{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:25:46Z","timestamp":1760059546706,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"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":["92360308"],"award-info":[{"award-number":["92360308"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This research proposes a new method for time\u2013frequency analysis, termed the Local Entropy Optimization\u2013Adaptive Demodulation Reassignment Transform (LEOADRT), which is specifically designed to efficiently analyze complex, non-stationary mechanical vibration signals that exhibit multiple instantaneous frequencies or where the instantaneous frequency ridges are in close proximity to each other. The method introduces a demodulation term to account for the signal\u2019s dynamic behavior over time, converting each component into a stationary signal. Based on the local optimal theory of R\u00e9nyi entropy, the demodulation parameters are precisely determined to optimize the time\u2013frequency analysis. Then, the energy redistribution of the ridges already generated in the time\u2013frequency map is performed using the maximum local energy criterion, significantly improving time\u2013frequency resolution. Experimental results demonstrate that the performance of the LEOADRT algorithm is superior to existing methods such as SBCT, EMCT, VSLCT, and GLCT, especially in processing complex non-stationary signals with non-proportionality and closely spaced frequency intervals. This method provides strong support for mechanical fault diagnosis, condition monitoring, and predictive maintenance, making it particularly suitable for real-time analysis of multi-component and cross-frequency signals.<\/jats:p>","DOI":"10.3390\/e27070660","type":"journal-article","created":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T08:13:56Z","timestamp":1750407236000},"page":"660","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Local Entropy Optimization\u2013Adaptive Demodulation Reassignment Transform for Advanced Analysis of Non-Stationary Mechanical Signals"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-1349-2491","authenticated-orcid":false,"given":"Yuli","family":"Niu","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongchao","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-8456-9830","authenticated-orcid":false,"given":"Hengshan","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianxin","family":"Tan","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"China Suntien Green Energy Co., Ltd., Shijiazhuang 050051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7256-883X","authenticated-orcid":false,"given":"Tianyang","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"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"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jia, S., Wang, J., Zhang, X., and Han, B. 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