{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T02:28:56Z","timestamp":1772072936781,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T00:00:00Z","timestamp":1719446400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Jilin Province, China","award":["20240101104JC"],"award-info":[{"award-number":["20240101104JC"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Partial discharge (PD) fault diagnosis is of great importance for ensuring the safe and stable operation of power transformers. To address the issues of low accuracy in traditional PD fault diagnostic methods, this paper proposes a novel method for the power transformer PD fault diagnosis. It incorporates the approximate entropy (ApEn) of symplectic geometry mode decomposition (SGMD) into the optimized bidirectional long short-term memory (BILSTM) neural network. This method extracts dominant PD features employing SGMD and ApEn. Meanwhile, it improves the diagnostic accuracy with the optimized BILSTM by introducing the golden jackal optimization (GJO). Simulation studies evaluate the performance of FFT, EMD, VMD, and SGMD. The results show that SGMD\u2013ApEn outperforms other methods in extracting dominant PD features. Experimental results verify the effectiveness and superiority of the proposed method by comparing different traditional methods. The proposed method improves PD fault recognition accuracy and provides a diagnostic rate of 98.6%, with lower noise sensitivity.<\/jats:p>","DOI":"10.3390\/e26070551","type":"journal-article","created":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T11:19:02Z","timestamp":1719487142000},"page":"551","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Partial Discharge Fault Diagnosis in Power Transformers Based on SGMD Approximate Entropy and Optimized BILSTM"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1480-1314","authenticated-orcid":false,"given":"Haikun","family":"Shang","sequence":"first","affiliation":[{"name":"Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education, Northeast Electric Power University, Jilin 132012, China"}]},{"given":"Zixuan","family":"Zhao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education, Northeast Electric Power University, Jilin 132012, China"}]},{"given":"Jiawen","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education, Northeast Electric Power University, Jilin 132012, China"}]},{"given":"Zhiming","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education, Northeast Electric Power University, Jilin 132012, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jin, L., Kim, D., Abu-Siada, A., and Kumar, S. 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