{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T03:57:40Z","timestamp":1771041460515,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,1]],"date-time":"2018-12-01T00:00:00Z","timestamp":1543622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A motor bearing system is a nonlinear dynamics system with nonlinear support stiffness. It is an asymmetry system, which plays an extremely important role in rotating machinery. In this paper, a center frequency method of double thresholds is proposed to improve the variational mode decomposition (VMD) method, then an adaptive VMD (called DTCFVMD) method is obtained to extract the fault feature. In the DTCFVMD method, a center frequency method of double thresholds is a symmetry method, which is used to determine the decomposed mode number of VMD according to the power spectrum of the signal. The proposed DTCFVMD method is used to decompose the nonlinear and non-stationary vibration signals of motor bearing in order to obtain a series of intrinsic mode functions (IMFs) under different scales. Then, the Hilbert transform is used to analyze the envelope of each mode component and calculate the power spectrum of each mode component. Finally, the power spectrum is used to extract the fault feature frequency for determining the fault type of the motor bearing. To test and verify the effectiveness of the DTCFVMD method, the actual fault vibration signal of the motor bearing is selected in here. The experimental results show that the center frequency method of double thresholds can effectively determine the mode number of the VMD method, and the proposed DTCFVMD method can accurately extract the clear time frequency characteristics of each mode component, and obtain the fault characteristics of characteristics; frequency, rotating frequency, and frequency doubling and so on.<\/jats:p>","DOI":"10.3390\/sym10120684","type":"journal-article","created":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T06:02:09Z","timestamp":1543816929000},"page":"684","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Research on an Adaptive Variational Mode Decomposition with Double Thresholds for Feature Extraction"],"prefix":"10.3390","volume":"10","author":[{"given":"Wu","family":"Deng","sequence":"first","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"},{"name":"Co-Innovation Center of Shandong Colleges and Universities: Future Intelligent Computing, Yantai 264005, China"},{"name":"Traction Power State Key Laboratory of Southwest Jiaotong University, Chengdu 610031, China"},{"name":"Guangxi Key Lab of Multi-Source Information Mining &amp; Security, Guangxi Normal University, Guilin 541004, China"},{"name":"Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China"},{"name":"Liaoning Key Laboratory of Welding and Reliability of Rail Transportation Equipment, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Hailong","family":"Liu","sequence":"additional","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Shengjie","family":"Zhang","sequence":"additional","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Haodong","family":"Liu","sequence":"additional","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Huimin","family":"Zhao","sequence":"additional","affiliation":[{"name":"Software Institute, Dalian Jiaotong University, Dalian 116028, China"},{"name":"Traction Power State Key Laboratory of Southwest Jiaotong University, Chengdu 610031, China"},{"name":"Liaoning Key Laboratory of Welding and Reliability of Rail Transportation Equipment, Dalian Jiaotong University, Dalian 116028, China"}]},{"given":"Jinzhao","family":"Wu","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.jsv.2018.05.020","article-title":"Planetary gearbox fault diagnosis based on data-driven valued characteristic multigranulation model with incomplete diagnostic information","volume":"429","author":"Yu","year":"2018","journal-title":"J. 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