{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:33:55Z","timestamp":1760783635082,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2013,1,18]],"date-time":"2013-01-18T00:00:00Z","timestamp":1358467200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Planetary gearboxes exhibit complicated dynamic responses which are more difficult to detect in vibration signals than fixed-axis gear trains because of the special gear transmission structures. Diverse advanced methods have been developed for this challenging task to reduce or avoid unscheduled breakdown and catastrophic accidents.  It is feasible to make fault features distinct by using multiwavelet denoising which depends on the feature separation and the threshold denoising. However, standard and fixed multiwavelets are not suitable for accurate fault feature detections because they are usually independent of the measured signals. To overcome this drawback, a method to construct customized multiwavelets based on the redundant symmetric lifting scheme is proposed in this paper. A novel indicator which combines kurtosis and entropy is applied to select the optimal multiwavelets, because kurtosis is sensitive to sharp impulses and entropy is effective for periodic impulses. The improved neighboring coefficients method is introduced into multiwavelet denoising. The vibration signals of a planetary gearbox from a satellite communication antenna on a measurement ship are captured under various motor speeds. The results show the proposed method could accurately detect the incipient pitting faults on two neighboring teeth in the planetary gearbox.<\/jats:p>","DOI":"10.3390\/s130101183","type":"journal-article","created":{"date-parts":[[2013,1,18]],"date-time":"2013-01-18T11:04:23Z","timestamp":1358507063000},"page":"1183-1209","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Customized Multiwavelets for Planetary Gearbox Fault Detection Based on Vibration Sensor Signals"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6330-2514","authenticated-orcid":false,"given":"Hailiang","family":"Sun","sequence":"first","affiliation":[{"name":"State Key Laboratory for Manufacturing and Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China"}]},{"given":"Yanyang","family":"Zi","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing and Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China"}]},{"given":"Zhengjia","family":"He","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing and Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China"}]},{"given":"Jing","family":"Yuan","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing and Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China"},{"name":"Shanghai Institute of Radio Equipment, Shanghai 200090, China"}]},{"given":"Xiaodong","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing and Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China"},{"name":"Technology Center, CNPC Logging Co., Xi'an 710077, Shaanxi, China"}]},{"given":"Lue","family":"Chen","sequence":"additional","affiliation":[{"name":"Beijing Aerospace Control Center, Beijing 100094, China"}]}],"member":"1968","published-online":{"date-parts":[[2013,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1115\/1.2827360","article-title":"Rotary machine health diagnosis based on empirical mode decompositon","volume":"130","author":"Yan","year":"2008","journal-title":"J. Vib. Acoust."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1115\/1.1403735","article-title":"Fourier series analysis of epicyclic gearbox vibration","volume":"124","author":"James","year":"2002","journal-title":"J. Vib. Acoust."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/j.mechmachtheory.2005.10.001","article-title":"Tooth contact analysis of a misaligned isostatic planetary gear train","volume":"41","author":"Vecchiato","year":"2006","journal-title":"Mech. Mach. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Lei, Y.G., Kong, D.T., Lin, J., and Zuo, M.J. (2012). Fault detection of planetary gearboxes using new diagnostic parameters. Meas. Sci. Technol.","DOI":"10.1088\/0957-0233\/23\/5\/055605"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2095","DOI":"10.1016\/j.ymssp.2006.05.010","article-title":"Detection of a fatigue crack ina UH-60A planet gear carrier using vibration analysis","volume":"20","author":"Blunt","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Mosher, M. (2003, January 2\u20136). Understanding Vibration Spectra of Planetary Gear Systems for Fault Detection. Chicago, IL, USA.","DOI":"10.1115\/DETC2003\/PTG-48082"},{"key":"ref_7","unstructured":"Hines, J.A., Muench, D.S., Keller, J.A., and Garga, A.K. (2005, January 1\u20133). Effects of Time-Synchronous Averaging Implementations on HUMS Features for UH-60A Planetary Carrier Cracking. Grapevine, TX, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1016\/j.jsv.2009.01.004","article-title":"A theoretical and experimental investigation of modulation sidebands of planetary gear sets","volume":"323","author":"Inalpolat","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1352","DOI":"10.1016\/j.ymssp.2008.07.019","article-title":"Application of spectral kurtosis for detection of a tooth crack in the planetary gear of a wind turbine","volume":"23","author":"Barszcz","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_10","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_11","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.ymssp.2008.03.016","article-title":"Vibration condition monitoring of planetary gearbox under varying external load","volume":"23","author":"Bartelmus","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.rser.2007.05.008","article-title":"Condition monitoring and fault detection of wind turbines and related algorithms: A review","volume":"13","author":"Hameed","year":"2009","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2005","DOI":"10.3390\/s120202005","article-title":"A method based on multi-sensor data fusion for fault detection of planetary gearboxes","volume":"12","author":"Lei","year":"2012","journal-title":"Sensors"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Daubechies, I. (1992). Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611970104"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Keinert, F. (2004). Wavelets and Multiwavelets, Chapman and Hall\/CRC Press.","DOI":"10.1201\/9780203011591"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1006\/jath.1994.1085","article-title":"Fractal functions and wavelet expansions based on several scaling functions","volume":"78","author":"Geronimo","year":"1994","journal-title":"J. Approx. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1158","DOI":"10.1137\/S0036141093256526","article-title":"Construction of orthogonal wavelets using fractal interpolation functions","volume":"27","author":"Geronimo","year":"1996","journal-title":"SIAM J. Math. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0168-9274(95)00111-5","article-title":"A study of orthonormal multiwavelets","volume":"20","author":"Chui","year":"1996","journal-title":"Appl. Numer. Math."},{"key":"ref_19","unstructured":"Strela, V., and Strang, G. (1995). Approximation Theory, Wavelets and Applications, Kluwer."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1016\/S0022-460X(02)00992-6","article-title":"Development of vibration signature analysis using multiwavelet systems","volume":"261","author":"Khadem","year":"2003","journal-title":"J. Sound Vib."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2801","DOI":"10.1007\/s11431-009-0253-7","article-title":"Gearbox fault diagnosis of rolling mills using multiwavelet sliding window neighbouring coefficient denoising and optimal blind deconvolution","volume":"52","author":"Yuan","year":"2009","journal-title":"Sci. China Ser. E Technol. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1016\/j.ymssp.2007.09.008","article-title":"Rotating machinery fault diagnosis using signal-adapted lifting scheme","volume":"22","author":"Li","year":"2008","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1006\/acha.1996.0015","article-title":"The lifting scheme: A custom-design construction of biorthogonal wavelets","volume":"3","author":"Sweldens","year":"1996","journal-title":"Appl. Comput. Harmonic Anal."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1137\/S0036141095289051","article-title":"The lifting scheme: A construction of second generation wavelet","volume":"29","author":"Sweldens","year":"1998","journal-title":"SIAM J. Math. Anal."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wang, X.D., Zi, Y.Y., and He, Z.J. (2009). Multiwavelet construction via an adaptive symmetric lifting scheme and its applications for rotating machinery fault diagnosis. Meas. Sci. Technol.","DOI":"10.1088\/0957-0233\/20\/4\/045103"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1016\/j.ymssp.2009.11.003","article-title":"Gear fault detection using customized multiwavelet lifting schemes","volume":"24","author":"Yuan","year":"2010","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","unstructured":"Mallat, S. (2003). A Wavelet Tour of Signal Processing, China Machine Press."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.ymssp.2010.03.010","article-title":"Multiwavelet denoising with improved neighboring coefficients for application on rolling bearing fault diagnosis","volume":"25","author":"Wang","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/78.482009","article-title":"Design of prefilters for discrete multiwavelet transform","volume":"44","author":"Xia","year":"1996","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1109\/83.753742","article-title":"The application of multiwavelet filter banks to signal and image processing","volume":"8","author":"Strela","year":"1996","journal-title":"IEEE Trans. Image Process."},{"key":"ref_31","unstructured":"Bradley, A.P. (2003, January 10\u201312). Shift-Invariance in the Discrete Wavelet Transform. Sydney, Australia."},{"key":"ref_32","unstructured":"Bulat, J. (2000, January 17\u201320). Image Compression Using Lifted Wavelet Packets. Ustron, Poland."},{"key":"ref_33","first-page":"127","article-title":"Incorporating information on neighboring coefficients into wavelet estimation","volume":"63","author":"Cai","year":"2001","journal-title":"Sankhya"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1109\/LSP.2003.811586","article-title":"Multiwavelets denoising using neighboring coefficients","volume":"10","author":"Chen","year":"2003","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1006\/jsvi.2000.2864","article-title":"Feature extraction based on Morlet wavelet and its application for mechanical fault diagnosis","volume":"234","author":"Lin","year":"2000","journal-title":"J. Sound Vib."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.ymssp.2004.09.001","article-title":"The spectral kurtosis: A useful tool for characterising non-stationary signals","volume":"20","author":"Antoni","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_37","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."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/1\/1183\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:44:24Z","timestamp":1760219064000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/1\/1183"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,18]]},"references-count":37,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1]]}},"alternative-id":["s130101183"],"URL":"https:\/\/doi.org\/10.3390\/s130101183","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2013,1,18]]}}}