{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T23:38:11Z","timestamp":1785800291464,"version":"3.56.0"},"reference-count":29,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T00:00:00Z","timestamp":1631059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11802184"],"award-info":[{"award-number":["11802184"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Fault detection of axle bearings is crucial to promote the safe, efficient, and reliable running of high-speed trains. In recent decades, time\u2212frequency analysis (TFA) techniques have been widely used in mechanical equipment fault diagnoses. Time-reassigned multisynchrosqueezing transform (TMSST), as a novel time\u2212frequency representation (TFR) algorithm, is more suitable for dealing with strong frequency-varying signals. However, TMSST TFR results are subject to noise interference. It is difficult to extract the accurate time\u2212frequency (TF) fault feature of the axle bearing under a complex working environment. In addition, determination of the TMSST algorithm parameters depends on the personnel\u2019s subjective experience. Therefore, the TMSST result has a great randomicity and has the disadvantage of having a poor reliability. To address the above issues, a hybrid SVD-based denoising and self-adaptive TMSST is proposed for axle bearing fault detection in this paper. The main improvements of the proposed algorithm include the following two aspects: (1) An SVD-based denoising method using the maximum SV mean to determine the reasonable SV order is adopted to eliminate noise interference and to reserve useful fault impulse information. (2) A new evaluation metric, named time\u2212frequency spectrum permutation entropy (TFS-PEn), is put forward for the quantitative evaluation of the performance of TFR for the TMSST, and then a water cycle algorithm (WCA)-based optimized TMSST can adaptively determine the optimal algorithm parameters. In both the simulation and experimental tests, the superiority and effectiveness of the proposed method is compared with the TMSST, short-time Fourier transform (STFT), MSST, wavelet transform (WT), and Hilbert-Huang transform (HHT) methods. The results show that the proposed algorithm has a better performance for extracting the weak fault features of axle bearing under a strong background noise environment.<\/jats:p>","DOI":"10.3390\/s21186025","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T21:28:45Z","timestamp":1631136525000},"page":"6025","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["A Hybrid SVD-Based Denoising and Self-Adaptive TMSST for High-Speed Train Axle Bearing Fault Detection"],"prefix":"10.3390","volume":"21","author":[{"given":"Feiyue","family":"Deng","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"},{"name":"School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7114-0797","authenticated-orcid":false,"given":"Yongqiang","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rujiang","family":"Hao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.engfailanal.2015.02.008","article-title":"Observing early stage rail axle bearing damage","volume":"56","author":"Symonds","year":"2015","journal-title":"Eng. Fail. Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"108367","DOI":"10.1016\/j.measurement.2020.108367","article-title":"Teager energy spectral kurtosis of wavelet packet transform and its application in locating the sound source of fault bearing of belt conveyor","volume":"173","author":"Zhang","year":"2020","journal-title":"Measurement"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.mechmachtheory.2018.07.017","article-title":"Use of the correlated EEMD and time-spectral kurtosis for bearing defect detection under large speed variation","volume":"129","author":"Chen","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.ymssp.2017.09.007","article-title":"Train axle bearing fault detection using a feature selection scheme based multi-scale morphological filter","volume":"101","author":"Li","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"085014","DOI":"10.1088\/0957-0233\/26\/8\/085014","article-title":"SVD principle analysis and fault diagnosis for bearings based on the correlation coefficient","volume":"26","author":"Qiao","year":"2015","journal-title":"Meas. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.ymssp.2014.01.011","article-title":"Sparse representation based latent components analysis for machinery weak fault detection","volume":"46","author":"Tang","year":"2014","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble empirical mode decomposition: A noise-assistant data analysis method","volume":"1","author":"Wu","year":"2009","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.measurement.2019.05.049","article-title":"Application of a new EWT-based denoising technique in bearing fault diagnosis","volume":"144","author":"Chegini","year":"2019","journal-title":"Measurement"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"30069","DOI":"10.1007\/s11042-020-09534-w","article-title":"A fault diagnosis method of rolling bearing based on VMD Tsallis entropy and FCM clustering","volume":"79","author":"Yan","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.ymssp.2018.05.019","article-title":"Sympletic geometry mode decomposition and its application to rotating machinery compound fault diagnosis","volume":"114","author":"Pan","year":"2019","journal-title":"Mech. Syst. Sig. Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.jsv.2018.10.010","article-title":"Detection of rub-impact fault for rotor-stator systems: A novel method based on adaptive chirp mode decomposition","volume":"440","author":"Chen","year":"2019","journal-title":"J. Sound Vib."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.ymssp.2013.01.017","article-title":"Recent advances in time\u2013frequency analysis methods for machinery fault diagnosis: A review with application examples","volume":"38","author":"Feng","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/j.ymssp.2014.07.009","article-title":"Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions","volume":"52\u201353","author":"Feng","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.1109\/TASSP.1985.1164760","article-title":"Wigner\u2013Ville spectral analysis of nonstationary processes","volume":"33","author":"Martin","year":"1985","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.acha.2010.08.002","article-title":"Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool","volume":"30","author":"Daubechies","year":"2011","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3168","DOI":"10.1109\/TSP.2017.2686355","article-title":"High-order synchrosqueezingtransform for multicomponent signals analysis\u2014With an application to gravitational-wave signal","volume":"65","author":"Pham","year":"2017","journal-title":"IEEE Trans.Signal Process"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2078","DOI":"10.1137\/100798818","article-title":"Synchrosqueezing-based recovery of instantaneous frequency from nonuniform samples","volume":"43","author":"Thakur","year":"2011","journal-title":"Siam J. Math. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TSP.2013.2276393","article-title":"Matching demodulation transform and synchrosqueezing in time-frequency analysis","volume":"62","author":"Wang","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5441","DOI":"10.1109\/TIE.2018.2868296","article-title":"Multisynchrosqueezing Transform","volume":"66","author":"Yu","year":"2018","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1486","DOI":"10.1109\/TIE.2020.2970571","article-title":"Time-reassigned Multisynchrosqueezing Transformfor Bearing Fault Diagnosis of Rotating Machinery","volume":"68","author":"Yu","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1177\/0142331212472929","article-title":"Fault diagnosis and health assessment for bearings using the Mahalanobis\u2013Taguchi system based on EMD-SVD","volume":"35","author":"Wang","year":"2013","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/j.ymssp.2014.07.019","article-title":"Study on Hankel matrix-based SVD and its application in rolling element bearing fault diagnosis","volume":"52\u201353","author":"Jiang","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.ymssp.2012.08.019","article-title":"Roller element bearing fault diagnosis using singular spectrum analysis","volume":"35","author":"Muruganatham","year":"2013","journal-title":"Mech. Syst.Signal Process."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"045011","DOI":"10.1088\/1361-6501\/aa5c2a","article-title":"Self adaptive multi-scale morphology AVG-Hat filter and its application to fault feature extraction for wheel bearing","volume":"28","author":"Deng","year":"2017","journal-title":"Meas. Sci. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.ymssp.2011.11.022","article-title":"Permutation entropy: A nonlinear statistical measure for status characterization of rotary machines","volume":"29","author":"Yan","year":"2012","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.asoc.2015.01.050","article-title":"Water cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems","volume":"30","author":"Sadollah","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.compstruc.2012.07.010","article-title":"Water cycle algorithm\u2014A novel metaheuristic optimization method for solving constrained engineering optimization problems","volume":"110","author":"Eskandar","year":"2012","journal-title":"J. Comput. Struct."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.ymssp.2015.04.004","article-title":"Criterion fusion for spectral segmentation and its application to optimal demodulation of bearing vibration signals","volume":"64\u201365","author":"Li","year":"2015","journal-title":"Mech. Syst. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/18\/6025\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:59:07Z","timestamp":1760165947000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/18\/6025"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,8]]},"references-count":29,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["s21186025"],"URL":"https:\/\/doi.org\/10.3390\/s21186025","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,8]]}}}