{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T08:13:39Z","timestamp":1769501619490,"version":"3.49.0"},"reference-count":46,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,13]],"date-time":"2018-11-13T00:00:00Z","timestamp":1542067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51705130\uff0c51706058"],"award-info":[{"award-number":["51705130\uff0c51706058"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hebei University Science and Technology Research Youth Fund Project","award":["QN2018168"],"award-info":[{"award-number":["QN2018168"]}]},{"name":"China National Key Laboratory of vehicle transmission fund project","award":["9140C340101101"],"award-info":[{"award-number":["9140C340101101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It is a difficult task to analyze the coupling characteristics of rotating machinery fault signals under the influence of complex and nonlinear interference signals. This difficulty is due to the strong noise background of rotating machinery fault feature extraction and weaknesses, such as modal mixing problems, in the existing Ensemble Empirical Mode Decomposition (EEMD) time\u2013frequency analysis methods. To quantitatively study the nonlinear synchronous coupling characteristics and information transfer characteristics of rotating machinery fault signals between different frequency scales under the influence of complex and nonlinear interference signals, a new nonlinear signal processing method\u2014the harmonic assisted multivariate empirical mode decomposition method (HA-MEMD)\u2014is proposed in this paper. By adding additional high-frequency harmonic-assisted channels and reducing them, the decomposing precision of the Intrinsic Mode Function (IMF) can be effectively improved, and the phenomenon of mode aliasing can be mitigated. Analysis results of the simulated signals prove the effectiveness of this method. By combining HA-MEMD with the transfer entropy algorithm and introducing signal processing of the rotating machinery, a fault detection method of rotating machinery based on high-frequency harmonic-assisted multivariate empirical mode decomposition-transfer entropy (HA-MEMD-TE) was established. The main features of the mechanical transmission system were extracted by the high-frequency harmonic-assisted multivariate empirical mode decomposition method, and the signal, after noise reduction, was used for the transfer entropy calculation. The evaluation index of the rotating machinery state based on HA-MEMD-TE was established to quantitatively describe the degree of nonlinear coupling between signals to effectively evaluate and diagnose the operating state of the mechanical system. By adding noise to different signal-to-noise ratios, the fault detection ability of HA-MEMD-TE method in the background of strong noise is investigated, which proves that the method has strong reliability and robustness. In this paper, transfer entropy is applied to the fault diagnosis field of rotating machinery, which provides a new effective method for early fault diagnosis and performance degradation-state recognition of rotating machinery, and leads to relevant research conclusions.<\/jats:p>","DOI":"10.3390\/e20110873","type":"journal-article","created":{"date-parts":[[2018,11,14]],"date-time":"2018-11-14T02:42:41Z","timestamp":1542163361000},"page":"873","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Early Fault Detection Method for Rotating Machinery Based on Harmonic-Assisted Multivariate Empirical Mode Decomposition and Transfer Entropy"],"prefix":"10.3390","volume":"20","author":[{"given":"Zhe","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Vehicle Engineering, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Key Laboratory of Vehicle Transmission, China North Vehicle Research Institute, Beijing 100072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lixin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lifeng","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingbo","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.anucene.2016.11.038","article-title":"Cofrentes nuclear power plant instability analysis using ensemble empirical mode decomposition","volume":"101","author":"Montalvo","year":"2017","journal-title":"Ann. 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