{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T17:51:34Z","timestamp":1773424294602,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T00:00:00Z","timestamp":1586390400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Reliable condition indicators are necessary to perform effective diagnosis and prognosis. However, the vibration signals are often corrupted with non-Gaussian noise and rotating machines may operate under time-varying operating conditions. This impedes the application of conventional condition indicators. The synchronous average of the squared envelope is a relatively simple yet effective method to perform fault detection, fault identification and fault trending under constant and time-varying operating conditions. However, its performance is impeded by the presence of impulsive signal components attributed to impulsive noise or the presence of other damage modes in the machine. In this work, it is proposed that the synchronous median of the squared envelope should be used instead of the synchronous average of the squared envelope for gearbox fault diagnosis. It is shown on numerical and experimental datasets that the synchronous median is more robust to the presence of impulsive signal components and is therefore more reliable for estimating the condition of specific machine components.<\/jats:p>","DOI":"10.3390\/s20072115","type":"journal-article","created":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T14:42:03Z","timestamp":1586443323000},"page":"2115","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["A Simple Condition Monitoring Method for Gearboxes Operating in Impulsive Environments"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0315-5289","authenticated-orcid":false,"given":"Stephan","family":"Schmidt","sequence":"first","affiliation":[{"name":"Centre for Asset Integrity Management, Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4781-9972","authenticated-orcid":false,"given":"Radoslaw","family":"Zimroz","sequence":"additional","affiliation":[{"name":"Faculty of Geoengineering, Mining and Geology, Wroclaw University of Science and Technology, Na Grobli 15, 50-421 Wroclaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3392-1108","authenticated-orcid":false,"given":"Fakher","family":"Chaari","sequence":"additional","affiliation":[{"name":"Laboratory of Mechanics, Modelling and Production, National School of Engineers of Sfax, BP1173, Sfax 3038, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6164-9490","authenticated-orcid":false,"given":"P. Stephan","family":"Heyns","sequence":"additional","affiliation":[{"name":"Centre for Asset Integrity Management, Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed","family":"Haddar","sequence":"additional","affiliation":[{"name":"Laboratory of Mechanics, Modelling and Production, National School of Engineers of Sfax, BP1173, Sfax 3038, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/j.ymssp.2017.11.016","article-title":"Machinery health prognostics: A systematic review from data acquisition to RUL prediction","volume":"104","author":"Lei","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1016\/j.ymssp.2005.09.012","article-title":"A review on machinery diagnostics and prognostics implementing condition-based maintenance","volume":"20","author":"Jardine","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.ymssp.2013.09.010","article-title":"Diagnostics of bearings in presence of strong operating conditions non-stationarity\u2014A procedure of load-dependent features processing with application to wind turbine bearings","volume":"46","author":"Zimroz","year":"2014","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1528","DOI":"10.1016\/j.ymssp.2009.01.014","article-title":"A new feature for monitoring the condition of gearboxes in non-stationary operating conditions","volume":"23","author":"Bartelmus","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.ymssp.2018.03.052","article-title":"Gearbox condition monitoring in wind turbines: A review","volume":"111","author":"Salameh","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1108\/13552511211265785","article-title":"On the operation and maintenance practices of wind power asset","volume":"18","author":"Liyanage","year":"2012","journal-title":"J. Qual. Maint. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1016\/j.rser.2015.10.149","article-title":"Fault analysis of wind turbines in China","volume":"55","author":"Lin","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.ymssp.2014.03.011","article-title":"Selection of informative frequency band in local damage detection in rotating machinery","volume":"48","author":"Obuchowski","year":"2014","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1016\/j.ymssp.2005.05.009","article-title":"Transmission path phase compensation for gear monitoring under fluctuating load conditions","volume":"20","author":"Stander","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1006\/mssp.2000.1290","article-title":"Application of synchronous averaging to vibration monitoring of rolling element bearings","volume":"14","author":"McFadden","year":"2000","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1006\/mssp.2001.1416","article-title":"Early detection of gear tooth cracking using the resonance demodulation technique","volume":"15","author":"Wang","year":"2001","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106739","DOI":"10.1016\/j.ymssp.2020.106739","article-title":"A methodology for identifying information rich frequency bands for diagnostics of mechanical components-of-interest under time-varying operating conditions","volume":"142","author":"Schmidt","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/j.ymssp.2019.02.005","article-title":"A pre-processing methodology to enhance novel information for rotating machine diagnostics","volume":"124","author":"Schmidt","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/j.ymssp.2018.11.051","article-title":"Localised gear anomaly detection without historical data for reference density estimation","volume":"121","author":"Schmidt","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.ymssp.2016.06.033","article-title":"Envelope analysis of rotating machine vibrations in variable speed conditions: A comprehensive treatment","volume":"84","author":"Abboud","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","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_17","doi-asserted-by":"crossref","first-page":"106303","DOI":"10.1016\/j.ymssp.2019.106303","article-title":"Optimal demodulation-band selection for envelope-based diagnostics: A comparative study of traditional and novel tools","volume":"134","author":"Smith","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"106673","DOI":"10.1016\/j.ymssp.2020.106673","article-title":"Bearing diagnostics under strong electromagnetic interference based on Integrated Spectral Coherence","volume":"140","author":"Mauricio","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.ymssp.2018.05.012","article-title":"A statistical methodology for the design of condition indicators","volume":"114","author":"Antoni","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1016\/S0888-3270(03)00088-8","article-title":"Cyclostationary modelling of rotating machine vibration signals","volume":"18","author":"Antoni","year":"2004","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1006\/mssp.1996.0056","article-title":"Analysis of computed order tracking","volume":"11","author":"Fyfe","year":"1997","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.ymssp.2016.02.053","article-title":"A multi-order probabilistic approach for instantaneous angular speed tracking debriefing of the CMMNO\u201914 diagnosis contest","volume":"81","author":"Antoni","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"106964","DOI":"10.1016\/j.measurement.2019.106964","article-title":"Normalisation of the amplitude modulation caused by time-varying operating conditions for condition monitoring","volume":"149","author":"Schmidt","year":"2020","journal-title":"Measurement"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Huber, P.J., and Ronchetti, E.M. (2009). Robust Statistics, Wiley. [2nd ed.].","DOI":"10.1002\/9780470434697"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Maronna, R.A., Martin, R.D., and Yohai, V.J. (2006). Robust statistics: Theory and Methods, Wiley.","DOI":"10.1002\/0470010940"},{"key":"ref_26","first-page":"252","article-title":"A summary of fault modelling and predictive health monitoring of rolling element bearings","volume":"60","author":"Jantunen","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1177\/1475921716636337","article-title":"A unified approach to detecting and trending changes caused by mechanical faults in rotating machinery","volume":"15","author":"Wang","year":"2016","journal-title":"Struct. Health Monit."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.ymssp.2017.07.032","article-title":"A novelty detection diagnostic methodology for gearboxes operating under fluctuating operating conditions using probabilistic techniques","volume":"100","author":"Schmidt","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"106612","DOI":"10.1016\/j.ymssp.2019.106612","article-title":"Deep digital twins for detection, diagnostics and prognostics","volume":"140","author":"Booyse","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"106682","DOI":"10.1016\/j.ymssp.2020.106682","article-title":"A semi-supervised Support Vector Data Description-based fault detection method for rolling element bearings based on cyclic spectral analysis","volume":"140","author":"Liu","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.ymssp.2015.12.034","article-title":"Optimised Spectral Kurtosis for bearing diagnostics under electromagnetic interference","volume":"75","author":"Smith","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.apacoust.2018.04.025","article-title":"Multiple local damage detection method based on time-frequency representation and agglomerative hierarchical clustering of temporary spectral content","volume":"147","author":"Obuchowski","year":"2019","journal-title":"Appl. Acoust."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1016\/j.ymssp.2019.05.020","article-title":"Novel method of informative frequency band selection for vibration signal using Nonnegative Matrix Factorization of spectrogram matrix","volume":"130","author":"Wodecki","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.ymssp.2013.08.015","article-title":"A new statistical modeling and detection method for rolling element bearing faults based on alpha-stable distribution","volume":"41","author":"Yu","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"\u017bak, G., Teuerle, M., Wy\u0142oma\u0144ska, A., and Zimroz, R. (2017). Measures of dependence for alpha-stable distributed processes and its application to diagnostics of local damage in presence of impulsive noise. Shock Vib., 2017.","DOI":"10.1155\/2017\/1963769"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.apacoust.2016.11.008","article-title":"Application of tempered stable distribution for selection of optimal frequency band in gearbox local damage detection","volume":"128","author":"Kruczek","year":"2017","journal-title":"Appl. Acoust."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.ymssp.2019.02.031","article-title":"Review and comparison of tacholess instantaneous speed estimation methods on experimental vibration data","volume":"129","author":"Peeters","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.ymssp.2013.03.024","article-title":"A tacho-less order tracking technique for large speed variations","volume":"40","author":"Zhao","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.ymssp.2012.05.009","article-title":"A two-step procedure for estimation of instantaneous rotational speed with large fluctuations","volume":"38","author":"Urbanek","year":"2013","journal-title":"Mech. Syst. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/7\/2115\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:16:48Z","timestamp":1760174208000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/7\/2115"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,4,9]]},"references-count":39,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,4]]}},"alternative-id":["s20072115"],"URL":"https:\/\/doi.org\/10.3390\/s20072115","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,4,9]]}}}