{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T04:31:38Z","timestamp":1774499498422,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,2,13]],"date-time":"2017-02-13T00:00:00Z","timestamp":1486944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51205427"],"award-info":[{"award-number":["51205427"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Equipment Advanced Research Foundation","award":["9140A27020115JB35071"],"award-info":[{"award-number":["9140A27020115JB35071"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The kurtosis-based indexes are usually used to identify the optimal resonant frequency band. However, kurtosis can only describe the strength of transient impulses, which cannot differentiate impulse noises and repetitive transient impulses cyclically generated in bearing vibration signals. As a result, it may lead to inaccurate results in identifying resonant frequency bands, in demodulating fault features and hence in fault diagnosis. In view of those drawbacks, this manuscript redefines the correlated kurtosis based on kurtosis and auto-correlative function, puts forward an improved correlated kurtosis based on squared envelope spectrum of bearing vibration signals. Meanwhile, this manuscript proposes an optimal resonant band demodulation method, which can adaptively determine the optimal resonant frequency band and accurately demodulate transient fault features of rolling bearings, by combining the complex Morlet wavelet filter and the Particle Swarm Optimization algorithm. Analysis of both simulation data and experimental data reveal that the improved correlated kurtosis can effectively remedy the drawbacks of kurtosis-based indexes and the proposed optimal resonant band demodulation is more accurate in identifying the optimal central frequencies and bandwidth of resonant bands. Improved fault diagnosis results in experiment verified the validity and advantage of the proposed method over the traditional kurtosis-based indexes.<\/jats:p>","DOI":"10.3390\/s17020360","type":"journal-article","created":{"date-parts":[[2017,2,15]],"date-time":"2017-02-15T10:09:07Z","timestamp":1487153347000},"page":"360","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["Optimal Resonant Band Demodulation Based on an Improved Correlated Kurtosis and Its Application in Bearing Fault Diagnosis"],"prefix":"10.3390","volume":"17","author":[{"given":"Xianglong","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Academy of Armored Forces Engineering, Beijing 100072, China"}]},{"given":"Bingzhi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Beijing Special Vehicle Research Institute, Beijing 100072, China"}]},{"given":"Fuzhou","family":"Feng","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Academy of Armored Forces Engineering, Beijing 100072, China"}]},{"given":"Pengcheng","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Academy of Armored Forces Engineering, Beijing 100072, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.ymssp.2015.04.021","article-title":"Rolling element bearing diagnostics using the Case Western Reserve University data: A benchmark study","volume":"64\u201365","author":"Smith","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chen, X., Feng, F., and Zhang, B. (2016). Weak Fault Feature Extraction of Rolling Bearings Based on an Improved Kurtogram. Sensors, 9.","DOI":"10.3390\/s16091482"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.ymssp.2004.09.001","article-title":"The spectral kurtosis: A useful tool for characterizing non-stationary signals","volume":"20","author":"Antoni","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/j.ymssp.2004.09.002","article-title":"The spectral kurtosis: Application to the vibratory surveillance and diagnostics of rotating machines","volume":"20","author":"Antoni","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.ymssp.2015.04.039","article-title":"Spectral kurtosis for fault detection, diagnosis and prognostics of rotating machines: A review with applications","volume":"66","author":"Wang","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1738","DOI":"10.1016\/j.ymssp.2010.12.011","article-title":"Application of an improved kurtogram method for fault diagnosis of rolling element bearings","volume":"25","author":"Lei","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_8","first-page":"243","article-title":"Rolling element bearings fault diagnosis based on correlated kurtosis kurtogram","volume":"17","author":"Zhang","year":"2015","journal-title":"J. Vibroeng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ymssp.2013.03.021","article-title":"Detecting of transient vibration signatures using an improved fast spatial\u2013spectral ensemble kurtosis kurtogram and its applications to mechanical signature analysis of short duration data from rotating machinery","volume":"40","author":"Chen","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.ymssp.2012.10.003","article-title":"An enhanced Kurtogram method for fault diagnosis of rolling element bearings","volume":"35","author":"Wang","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.ymssp.2010.05.018","article-title":"A novel method for the optimal band selection for vibration signal demodulation and comparison with the Kurtogram","volume":"25","author":"Barszcz","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.ymssp.2013.05.024","article-title":"The design of a new sparsogram for fast bearing fault diagnosis: Part 1 of the two related manuscripts that have a joint title as \u201cTwo automatic vibration-based fault diagnostic methods using the novel sparsity measurement\u2014Parts 1 and 2\u201d","volume":"40","author":"Tse","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.ymssp.2015.04.034","article-title":"The infogram: Entropic evidence of the signature of repetitive transients","volume":"74","author":"Antoni","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","first-page":"132","article-title":"Criterion fusion for spectral segmentation and its application to optimal demodulation of bearing vibration signals","volume":"64\u201365","author":"Li","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1016\/j.ymssp.2013.05.018","article-title":"The automatic selection of an optimal wavelet filter and its enhancement by the new sparsogram for bearing fault detection","volume":"40","author":"Tse","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","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":"2008","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/MIE.2013.2287651","article-title":"Trends in Fault Diagnosis for Electrical Machines: A Review of Diagnostic Techniques","volume":"8","author":"Henao","year":"2014","journal-title":"IEEE Ind. Electron. Mag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1846","DOI":"10.1109\/TIE.2014.2361115","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. Electron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.ymssp.2012.06.010","article-title":"Maximum correlated Kurtosis deconvolution and application on gear tooth chip fault detection","volume":"33","author":"McDonald","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.ymssp.2013.10.007","article-title":"The relationship between kurtosis- and envelope-based indexes for the diagnostic of rolling element bearings","volume":"43","author":"Borghesani","year":"2014","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_21","first-page":"243","article-title":"Bearing fault diagnosis and degradation analysis based on improved empirical mode decomposition and maximum correlated kurtosis deconvolution","volume":"17","author":"Zhang","year":"2015","journal-title":"J. Vibroeng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"29363","DOI":"10.3390\/s151129363","article-title":"Early Fault Diagnosis of Bearings Using an Improved Spectral Kurtosis by Maximum Correlated Kurtosis Deconvolution","volume":"15","author":"Jia","year":"2015","journal-title":"Sensors"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/j.measurement.2010.01.001","article-title":"An adaptive Morlet wavelet filter for time-of-flight estimation in ultrasonic damage assessment","volume":"43","author":"Chen","year":"2010","journal-title":"Measurement"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1458","DOI":"10.1016\/j.ymssp.2009.11.011","article-title":"Rolling element bearing faults diagnosis based on optimal Morlet wavelet filter and autocorrelation enhancement","volume":"24","author":"Su","year":"2010","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.sigpro.2013.05.013","article-title":"Adaptive spectral kurtosis filtering based on Morlet wavelet and its application for signal transients detection","volume":"96","author":"Liu","year":"2014","journal-title":"Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.1016\/j.measurement.2009.04.001","article-title":"Bearing fault detection based on optimal wavelet filter and sparse code shrinkage","volume":"42","author":"He","year":"2009","journal-title":"Measurement"},{"key":"ref_27","unstructured":"Case Western Reserve University Bearing Data Center Website. Available online: http:\/\/csegroups.case.edu\/bearingdatacenter\/."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/2\/360\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:28:07Z","timestamp":1760207287000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/2\/360"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,13]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,2]]}},"alternative-id":["s17020360"],"URL":"https:\/\/doi.org\/10.3390\/s17020360","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,13]]}}}