{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T16:35:50Z","timestamp":1774542950870,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,26]],"date-time":"2018-12-26T00:00:00Z","timestamp":1545782400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Dual-tree complex wavelet transform has been successfully applied to the composite diagnosis of a gearbox and has achieved good results. However, it has some fatal weaknesses, so this paper proposes an improved dual-tree complex wavelet transform (IDTCWT), and combines minimum entropy deconvolution (MED) to diagnose the composite fault of a gearbox. Firstly, the number of decomposition levels and the effective sub-bands of the DTCWT are adaptively determined according to the correlation coefficient matrix. Secondly, frequency mixing is removed by notch filter. Thirdly, each of the obtained sub-bands further reduces the noise by minimum entropy deconvolution. Then, the proposed method and the existing adaptive noise reduction methods, such as empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and variational mode decomposition (VMD), are used to decompose the two sets of simulation signals in comparison, and the feasibility of the proposed method has been verified. Finally, the proposed method is applied to the compound fault vibration signal of a gearbox. The results show the proposed method successfully extracts the outer ring fault at a frequency of 160 Hz, the gearbox fault with a characteristic frequency of 360 Hz and its double frequency of 720 Hz, and that there is no mode mixing. The method proposed in this paper provides a new idea for the feature extraction of a gearbox compound fault.<\/jats:p>","DOI":"10.3390\/e21010018","type":"journal-article","created":{"date-parts":[[2018,12,26]],"date-time":"2018-12-26T11:31:21Z","timestamp":1545823881000},"page":"18","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Gearbox Composite Fault Diagnosis Method Based on Minimum Entropy Deconvolution and Improved Dual-Tree Complex Wavelet Transform"],"prefix":"10.3390","volume":"21","author":[{"given":"Ziying","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical, Electronic and Information Engineering, China University of Mining and Technology (CUMT), Xueyuan Road, Beijing 100083, China"},{"name":"Shanxi Institute of Energy, Daxue Road, Jinzhong 030600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic and Information Engineering, China University of Mining and Technology (CUMT), Xueyuan Road, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Panpan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shanxi Institute of Energy, Daxue Road, Jinzhong 030600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fengbiao","family":"Wu","sequence":"additional","affiliation":[{"name":"Shanxi Institute of Energy, Daxue Road, Jinzhong 030600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuehui","family":"Li","sequence":"additional","affiliation":[{"name":"Shanxi Institute of Energy, Daxue Road, Jinzhong 030600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, Z., Wang, J., and Du, W. (2018). Research on Fault Diagnosis of Gearbox with Improved Variational Mode Decomposition. Sensors, 18.","DOI":"10.3390\/s18103510"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Du, W., Zhou, J., Wang, Z., Li, R., and Wang, J. (2018). Application of Improved Singular Spectrum Decomposition Method for Composite Fault Diagnosis of Gear Boxes. Sensors, 18.","DOI":"10.3390\/s18113804"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wang, Z., Wang, J., Zhao, Z., and Wang, R. (2017). A Novel Method for Multi-Fault Feature Extraction of a Gearbox under Strong Background Noise. Entropy, 20.","DOI":"10.3390\/e20010010"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5369","DOI":"10.1007\/s00034-018-0819-3","article-title":"EMD Threshold Denoising Algorithm Based on Variance Estimation","volume":"37","author":"Wang","year":"2018","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6506","DOI":"10.1109\/TIE.2017.2650873","article-title":"Application of Bandwidth EMD and Adaptive Multiscale Morphology Analysis for Incipient Fault Diagnosis of Rolling Bearings","volume":"64","author":"Li","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, Z., Wang, J., Kou, Y., Zhang, J., Ning, S., and Zhao, Z. (2017). Weak Fault Diagnosis of Wind Turbine Gearboxes Based on MED-LMD. Entropy, 19.","DOI":"10.3390\/e19060277"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble empirical mode decomposition: A noise-assisted data analysis method. Advances in adaptive data analysis","volume":"1","author":"Wu","year":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.jsv.2016.01.046","article-title":"EEMD-based multiscale ICA method for slewing bearing fault detection and diagnosis","volume":"370","author":"Matej","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.isatra.2014.09.006","article-title":"A novel procedure for diagnosing multiple faults in rotating machinery","volume":"55","author":"Wang","year":"2015","journal-title":"Isa Trans."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational mode decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ymssp.2015.08.023","article-title":"Wavelet transform based on inner product in fault diagnosis of rotating machinery: A review","volume":"70","author":"Chen","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1109\/TIM.2016.2613359","article-title":"Matching Synchrosqueezing Wavelet Transform and Application to Aeroengine Vibration Monitoring","volume":"66","author":"Wang","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.ymssp.2017.08.038","article-title":"Sparsity guided empirical wavelet transform for fault diagnosis of rolling element bearings","volume":"101","author":"Wang","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1109\/TIP.2010.2069711","article-title":"Enhanced Shift and Scale Tolerance for Rotation Invariant Polar Matching with Dual-Tree Wavelets","volume":"20","author":"Nelson","year":"2011","journal-title":"IEEE Trans. Image Process. Publ. IEEE Signal Process. Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1007\/s11222-017-9784-0","article-title":"The locally stationary dual-tree complex wavelet model","volume":"28","author":"Nelson","year":"2018","journal-title":"Stat. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6251","DOI":"10.1109\/TSP.2011.2166389","article-title":"A Dual-Tree Rational-Dilation Complex Wavelet Transform","volume":"59","author":"Bayram","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.isatra.2017.03.017","article-title":"Rolling bearing fault diagnosis using adaptive deep belief network with dual-tree complex wavelet packet","volume":"69","author":"Shao","year":"2017","journal-title":"Isa Trans."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1007\/s12206-017-0202-5","article-title":"Fault identification method for planetary gear based on DT-CWT threshold denoising and LE","volume":"31","author":"Chen","year":"2017","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1177\/0954406215573976","article-title":"Two-stage feature selection for bearing fault diagnosis based on dual-tree complex wavelet transform and empirical mode decomposition","volume":"230","author":"Van","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part C"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"025017","DOI":"10.1088\/0957-0233\/27\/2\/025017","article-title":"A new multiscale noise tuning stochastic resonance for enhanced fault diagnosis in wind turbine drivetrains","volume":"27","author":"Hu","year":"2016","journal-title":"Meas. Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Sun, W., Yao, B., Zeng, N., Chen, B., He, Y., Cao, X., and He, W. (2017). An Intelligent Gear Fault Diagnosis Methodology Using a Complex Wavelet Enhanced Convolutional Neural Network. Materials, 10.","DOI":"10.3390\/ma10070790"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Xiao, Y., Hong, Y., Chen, X., and Chen, W. (2017). The Application of Dual-Tree Complex Wavelet Transform (DTCWT) Energy Entropy in Misalignment Fault Diagnosis of Doubly-Fed Wind Turbine (DFWT). Entropy, 19.","DOI":"10.3390\/e19110587"},{"key":"ref_23","first-page":"5044","article-title":"Fault diagnosis of planetary gear based on entropy feature fusion of DTCWT and OKFDA","volume":"24","author":"Chen","year":"2018","journal-title":"J. Vib. Control"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Xu, J., Wang, Z.B., and Tan, C. (2016). Adaptive Wavelet Threshold Denoising Method for Machinery Sound Based on Improved Fruit Fly Optimization Algorithm. Appl. Sci., 6.","DOI":"10.3390\/app6070199"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1016\/j.asoc.2015.10.061","article-title":"Adaptive threshold based on wavelet transform applied to the segmentation of single and combined power quality disturbances","volume":"38","author":"Andrade","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1016\/j.ymssp.2006.02.005","article-title":"Application of a Minimum Entropy Deconvolution Filter to Enhance Autoregressive Model Based Gear Tooth Fault Detection Technique","volume":"21","author":"Endo","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2616","DOI":"10.1016\/j.ymssp.2006.12.002","article-title":"The Enhancement of Fault Detection and Diagnosis in Rolling Element Bearings Using Minimum Entropy Deconvolution Combined with Spectral Kurtosis","volume":"21","author":"Sawalhi","year":"2007","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.jsv.2017.04.036","article-title":"Rolling bearing fault diagnosis based on time-delayed feedback monostable stochastic resonance and adaptive minimum entropy deconvolution","volume":"401","author":"Li","year":"2017","journal-title":"J. Sound Vib."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.ymssp.2016.03.016","article-title":"Identification of multiple faults in rotating machinery based on minimum entropy deconvolution combined with spectral kurtosis","volume":"81","author":"He","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.jsv.2016.11.033","article-title":"Minimum entropy deconvolution optimized sinusoidal synthesis and its application to vibration based fault detection","volume":"390","author":"Li","year":"2017","journal-title":"J. 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