{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:03:24Z","timestamp":1760058204675,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T00:00:00Z","timestamp":1742169600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Start-up Fund for New Talented Researchers of the Nanjing Vocational University of Industry Technology","award":["YK22-02-09"],"award-info":[{"award-number":["YK22-02-09"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Fault diagnosis is crucial for ensuring the reliability and safety of wind energy conversion systems (WECSs). However, existing methods are often specific to components or specific types of wind turbines and face challenges, such as difficulty in threshold setting and low accuracy in diagnosing faults at early stages. To address these challenges, this paper proposes a novel fault diagnosis method based on self-organizing neural networks (SONNs) and probability density functions (PDFs). First, an improved set-valued observer (ISVO) is designed to accurately estimate the states of WECSs, considering the time delay and unknown nonlinearity of overall model. Then, the PDF is derived by fitting the estimation error data to characterize three common multiplicative faults of the pitch system actuators. Two types of SONNs are developed to cluster the parameter sets of the PDF. Finally, the PDFs of the estimation error are reconstructed based on the clustering results, thereby designing fault diagnosis strategies that enable a rapid and highly accurate diagnosis of early-stage faults. Simulation results demonstrate that the proposed strategies achieved an early fault diagnosis accuracy rate of over 90%, with the fastest diagnosis time being approximately 0.11 s. Under the same fault conditions, the diagnosis time is 1 s faster than that of a k-means-based fault diagnosis strategy. This study provides a threshold-free, high-accuracy, and rapid fault diagnosis strategy for early fault diagnosis in WECS. By combining neural networks, the proposed method addresses the issue of threshold dependency in fault diagnosis, with potential applications in improving the reliability and safety of wind power generation.<\/jats:p>","DOI":"10.3390\/sym17030448","type":"journal-article","created":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T11:04:22Z","timestamp":1742209462000},"page":"448","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Improved Set-Valued Observer and Probability Density Function-Based Self-Organizing Neural Networks for Early Fault Diagnosis in Wind Energy Conversion Systems"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7613-5775","authenticated-orcid":false,"given":"Ruinan","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Nanjing Vocational University of Industry Technology, Nanjing 210023, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1177\/0309524X17709730","article-title":"Improved power curve monitoring of wind turbines","volume":"41","author":"Morshedizadeh","year":"2017","journal-title":"Wind Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Gao, Z., and Liu, X. 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