{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T10:27:42Z","timestamp":1779359262847,"version":"3.51.4"},"reference-count":79,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,4,4]],"date-time":"2023-04-04T00:00:00Z","timestamp":1680566400000},"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>In the last decade, research centered around the fault diagnosis of rotating machinery using non-contact techniques has been significantly on the rise. For the first time worldwide, innovative techniques for the diagnosis of rotating machinery, based on electrical motors, including generic, nonlinear, higher-order cross-correlations of spectral moduli of the third and fourth order (CCSM3 and CCSM4, respectively), have been comprehensively validated by modeling and experiments. The existing higher-order cross-correlations of complex spectra are not sufficiently effective for the fault diagnosis of rotating machinery. The novel technology CCSM3 was comprehensively experimentally validated for induction motor bearing diagnosis via motor current signals. Experimental results, provided by the validated technology, confirmed high overall probabilities of correct diagnosis for bearings at early stages of damage development. The novel diagnosis technologies were compared with existing diagnosis technologies, based on triple and fourth cross-correlations of the complex spectra. The comprehensive validation and comparison of the novel cross-correlation technologies confirmed an important non-traditional novel outcome: the technologies based on cross-correlations of spectral moduli were more effective for damage diagnosis than the technologies based on cross-correlations of the complex spectra. Experimental and simulation validations confirmed a high probability of correct diagnosis via the CCSM at the early stage of fault development. The average total probability of incorrect diagnosis for the CCSM3 for all experimental results of 8 tested bearings, estimated via 6528 diagnostic features, was 1.475%. The effectiveness gains in the total probability of incorrect diagnosis for the CCSM3 in comparison with the CCCS3 were 26.8 for the experimental validation and 18.9 for the simulation validation. The effectiveness gains in the Fisher criterion for the CCSM3 in comparison with the CCCS3 were 50.7 for the simulation validation and 104.7 for the experimental validation.<\/jats:p>","DOI":"10.3390\/s23073731","type":"journal-article","created":{"date-parts":[[2023,4,5]],"date-time":"2023-04-05T02:11:41Z","timestamp":1680660701000},"page":"3731","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Novel Investigation of Higher Order Spectral Technologies for Fault Diagnosis of Motor-Based Rotating Machinery"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5617-5254","authenticated-orcid":false,"given":"Tomasz","family":"Ciszewski","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering, Gdynia Maritime University, 81-255 Gdynia, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Len","family":"Gelman","sequence":"additional","affiliation":[{"name":"School of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8593-6830","authenticated-orcid":false,"given":"Andrew","family":"Ball","sequence":"additional","affiliation":[{"name":"School of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdulmumeen Onimisi","family":"Abdullahi","sequence":"additional","affiliation":[{"name":"School of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Biebele","family":"Jamabo","sequence":"additional","affiliation":[{"name":"School of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michal","family":"Ziolko","sequence":"additional","affiliation":[{"name":"Faculty of Electrical and Control Engineering, Gda\u0144sk University of Technology, 80-233 Gdansk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ciszewski, T., Gelman, L., and Ball, A. (2022). Novel nonlinear high order technologies for damage diagnosis of complex assets. Electronics, 11.","DOI":"10.3390\/electronics11233885"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ciszewski, T., Gelman, L., and Ball, A. (2020). Novel fault identification for electromechanical systems via spectral technique and electrical data processing. Electronics, 9.","DOI":"10.3390\/electronics9101560"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Soli\u0144ski, K., Soli\u0144ski, K., and Ball, A. (2020). Novel higher-order spectral cross-correlation technologies for vibration sensor-based diagnosis of gearboxes. Sensors, 20.","DOI":"10.3390\/s20185131"},{"key":"ref_4","first-page":"431","article-title":"Current-based higher-order spectral covariance as a bearing diagnostic feature for induction motors","volume":"58","author":"Ciszewski","year":"2016","journal-title":"Insight-Non-Destr. Test. Cond. Monit."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.ymssp.2009.07.004","article-title":"The new chirp-Wigner higher order spectra for transient signals with any known nonlinear frequency variation","volume":"24","author":"Gelman","year":"2010","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_6","first-page":"6","article-title":"Motor bearing damage detection, using stator current monitoring","volume":"31","author":"Schoen","year":"1995","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Areias, I.A.d.S., Borges da Silva, L.E., Bonaldi, E.L., de Lacerda de Oliveira, L.E., Lambert-Torres, G., and Bernardes, V.A. (2019). Evaluation of current signature in bearing defects by envelope analysis of the vibration in induction motors. Energies, 12.","DOI":"10.3390\/en12214029"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"106908","DOI":"10.1016\/j.ymssp.2020.106908","article-title":"Signal based condition monitoring techniques for fault detection and diagnosis of induction motors: A state-of-the-art review","volume":"144","author":"Gangsar","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sintoni, M., Macrelli, E., Bellini, A., and Bianchini, C. (2023). Condition monitoring of induction machines: Quantitative analysis and comparison. Sensors, 23.","DOI":"10.3390\/s23021046"},{"key":"ref_10","first-page":"409","article-title":"Novel spectral kurtosis technology for adaptive vibration condition monitoring of multi-stage gearboxes","volume":"58","author":"Gelman","year":"2016","journal-title":"Insight-Non-Destr. Test. Cond. Monit."},{"key":"ref_11","first-page":"507","article-title":"Vibration detection of local gear damage by advanced demodulation and residual techniques, proceedings of the institution of mechanical engineers","volume":"223","author":"Combet","year":"2009","journal-title":"Part G J. Aerosp. Eng."},{"key":"ref_12","first-page":"437","article-title":"Local damage diagnosis in gearboxes using novel wavelet technology","volume":"52","author":"Gryllias","year":"2010","journal-title":"Int. J. Insight-Non-Destr. Test. Cond. Monit."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1006\/mssp.2000.1295","article-title":"Condition monitoring diagnosis methods of gearbox units","volume":"14","author":"Gelman","year":"2000","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Kolbe, S., Gelman, L., and Ball, A. (2021). Novel prediction of diagnosis effectiveness for adaptation of the spectral kurtosis technology to varying operating conditions. Sensors, 21.","DOI":"10.3390\/s21206913"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Gelman, L., Soli\u0144ski, K., and Ball, A. (2021). Novel instantaneous wavelet bicoherence for vibration fault detection in gear systems. Energies, 14.","DOI":"10.3390\/en14206811"},{"key":"ref_16","first-page":"434","article-title":"Novel adaptation of the spectral kurtosis for vibration diagnosis of gearboxes in non-stationary conditions","volume":"59","author":"Gelman","year":"2017","journal-title":"Int. J. Insight-Non-Destr. Test. Cond. Monit."},{"key":"ref_17","first-page":"440","article-title":"Vibration diagnosis of a gearbox by wavelet bicoherence technology","volume":"59","author":"Gelman","year":"2017","journal-title":"Int. J. Insight-Non-Destr. Test. Cond. Monit."},{"key":"ref_18","first-page":"e2672","article-title":"Vibration health monitoring of rolling bearings under variable speed conditions by novel demodulation technique","volume":"28","author":"Zhao","year":"2020","journal-title":"Struct. Control. Health Monit."},{"key":"ref_19","first-page":"2153","article-title":"Novel technology based on the spectral kurtosis and wavelet transform for rolling bearing diagnosis","volume":"4","author":"Gelman","year":"2013","journal-title":"Int. J. Progn. Health Manag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.engstruct.2014.08.030","article-title":"Vibration diagnostics of rolling bearings by novel nonlinear non-stationary wavelet bicoherence technology","volume":"80","author":"Gelman","year":"2014","journal-title":"Eng. Struct."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Gelman, L., and Persin, G. (2022). Novel fault diagnosis of bearings and gearboxes based on simultaneous processing of spectral kurtoses. Appl. Sci., 12.","DOI":"10.3390\/app12199970"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/S0963-8695(01)00044-5","article-title":"Rolling element bearing fault diagnosis using wavelet packets","volume":"35","author":"Nikolaou","year":"2002","journal-title":"NDT E Int."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1016\/S0888-3270(03)00077-3","article-title":"Bearing fault diagnosis based on wavelet transform and fuzzy inference","volume":"18","author":"Lou","year":"2004","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3253","DOI":"10.1177\/1077546314562621","article-title":"An automated approach for bearing damage detection","volume":"22","author":"Yaqub","year":"2016","journal-title":"J. Vib. Control."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1155\/2002\/592436","article-title":"Wavelet based demodulation of vibration signals generated by defects in rolling element bearings","volume":"9","author":"Yiakopoulos","year":"2002","journal-title":"Shock Vib."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yang, D., Karimi, H.R., and Gelman, L. (2022). A fuzzy fusion rotating machinery fault diagnosis framework based on the enhancement deep convolutional neural networks. Sensors, 22.","DOI":"10.3390\/s22020671"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Farhat, M.H., Gelman, L., Conaghan, G., Kluis, W., and Ball, A. (2022). Novel diagnosis technologies for a lack of oil lubrication in gearmotor systems, based on motor current signature analysis. Sensors, 22.","DOI":"10.3390\/s22239507"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/j.ymssp.2019.06.010","article-title":"Stator current model for detecting rolling bearing faults in induction motors using magnetic equivalent circuits","volume":"131","author":"Han","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1016\/j.ymssp.2004.10.001","article-title":"A current monitoring system for diagnosing electrical failures in induction motors","volume":"20","author":"Acosta","year":"2006","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.ymssp.2017.12.010","article-title":"The reflection of evolving bearing faults in the stator current\u2019s extended park vector approach for induction machines","volume":"107","author":"Corne","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Silva, J.L.H., and Cardoso, A.J.M. (2005, January 6\u201310). Bearing failures diagnosis in three-phase induction motors by extended Park\u2019s vector approach. Proceedings of the 31st Annual Conference of IEEE Industrial Electronics Society, IECON 2005, Raleigh, NC, USA.","DOI":"10.1109\/IECON.2005.1569315"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"108723","DOI":"10.1016\/j.measurement.2020.108723","article-title":"A novel methodology for fault size estimation of ball bearings using stator current signal","volume":"171","author":"Wang","year":"2021","journal-title":"Measurement"},{"key":"ref_33","unstructured":"Treetrong, J. (2010, January 17\u201319). Fault detection and diagnosis of induction motors based on higher-order spectrum. Proceedings of the International Multi Conference of Engineers and Computer Scientists 2010, Hong Kong, China."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Tulicki, J., Su\u0142owicz, M., and Prag\u0142owska-Ry\u0142ko, N. (2016, January 4\u20138). Application of the bispectral analysis in the diagnosis of cage induction motors. Proceedings of the 2016 13th Selected Issues of Electrical Engineering and Electronics (wzee), Rzeszow, Poland.","DOI":"10.1109\/WZEE.2016.7800196"},{"key":"ref_35","first-page":"213","article-title":"An advanced park\u2019s vectors approach for bearing fault detection","volume":"42","author":"Zarei","year":"2006","journal-title":"IEEE Int. Conf. Ind. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1813","DOI":"10.1109\/TIE.2008.917108","article-title":"Models for bearing damage detection in induction motors using stator current monitoring","volume":"55","author":"Granjon","year":"2008","journal-title":"Ieee trans. Ind. Electron."},{"key":"ref_37","unstructured":"Eren, L., Karahoca, A., and Devaney, M.J. (2004, January 18\u201320). Neural network based motor bearing fault detection. Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conferenc, Como, Italy."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Eren, L., Teotrakool, K., and Devaney, M.J. (2007, January 1\u20133). Bearing fault detection via wavelet packet decomposition with spectral post processing. Proceedings of the 2007 IEEE Instrumentation & Measurement Technology Conference IMTC 2007, Warsaw, Poland.","DOI":"10.1109\/IMTC.2007.379444"},{"key":"ref_39","first-page":"1","article-title":"Novel intelligent data processing technology, based on nonstationary nonlinear wavelet bispectrum, for vibration fault diagnosis","volume":"50","author":"Patel","year":"2023","journal-title":"IAENG Int. J. Comput. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1002\/tee.22595","article-title":"A bearing outer raceway fault detection method in induction motors based on instantaneous frequency of the stator current","volume":"13","author":"Song","year":"2018","journal-title":"IEEE J. Trans. Electr. Electron. Eng."},{"key":"ref_41","first-page":"263","article-title":"Detection of bearing faults of induction motor using park\u2019s vector approach","volume":"1","author":"Dahiya","year":"2010","journal-title":"Int. J. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Saeidi, M., Zarei, J., Hassani, H., Zamani, A., and Majid, S. (2014, January 3\u20135). Bearing fault detection via park\u2019s vector approach based on anfis. Proceedings of the 2014 International Conference on Mechatronics and Control (ICMC), Jinzhou, China.","DOI":"10.1109\/ICMC.2014.7232006"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1007\/s00521-017-3038-0","article-title":"Analysis of distributed faults in inner and outer race of bearing via Park vector analysis method","volume":"31","author":"Irfan","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Koteleva, N., Korolev, N., Zhukovskiy, Y., and Baranov, G. (2021). A soft sensor for measuring the wear of an induction motor bearing by the park\u2019s vector components of current and voltage. Sensors, 21.","DOI":"10.3390\/s21237900"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.triboint.2008.06.002","article-title":"An advanced Park\u2019s vectors approach for bearing fault detection","volume":"42","author":"Zarei","year":"2009","journal-title":"Tribol. Int."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.ymssp.2017.01.046","article-title":"introducing the filtered park\u2019s and filtered extended park\u2019s vector approach to detect broken rotor bars in induction motors independently from the rotor slots number","volume":"93","author":"Gyftakis","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Messaoudi, M., Flah, A., Alotaibi, A.A., Althobaiti, A., Sbita, L., and Ziad El-Bayeh, C. (2022). Diagnosis and fault detection of rotor bars in squirrel cage induction motors using combined park\u2019s vector and extended park\u2019s vector approaches. Electronics, 11.","DOI":"10.3390\/electronics11030380"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Bouslimani, S., Drid, S., Chrifi-Alaoui, L., Bussy, P., Ouriagli, M., and Delahoche, L. (2014, January 21\u201323). An extended Park\u2019s vector approach to detect broken bars faults in induction motor. Proceedings of the 15th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), Hammamet, Tunisia.","DOI":"10.1109\/STA.2014.7086754"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"163","DOI":"10.4028\/www.scientific.net\/AMR.382.163","article-title":"Motor broken-bar fault diagnosis based on park vector and wavelet neural network","volume":"Volume 382","author":"Zhang","year":"2011","journal-title":"Advanced Materials Research"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Zarei, J., Hassani, H., Wei, Z., and Karimi, H.R. (2014, January 1\u20134). Broken rotor bars detection via Park\u2019s vector approach based on ANFIS. Proceedings of the IEEE 23rd International Symposium on Industrial Electronics (ISIE), Istanbul, Turkey.","DOI":"10.1109\/ISIE.2014.6864999"},{"key":"ref_51","unstructured":"Guo, Q., Li, X., Yu, H., Hu, W., and Hu, J. (2008). International Symposium on Neural Networks, Springer. Advances in Neural Networks\u2014ISNN."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Estima, J.O., Freire, N.M., and Cardoso, A.M. (2013, January 11\u201312). Recent advances in fault diagnosis by Park\u2019s vector approach. Proceedings of the 2013 IEEE Workshop on Electrical Machines Design, Control and Diagnosis (WEMDCD), Paris, France.","DOI":"10.1109\/WEMDCD.2013.6525187"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1109\/28.952496","article-title":"Stator winding fault diagnosis in three-phase synchronous and asynchronous motors, by the extended Park\u2019s vector approach","volume":"37","author":"Cruz","year":"2001","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/28.845047","article-title":"Monitoring and diagnosis of induction motors electrical faults using a current Park\u2019s vector pattern learning approach","volume":"36","author":"Nejjari","year":"2000","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"3905","DOI":"10.1049\/iet-gtd.2020.0127","article-title":"Extended Park\u2019s vector method in early inter-turn short circuit fault detection for the stator windings of offshore wind doubly-fed induction generators","volume":"14","author":"Wei","year":"2020","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Sharma, A., Chatterji, S., and Mathew, L. (2017, January 12\u201313). A novel Park\u2019s vector approach for investigation of incipient stator fault using MCSA in three-phase induction motors. Proceedings of the International Conference on Innovations in Control, Communication and Information Systems (ICICCI), Greater Noida, India.","DOI":"10.1109\/ICICCIS.2017.8660892"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/0022-247X(84)90260-9","article-title":"Inequalities for absolute moments of a distribution: From laplace to von mises","volume":"98","author":"Beesack","year":"1984","journal-title":"J. Math. Anal. Appl."},{"key":"ref_58","unstructured":"Winkelbauer, A. (2014). Moments and absolute moments of the normal distribution. arXiv."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Eriksson, J., Ollila, E., and Koivunen, V. (2009, January 19\u201324). Statistics for complex random variables revisited. Proceedings of the 34th IEEE International Conference on Acoustics, Speech, and Signal Processing, Taipei, Taiwan.","DOI":"10.1109\/ICASSP.2009.4960396"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"5400","DOI":"10.1109\/TSP.2010.2054085","article-title":"Essential statistics and tools for complex random variables","volume":"58","author":"Eriksson","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1109\/LSP.2008.2005050","article-title":"On the circularity of a complex random variable","volume":"15","author":"Ollila","year":"2008","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Ao, S.I., Gelman, L., Karimi, H.R., and Tiboni, M. (2022). Advanced machine learning for sensing and condition monitoring. Appl. Sci., 12.","DOI":"10.3390\/app122312392"},{"key":"ref_63","unstructured":"Thomson, J., and Stewart, H.H. (1986). Nonlinear Dynamics and Chaos, John Willey."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1115\/1.3230406","article-title":"Dynamic analysis models of the tension leg platform","volume":"104","author":"Jefferys","year":"1982","journal-title":"ASME J. Energy Res. Technol."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/0020-7462(90)90017-4","article-title":"On the dynamics of oscillators with bilinear damping and stiffness","volume":"25","author":"Narsiavas","year":"1990","journal-title":"Int. J. Non-Linear Mech."},{"key":"ref_66","first-page":"93","article-title":"Observations of sub-critical super-harmonic and chaotic response in rotor-dynamics","volume":"11","author":"Ehrich","year":"1991","journal-title":"J. Vib. Acoust."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1687814018764148","DOI":"10.1177\/1687814018764148","article-title":"Nonlinear dynamic investigations on rolling element bearings: A review","volume":"10","author":"Sharma","year":"2018","journal-title":"Adv. Mech. Eng."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1016\/j.ymssp.2005.10.012","article-title":"Piece wise model and estimates of damping and natural frequency for a spur gear","volume":"21","author":"Gelman","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Gelman, L. (2014). The new second and higher order spectral technique for damage monitoring of structures and machinery. Int. J. Progn. Health Manag., 5.","DOI":"10.36001\/ijphm.2014.v5i2.2208"},{"key":"ref_70","first-page":"18","article-title":"Advantage of using the Fourier components pair instead of power spectral density for fatigue crack diagnostics","volume":"7","author":"Gelman","year":"2004","journal-title":"Int. J. Comadem"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1016\/j.ymssp.2009.01.007","article-title":"Adaptive diagnosis of the bilinear mechanical systems","volume":"23","author":"Gelman","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s11045-006-0005-9","article-title":"The new multidimensional time\/multi-frequency transform for higher order spectral analysis","volume":"18","author":"Gelman","year":"2007","journal-title":"Int. J. Multidimens. Syst. Signal Process."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"3085","DOI":"10.1121\/1.418805","article-title":"Theoretical bases of the free-oscillation method for acoustical nondestructive testing","volume":"101","author":"Bouraou","year":"1997","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1006\/jsvi.1998.1738","article-title":"Bispectral analysis of the bilinear oscillator with application to the detection of fatigue cracks","volume":"216","author":"Rivola","year":"1998","journal-title":"J. Sound Vib."},{"key":"ref_75","first-page":"937","article-title":"Comparison between second and higher order spectral analysis in detecting structural damages","volume":"2","author":"Rivola","year":"2000","journal-title":"Proc. Seventh Int. Conf. Recent Adv. Struct. Dyn."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1109\/TIA.2011.2153813","article-title":"Frequency demodulation approach to induction motor speed detection","volume":"47","author":"Gao","year":"2011","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_77","first-page":"e2526","article-title":"Novel vibration structural health monitoring technology by non-stationary higher order frequency response function","volume":"27","author":"Gelman","year":"2020","journal-title":"Int. J. Struct. Control. Health Monit."},{"key":"ref_78","first-page":"e2479","article-title":"Walters, M. Novel health monitoring technology for in-service diagnostics in aircraft engines","volume":"27","author":"Gelman","year":"2020","journal-title":"Int. J. Struct. Control. Health Monit."},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Farhat, M.H., Gelman, L., Conaghan, G., Kluis, W., and Ball, A. (2022). Novel online fault diagnosis via motor current signature analysis. Sensors, 22.","DOI":"10.3390\/s22239507"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/7\/3731\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:09:56Z","timestamp":1760123396000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/7\/3731"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,4]]},"references-count":79,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["s23073731"],"URL":"https:\/\/doi.org\/10.3390\/s23073731","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,4]]}}}