{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T17:45:30Z","timestamp":1774719930395,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,20]],"date-time":"2024-11-20T00:00:00Z","timestamp":1732060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education, Science and Technological Development, Republic of Serbia","award":["451-03-65\/2024-03\/200123"],"award-info":[{"award-number":["451-03-65\/2024-03\/200123"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>As reliance on wind energy intensifies globally, optimizing the efficiency and reliability of wind turbines is becoming vital. This paper explores sophisticated maintenance strategies, crucial for enhancing the operational sustainability of wind turbines. It introduces an innovative approach to maintenance scheduling that utilizes a mathematical model incorporating an alternating renewal process for accurately determining repair rate thresholds. These thresholds are important for identifying optimal maintenance timings, thereby averting failures and minimizing downtime. Central to this study are the obtained generalized analytical expressions that can be used to predict the total repair time for an observed entity. Four key lemmas are developed to establish formal proofs for the probability density function (PDF) and cumulative distribution function (CDF) of repair rates, both above and below critical repair rate thresholds. The core innovation of this study lies in the methodological application of PDFs and CDFs to set repair time thresholds that refine maintenance schedules. The model\u2019s effectiveness is illustrated using simulated data based on typical wind turbine components such as gearboxes, generators, and converters, validating its potential for improving system availability and operational readiness. By establishing measurable repair rate thresholds, the model effectively prioritizes maintenance tasks, extending the life of crucial turbine components and ensuring consistent energy output. Beyond enhancing theoretical understanding, this research provides practical insights that could inform broader maintenance strategies across various renewable energy systems, marking a significant advancement in the field of maintenance engineering<\/jats:p>","DOI":"10.3390\/axioms13110809","type":"journal-article","created":{"date-parts":[[2024,11,20]],"date-time":"2024-11-20T10:37:35Z","timestamp":1732099055000},"page":"809","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Mathematical Optimization of Wind Turbine Maintenance Using Repair Rate Thresholds"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6955-9887","authenticated-orcid":false,"given":"Nata\u0161a","family":"Kontrec","sequence":"first","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Pri\u0161tina in Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5868-1764","authenticated-orcid":false,"given":"Stefan","family":"Pani\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Pri\u0161tina in Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5361-7133","authenticated-orcid":false,"given":"Jelena","family":"Vujakovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Pri\u0161tina in Kosovska Mitrovica, Lole Ribara 29, 38220 Kosovska Mitrovica, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0476-1566","authenticated-orcid":false,"given":"Dejan","family":"Sto\u0161ovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Pri\u0161tina in Kosovska Mitrovica, Knjaza Milo\u0161a 7, 38220 Kosovska Mitrovica, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergei","family":"Khotnenok","sequence":"additional","affiliation":[{"name":"Laboratory of Autonomous Electronic Systems, Tomsk State University of Control Systems and Radioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,20]]},"reference":[{"key":"ref_1","unstructured":"Global Wind Energy Council (2024, October 10). Global Wind Report 2023. Available online: https:\/\/gwec.net\/globalwindreport2023\/."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Peng, H., Li, S., Shangguan, L., Fan, Y., and Zhang, H. (2023). Analysis of Wind Turbine Equipment Failure and Intelligent Operation and Maintenance Research. Sustainability, 15.","DOI":"10.3390\/su15108333"},{"key":"ref_3","first-page":"12","article-title":"Cost Composition and Price Mechanism of Offshore Wind Power","volume":"1","author":"Chen","year":"2022","journal-title":"Wind Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"110886","DOI":"10.1016\/j.rser.2021.110886","article-title":"Offshore Wind Turbine Operations and Maintenance: A State-of-the-Art Review","volume":"144","author":"Verma","year":"2021","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Palasai, W., Plengsa-Ard, C., and Kaewbumrung, M. (2024). Enhancing Wind Turbine Blade Preventive Maintenance Procedure through Computational Fluid Dynamics-Based Prediction of Wall Shear Stress. Sustainability, 16.","DOI":"10.3390\/su16072873"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Merizalde, Y., Hern\u00e1ndez-Callejo, L., Duque-Perez, O., and Alonso-G\u00f3mez, V. (2019). Maintenance Models Applied to Wind Turbines. A Comprehensive Overview. Energies, 12.","DOI":"10.3390\/en12020225"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chauhan, U., Pahuja, G.L., Singh, V., and Rani, A. (2015, January 17\u201320). Reliability analysis of wind turbine system using importance measures. Proceedings of the Annual IEEE India Conference (INDICON), New Delhi, India.","DOI":"10.1109\/INDICON.2015.7443292"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.engfailanal.2017.08.015","article-title":"Failure analysis on abnormal wear of roller bearings in gearbox for wind turbine","volume":"82","author":"Gong","year":"2017","journal-title":"Eng. Fail. Anal."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"M\u00e1rquez, F., Marug\u00e1n, A.P., Pinar P\u00e9rez, J.M., Hillmansen, S., and Papaelias, M. (2017). Optimal dynamic analysis of electrical\/electronic components in wind turbines. Energies, 10.","DOI":"10.3390\/en10081111"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Maatallah, H., Fuente, M.J., and Ouni, K. (2020, January 10\u201312). Condition monitoring of wind turbine bearings progressive degradation using principal component analysis. Proceedings of the Fifteenth International Conference on Ecological Vehicles and Renewable Energies (EVER), Monte-Carlo, Monaco.","DOI":"10.1109\/EVER48776.2020.9242979"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1109\/TSTE.2010.2049452","article-title":"An approach for condition-based maintenance optimization applied to wind turbine blades","volume":"1","author":"Besnard","year":"2010","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_12","first-page":"542","article-title":"Condition-based maintenance for the offshore wind turbine based on long short-term memory network","volume":"236","author":"Sun","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part O J. Risk Reliab."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"022051","DOI":"10.1088\/1757-899X\/1043\/2\/022051","article-title":"Research on opportunity maintenance strategy of wind turbines based on incomplete maintenance","volume":"1043","author":"Liu","year":"2021","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_14","first-page":"1171","article-title":"A stochastic model for achieving required level of availability based on the repair rate analysis","volume":"26","author":"Kontrec","year":"2019","journal-title":"Tehni\u010dki Vjesnik"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kontrec, N., Pani\u0107, S., Pani\u0107, B., and Markovi\u0107, A. (2024). Mathematical approach for system repair rate analysis used in maintenance decision making. Axioms, 10.","DOI":"10.3390\/axioms10020096"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kontrec, N., Vujakovi\u0107, J., To\u0161i\u0107, M., Pani\u0107, S., and Pani\u0107, B. (2021). Mathematical Modeling of Integral Characteristics of Repair Process under Maintenance Contracts. Symmetry, 13.","DOI":"10.22541\/au.161748353.34800868\/v1"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.renene.2012.02.030","article-title":"Opportunistic maintenance for wind farms considering multi-level imperfect maintenance thresholds","volume":"45","author":"Ding","year":"2012","journal-title":"Renew. Energy"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kang, J., Wang, Z., and Guedes Soares, C.G. (2020). Condition-based maintenance for offshore wind turbines based on support vector machine. 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