{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T18:28:35Z","timestamp":1772735315122,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,11]],"date-time":"2018-05-11T00:00:00Z","timestamp":1525996800000},"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>In order to remove noise and preserve the important features of a signal, a hybrid de-noising algorithm based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Permutation Entropy (PE), and Time-Frequency Peak Filtering (TFPF) is proposed. In view of the limitations of the conventional TFPF method regarding the fixed window length problem, CEEMDAN and PE are applied to compensate for this, so that the signal is balanced with respect to both noise suppression and signal fidelity. First, the Intrinsic Mode Functions (IMFs) of the original spectra are obtained using the CEEMDAN algorithm, and the PE value of each IMF is calculated to classify whether the IMF requires filtering, then, for different IMFs, we select different window lengths to filter them using TFPF; finally, the signal is reconstructed as the sum of the filtered and residual IMFs. The filtering results of a simulated and an actual gearbox vibration signal verify that the de-noising results of CEEMDAN-PE-TFPF outperforms other signal de-noising methods, and the proposed method can reveal fault characteristic information effectively.<\/jats:p>","DOI":"10.3390\/e20050361","type":"journal-article","created":{"date-parts":[[2018,5,14]],"date-time":"2018-05-14T02:57:20Z","timestamp":1526266640000},"page":"361","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["A Hybrid De-Noising Algorithm for the Gear Transmission System Based on CEEMDAN-PE-TFPF"],"prefix":"10.3390","volume":"20","author":[{"given":"Lili","family":"Bai","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhennan","family":"Han","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanfeng","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaohui","family":"Ning","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.ymssp.2012.09.015","article-title":"A review on empirical mode decomposition in fault diagnosis of rotating machinery","volume":"35","author":"Lei","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2016\/5714195","article-title":"Fault diagnosis for a multistage planetary gear set using model-based simulation and experimental investigation","volume":"2016","author":"Li","year":"2016","journal-title":"Shock Vib."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1177\/0142331215592064","article-title":"Denoising of hydropower unit vibration signal based on variational mode decomposition and approximate entropy","volume":"38","author":"An","year":"2016","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_4","first-page":"9263298","article-title":"The rolling bearing fault feature extraction based on the LMD and envelop demodulation","volume":"2015","author":"Ma","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Shi, Z.L., Song, W.Q., and Taheri, S. (2016). Improved LMD, permutation entropy and optimized K-means to fault diagnosis for roller bearings. Entropy, 18.","DOI":"10.3390\/e18030070"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.ymssp.2014.06.004","article-title":"A hybrid fault diagnosis method using morphological filter-translation invariant wavelet and improved ensemble empirical mode decomposition","volume":"50\u201351","author":"Meng","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2420","DOI":"10.1177\/1077546314547533","article-title":"Rolling bearing fault diagnosis approach using probabilistic principal component analysis denoising and cyclic bispectrum","volume":"22","author":"Jiang","year":"2016","journal-title":"J. Vib. Control"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.measurement.2015.10.015","article-title":"Natural gas pipeline leak aperture identification and location based on local mean decomposition analysis","volume":"79","author":"Sun","year":"2016","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1016\/j.ijleo.2012.02.008","article-title":"Study on temperature error processing technique for fiber optic gyroscope","volume":"124","author":"Chen","year":"2013","journal-title":"Optik"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"KS68","DOI":"10.1190\/geo2014-0423.1","article-title":"Microseismic and seismic denoising via ensemble empirical mode decomposition and adaptive thresholding","volume":"80","author":"Han","year":"2015","journal-title":"Geophysics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ymssp.2016.04.031","article-title":"Bayesian wavelet PCA methodology for turbo machinery damage diagnosis under uncertainty","volume":"80","author":"Xu","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/j.ijepes.2016.02.015","article-title":"Low cost microcontroller based fault detector, classifier, zone identifier and locator for transmission lines using wavelet transform and artificial neural network: A hardware co-simulation approach","volume":"81","author":"Koley","year":"2016","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1109\/LSP.2003.821662","article-title":"Empirical mode decomposition as a filter bank","volume":"11","author":"Flandrin","year":"2004","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.measurement.2016.05.065","article-title":"Adaptive sparsest narrow-band decomposition method and its application to rotor fault diagnosis","volume":"91","author":"Peng","year":"2016","journal-title":"Measurement"},{"key":"ref_15","first-page":"3255","article-title":"EEMD de-noising adaptively in Raman spectroscopy","volume":"33","author":"Zhang","year":"2013","journal-title":"Spectrosc. Spectr. Anal."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.ymssp.2016.03.007","article-title":"Pseudo-fault signal assisted EMD for fault detection and isolation in rotating machines","volume":"81","author":"Singh","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1016\/j.ymssp.2008.11.005","article-title":"Application of the EEMD method to rotor fault diagnosis of rotating machinery","volume":"23","author":"Lei","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2603","DOI":"10.1177\/1077546314550221","article-title":"An enhanced empirical mode decomposition method for blind component separation of a single-channel vibration signal mixture","volume":"22","author":"Wang","year":"2015","journal-title":"J. Vib. Control"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1250025","DOI":"10.1142\/S1793536912500252","article-title":"Noise-assisted EMD methods in action","volume":"4","author":"Colominas","year":"2012","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Torres, M.E., Colominas, M.A., and Schlotthauer, G. (2011, January 22\u201327). A complete ensemble empirical mode decomposition with adaptive noise. Proceedings of the 36th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic.","DOI":"10.1109\/ICASSP.2011.5947265"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1093\/gji\/ggv340","article-title":"Signal preserving and seismic random noise attenuation by Hurst exponent based time-frequency peak filtering","volume":"203","author":"Zhang","year":"2015","journal-title":"Geophys. J. Int."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2252","DOI":"10.1109\/LGRS.2015.2464233","article-title":"Curvature-varying hyperbolic trace TFPF for seismic random noise attenuation","volume":"12","author":"Zhuang","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1109\/LGRS.2014.2352671","article-title":"Noise attenuation for seismic data by Hyperbolic-Trace time-frequency peak filtering","volume":"12","author":"Zhang","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ning, S.H., Han, Z.N., Wang, Z.J., and Wu, X.F. (2016). Application of Sample Entropy Based LMD-TFPF De-Noising Algorithm for the Gear Transmission System. Entropy, 18.","DOI":"10.3390\/e18110414"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation entropy: A natural complexity measure for time series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1103\/PhysRevE.82.046212","article-title":"Permutation-information-theory approach to unveil delay dynamics from time-series analysis","volume":"82","author":"Zunino","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1097\/ALN.0b013e318182a91b","article-title":"Using Permutation Entropy to Measure the Electroencephalographic Effects of Sevoflurane","volume":"109","author":"Li","year":"2008","journal-title":"Anesthesiology"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wang, Z.J., Wang, J.Y., Kou, Y.F., Zhang, J.P., Ning, S.H., and Zhao, Z.F. (2017). Weak Fault Diagnosis of Wind Turbine Gearboxes Based on MED-LMD. Entropy, 19.","DOI":"10.3390\/e19060277"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble Empirical Mode Decomposition: A Noise-Assisted Data Analysis Method","volume":"1","author":"Wu","year":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.bspc.2014.06.009","article-title":"Improved complete ensemble EMD: A suitable tool for biomedical signal processing","volume":"14","author":"Colominas","year":"2014","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"287","DOI":"10.13031\/2013.22392","article-title":"Subsurface characterization using textural features extracted from GPR data","volume":"50","author":"Freeland","year":"2007","journal-title":"Trans. ASABE"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1883","DOI":"10.1016\/j.physleta.2017.03.052","article-title":"Permutation entropy based time series analysis: Equalities in the input signal can lead to false conclusions","volume":"381","author":"Zunino","year":"2017","journal-title":"Phys. Lett. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"022118","DOI":"10.1103\/PhysRevE.94.022118","article-title":"Permutation entropy of finite-length white-noise time series","volume":"94","author":"Douglas","year":"2016","journal-title":"Phys. Rev. E"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhan, L.W., and Li, C.W. (2017). A Comparative Study of Emprical Mode Decomposition-Based Filtering for Impact Signal. Entropy, 19.","DOI":"10.3390\/e19010013"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/5\/361\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:03:56Z","timestamp":1760195036000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/5\/361"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,11]]},"references-count":34,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["e20050361"],"URL":"https:\/\/doi.org\/10.3390\/e20050361","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,11]]}}}