{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T18:28:52Z","timestamp":1763836132226,"version":"build-2065373602"},"reference-count":63,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2020,9,11]],"date-time":"2020-09-11T00:00:00Z","timestamp":1599782400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>It is proposed a novel instantaneous frequency estimation technology, multi-generalized demodulation transform, for non-stationary signals, whose true time variations of instantaneous frequencies are unknown and difficult to extract from the time-frequency representation due to essentially noisy environment. Theoretical bases of the novel instantaneous frequency estimation technology are created. The main innovations are summarized as: (a) novel instantaneous frequency estimation technology, multi-generalized demodulation transform, is proposed, (b) novel instantaneous frequency estimation results, obtained by simulation, for four types of amplitude and frequency modulated non-stationary single and multicomponent signals under strong background noise (signal to noise ratio is \u22125 dB), and (c) novel experimental instantaneous frequency estimation results for defect frequency of rolling bearings for multiple defect frequency harmonics, using the proposed technology in non-stationary conditions and in conditions of different levels of noise interference, including a strong noise interference. Quantitative instantaneous frequency estimation errors are employed to evaluate performance of the proposed IF estimation technology. Simulation and experimental estimation results show high effectiveness of the proposed estimation technology.<\/jats:p>","DOI":"10.3390\/s20185201","type":"journal-article","created":{"date-parts":[[2020,9,13]],"date-time":"2020-09-13T21:11:32Z","timestamp":1600031492000},"page":"5201","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Novel Method for Vibration Sensor-Based Instantaneous Defect Frequency Estimation for Rolling Bearings Under Non-Stationary Conditions"],"prefix":"10.3390","volume":"20","author":[{"given":"Dezun","family":"Zhao","sequence":"first","affiliation":[{"name":"Centre for Efficiency and Performance Engineering (CEPE), School of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Len","family":"Gelman","sequence":"additional","affiliation":[{"name":"Centre for Efficiency and Performance Engineering (CEPE), School of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fulei","family":"Chu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8593-6830","authenticated-orcid":false,"given":"Andrew","family":"Ball","sequence":"additional","affiliation":[{"name":"Centre for Efficiency and Performance Engineering (CEPE), School of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1186\/s10033-019-0322-1","article-title":"Generalized demodulation transform for bearing fault diagnosis under nonstationary conditions and gear noise interferences","volume":"32","author":"Zhao","year":"2019","journal-title":"Chin. 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