":"2021","journal-title":"ISA Trans."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"213416","DOI":"10.1109\/ACCESS.2020.3040209","article-title":"Dictionary Learning via a Mixed Noise Model for Sparse Representation Classification of Rolling Bearings","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Jiang, Y., and Xie, J. (2022). VMD\u2013RP\u2013CSRN Based Fault Diagnosis Method for Rolling Bearings. Electronics, 11.","DOI":"10.3390\/electronics11234046"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"69795","DOI":"10.1109\/ACCESS.2019.2919126","article-title":"Bearing fault classification based on convolutional neural network in noise environment","volume":"7","author":"Jiang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"035005","DOI":"10.1088\/0957-0233\/27\/3\/035005","article-title":"Bearing fault diagnosis based on spectrum images of vibration signals","volume":"27","author":"Li","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"49","DOI":"10.3901\/JME.2015.21.049","article-title":"A deep learning-based method for machinery health monitoring with big data","volume":"51","author":"Lei","year":"2015","journal-title":"J. Mech. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Miao, Y., Shi, H., Li, C., Hua, J., and Lin, J. (2023). Period-refined CYCBD using time synchronous averaging for the feature extraction of bearing fault under heavy noise. Struct. Health Monit., 14759217231181514.","DOI":"10.1177\/14759217231181514"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1109\/TIM.2016.2647458","article-title":"Short-frequency Fourier transform for fault diagnosis of induction machines working in transient regime","volume":"66","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Wang, H., Zhu, H., and Li, H. (2023). Multi-Mode Data Generation and Fault Diagnosis of Bearings Based on STFT-SACGAN. Electronics, 12.","DOI":"10.3390\/electronics12081910"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Mohamed, M.A., Hassan, M.A.M., Albalawi, F., Ghoneim, S.S.M., Ali, Z.M., and Dardeer, M. (2021). Diagnostic modelling for induction motor faults via ANFIS algorithm and DWT-based feature extraction. Appl. Sci., 11.","DOI":"10.3390\/app11199115"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Gu, K., Zhang, Y., Liu, X., Li, H., and Ren, M. (2021). DWT-LSTM-based fault diagnosis of rolling bearings with multi-sensors. Electronics, 10.","DOI":"10.3390\/electronics10172076"},{"key":"ref_21","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_22","doi-asserted-by":"crossref","unstructured":"Wu, Y., Liu, X., and Zhou, Y. (2023). Deep PCA-Based Incipient Fault Diagnosis and Diagnosability Analysis of High-Speed Railway Traction System via FNR Enhancement. Machines, 11.","DOI":"10.3390\/machines11040475"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Chen, H., Li, S., and Li, M. (2022). Multi-Channel High-Dimensional Data Analysis with PARAFAC-GA-BP for Nonstationary Mechanical Fault Diagnosis. Int. J. Turbomach. Propuls. Power, 7.","DOI":"10.3390\/ijtpp7030019"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Torres, M.E., Colominas, M.A., Schlotthauer, G., and Flandrin, P. (2011, January 22\u201327). A Complete Ensemble Empirical Mode Decomposition with Adaptive Noise. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic.","DOI":"10.1109\/ICASSP.2011.5947265"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational mode decomposition","volume":"62","author":"Dragomiretskiy","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wang, Z., Wang, J., and Du, W. (2018). Research on Fault Diagnosis of Gearbox with Improved Variational Mode Decomposition. Sensors, 18.","DOI":"10.3390\/s18103510"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jsv.2018.07.039","article-title":"Initial center frequency-guided VMD for fault diagnosis of rotating machines","volume":"435","author":"Jiang","year":"2018","journal-title":"J. Sound Vib."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Jiang, W., Shan, Y., Xue, X., Ma, J., Chen, Z., and Zhang, N. (2023). Fault Diagnosis for Rolling Bearing of Combine Harvester Based on Composite-Scale-Variable Dispersion Entropy and Self-Optimization Variational Mode Decomposition Algorithm. Entropy, 25.","DOI":"10.3390\/e25081111"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ding, J., Huang, L., Xiao, D., and Li, X. (2020). GMPSO-VMD algorithm and its application to rolling bearing fault feature extraction. Sensors, 20.","DOI":"10.3390\/s20071946"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11432-015-0594-2","article-title":"Dynamic strategy based parallel ant colony optimization on GPUs for TSPs","volume":"60","author":"Zhou","year":"2017","journal-title":"Sci. China Inf. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ymssp.2017.11.029","article-title":"A parameter-adaptive VMD method based on grasshopper optimization algorithm to analyze vibration signals from rotating machinery","volume":"108","author":"Zhang","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_32","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_33","doi-asserted-by":"crossref","first-page":"4979","DOI":"10.1007\/s12206-022-0911-2","article-title":"Fault diagnosis method for rolling bearing based on VMD and improved SVM optimized by METLBO","volume":"36","author":"Tan","year":"2022","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"055004","DOI":"10.1088\/1361-6501\/ab0352","article-title":"An optimal variational mode decomposition for rolling bearing fault feature extraction","volume":"30","author":"Wei","year":"2019","journal-title":"Meas. Sci. Technol."},{"key":"ref_35","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. London. Ser. A Math. Phys. Eng. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1016\/j.ymssp.2017.02.013","article-title":"Research on variational mode decomposition in rolling bearings fault diagnosis of the multistage centrifugal pump","volume":"93","author":"Zhang","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3510710","DOI":"10.1109\/TIM.2021.3055802","article-title":"Novel convolutional neural network (NCNN) for the diagnosis of bearing defects in rotary machinery","volume":"70","author":"Kumar","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_38","unstructured":"(2023, June 07). Case Western Reserve University Bearing Data Center Website. Available online: https:\/\/engineering.case.edu\/bearingdatacenter."},{"key":"ref_39","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."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/23\/9441\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:31:23Z","timestamp":1760131883000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/23\/9441"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,27]]},"references-count":39,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["s23239441"],"URL":"https:\/\/doi.org\/10.3390\/s23239441","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,27]]}}}