{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T13:24:15Z","timestamp":1780320255192,"version":"3.54.1"},"reference-count":57,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T00:00:00Z","timestamp":1704931200000},"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>One of the common methods for implementing the condition-based maintenance of rotating machinery is vibration analysis. This tutorial describes some of the important signal processing methods existing in the field, which are based on a profound understanding of the component\u2019s physical behavior. Furthermore, this tutorial provides Python and MATLAB code examples to demonstrate these methods alongside explanatory videos. The goal of this article is to serve as a practical tutorial, enabling interested individuals with a background in signal processing to quickly learn the important principles of condition-based maintenance of rotating machinery using vibration analysis.<\/jats:p>","DOI":"10.3390\/s24020454","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T05:24:12Z","timestamp":1704950652000},"page":"454","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Signal Processing for the Condition-Based Maintenance of Rotating Machines via Vibration Analysis: A Tutorial"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9466-7516","authenticated-orcid":false,"given":"Omri","family":"Matania","sequence":"first","affiliation":[{"name":"BGU-PHM Laboratory, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. 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Available online: https:\/\/cris.technion.ac.il\/en\/publications\/mechanical-signature-analysis-theory-and-applications."},{"key":"ref_7","first-page":"14","article-title":"State of the art in monitoring rotating machinery\u2014Part 1","volume":"38","author":"Randall","year":"2004","journal-title":"Sound Vib."},{"key":"ref_8","first-page":"10","article-title":"State of the art in monitoring rotating machinery\u2014Part 2","volume":"38","author":"Randall","year":"2004","journal-title":"Sound Vib."},{"key":"ref_9","unstructured":"Klein, R. (2012, January 23\u201327). Condition indicators for gears. Proceedings of the Annual Conference of the Prognostics and Health Management Society 2012, PHM 2012, Minneapolis, MN, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1115\/1.1456906","article-title":"Differential Diagnosis of Gear and Bearing Faults","volume":"124","author":"Antoni","year":"2002","journal-title":"J. Vib. 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Codes and Videos for the Paper \u201cSignal Processing for Condition-Based Maintenance of Rotating Machinery Using Vibration Analysis: A Tutorial\u201d. Available online: https:\/\/github.com\/omriMatania\/sp_for_cbm_of_rotating_machines_using_vibration_analysis_tutorial.","DOI":"10.3390\/s24020454"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.ymssp.2010.07.017","article-title":"Rolling element bearing diagnostics\u2014A tutorial","volume":"25","author":"Randall","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"101945","DOI":"10.1016\/j.aei.2023.101945","article-title":"One-fault-shot learning for fault severity estimation of gears that addresses differences between simulation and experimental signals and transfer function effects","volume":"56","author":"Matania","year":"2023","journal-title":"Adv. Eng. Inform."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.ymssp.2015.04.021","article-title":"Rolling element bearing diagnosis 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_18","doi-asserted-by":"crossref","first-page":"107735","DOI":"10.1016\/j.measurement.2020.107735","article-title":"Latest developments in gear defect diagnosis and prognosis: A review","volume":"158","author":"Kumar","year":"2020","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2853","DOI":"10.1177\/1475921720972926","article-title":"A review on diagnostic and prognostic approaches for gears","volume":"20","author":"Kundu","year":"2021","journal-title":"Struct. Health Monit."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Randall, R.B. (2021). 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[2nd ed.].","DOI":"10.1002\/9781119477631"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Randall, R.B. (2021). Vibration-Based Condition Monitoring: Industrial, Automotive and Aerospace Applications, WILEY. [2nd ed.]. Available online: https:\/\/www.wiley.com\/en-us\/Vibration+based+Condition+Monitoring%3A+Industrial%2C+Automotive+and+Aerospace+Applications%2C+2nd+Edition-p-9781119477556.","DOI":"10.1002\/9781119477631"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.cja.2021.10.006","article-title":"Rotating machinery fault detection and diagnosis based on deep domain adaptation: A survey","volume":"36","author":"Zhang","year":"2021","journal-title":"Chin. J. Aeronaut."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Gnanasekaran, S., Jakkamputi, L.P., Rakkiyannan, J., Thangamuthu, M., and Bhalerao, Y. (2023). A Comprehensive Approach for Detecting Brake Pad Defects Using Histogram and Wavelet Features with Nested Dichotomy Family Classifiers. Sensors, 23.","DOI":"10.3390\/s23229093"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Gnanasekaran, S., Jakkamputi, L., Thangamuthu, M., Marikkannan, S.K., Rakkiyannan, J., Thangavelu, K., and Kotha, G. (2022). Condition Monitoring of an All-Terrain Vehicle Gear Train Assembly Using Deep Learning Algorithms with Vibration Signals. Appl. Sci., 12.","DOI":"10.3390\/app122110917"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Natarajan, S., Thangamuthu, M., Gnanasekaran, S., and Rakkiyannan, J. (2023). Digital Twin-Driven Tool Condition Monitoring for the Milling Process. 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Proceedings of the PHM Society European Conference, Bilbao, Spain.","DOI":"10.36001\/phme.2016.v3i1.1577"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"110748","DOI":"10.1016\/j.ymssp.2023.110748","article-title":"A novel hybrid physical AI-based strategy for fault severity estimation in spur gears with zero-shot learning","volume":"204","author":"Bachar","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2157","DOI":"10.1016\/j.ymssp.2011.01.022","article-title":"Angular resampling for vibration analysis in wind turbines under non-linear speed fluctuation","volume":"25","author":"Villa","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_32","unstructured":"(2022, October 16). Order Analysis Based on Resampling\u2014National Instruments. Available online: https:\/\/www.ni.com\/docs\/en-US\/bundle\/diadem\/page\/genmaths\/genmaths\/calc_oa_resampling.htm."},{"key":"ref_33","unstructured":"Braun, S. (2008). Discover Signal Processing: An Interactive Guide for Engineers, WILEY. Available online: https:\/\/www.wiley.com\/en-us\/Discover+Signal+Processing%3A+An+Interactive+Guide+for+Engineers+-p-9780470519707."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1016\/j.ymssp.2010.07.016","article-title":"The synchronous (time domain) average revisited","volume":"25","author":"Braun","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_35","unstructured":"Bechhoefer, E., and Kingsley, M. (October, January 27). A review of time synchronous average algorithms. Proceedings of the Annual Conference of the Prognostics and Health Management Society, PHM 2009, San Diego, CA, USA. Available online: https:\/\/papers.phmsociety.org\/index.php\/phmconf\/article\/view\/1666."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Randall, R.B. (2021). Vibration-Based Condition Monitoring: Industrial, Automotive and Aerospace Applications, WILEY. [2nd ed.]. Available online: https:\/\/www.wiley.com\/en-us\/Vibration+based+Condition+Monitoring%3A+Industrial%2C+Automotive+and+Aerospace+Applications%2C+2nd+Edition-p-9781119477556.","DOI":"10.1002\/9781119477631"},{"key":"ref_37","first-page":"69","article-title":"The Extraction of Periodic Waveforms by Time Domain Averaging","volume":"32","author":"Braun","year":"1975","journal-title":"Acustica"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0888-3270(87)90085-9","article-title":"A revised model for the extraction of periodic waveforms by time domain averaging","volume":"1","author":"McFadden","year":"1987","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_39","first-page":"259","article-title":"A New Method of Modeling Gear Faults","volume":"104","author":"Randall","year":"1982","journal-title":"J. Mech. Des."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1784\/204764211798303823","article-title":"Emphasising bearing tones for prognostics","volume":"1","author":"Klein","year":"2011","journal-title":"Int. J. Cond. Monit."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.ymssp.2017.03.040","article-title":"Comparison of methods for separating vibration sources in rotating machinery","volume":"97","author":"Klein","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Childers, D.G., Skinner, D.P., and Kemerait, R.C. (1977). The Cepstrum: A Guide to Processing, IEEE.","DOI":"10.1109\/PROC.1977.10747"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.ymssp.2016.12.026","article-title":"A history of cepstrum analysis and its application to mechanical problems","volume":"97","author":"Randall","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_44","unstructured":"Randall, R.B., and Sawalhi, N. (2014). Lecture Notes in Mechanical Engineering, Springer."},{"key":"ref_45","unstructured":"Peeters, C., Guillaume, P., and Helsen, J. (2016, January 19\u201321). Signal pre-processing using cepstral editing for vibrationbased bearing fault detection. Proceedings of the ISMA 2016, Leuven, Belgium. Available online: https:\/\/www.researchgate.net\/publication\/308658282_Signal_pre-processing_using_cepstral_editing_for_vibration-_based_bearing_fault_detection."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0022-460X(84)90595-9","article-title":"Model for the vibration produced by a single point defect in a rolling element bearing","volume":"96","author":"McFadden","year":"1984","journal-title":"J. Sound Vib."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Randall, R.B. (2021). Vibration-Based Condition Monitoring: Industrial, Automotive and Aerospace Applications, WILEY. Available online: https:\/\/www.wiley.com\/en-us\/Vibration+based+Condition+Monitoring%3A+Industrial%2C+Automotive+and+Aerospace+Applications%2C+2nd+Edition-p-9781119477556.","DOI":"10.1002\/9781119477631"},{"key":"ref_48","unstructured":"Braun, S. (2008). Discover Signal Processing: An Interactive Guide for Engineers, WILEY. Available online: https:\/\/www.wiley.com\/en-us\/Discover+Signal+Processing%3A+An+Interactive+Guide+for+Engineers+-p-9780470519707."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.jsv.2004.02.058","article-title":"A review of vibration-based techniques for helicopter transmission diagnostics","volume":"282","author":"Samuel","year":"2005","journal-title":"J. Sound Vib."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Randall, R.B. (2010). Vibration-Based Condition Monitoring\u2014Industrial, Aerospace and Automotive Applications, WILEY. [1st ed.].","DOI":"10.1002\/9780470977668"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Randall, R.B. (2021). Vibration-Based Condition Monitoring: Industrial, Automotive and Aerospace Applications, WILEY. [2nd ed.].","DOI":"10.1002\/9781119477631"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1115\/1.1456905","article-title":"Autoregressive Model-Based Gear Fault Diagnosis","volume":"124","author":"Wang","year":"2002","journal-title":"J. Vib. Acoust."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"109714","DOI":"10.1016\/j.ymssp.2022.109714","article-title":"Removal of transfer function effects from gear vibration signals under constant and variable speed conditions","volume":"184","author":"Lu","year":"2023","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Randall, R.B. (2021). Vibration-Based Condition Monitoring: Industrial, Automotive and Aerospace Applications, WILEY. 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