{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T04:07:15Z","timestamp":1774584435263,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T00:00:00Z","timestamp":1723766400000},"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":["52005032"],"award-info":[{"award-number":["52005032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72271025"],"award-info":[{"award-number":["72271025"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022C01010"],"award-info":[{"award-number":["2022C01010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2023A1515011532"],"award-info":[{"award-number":["2023A1515011532"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2024A1515010132"],"award-info":[{"award-number":["2024A1515010132"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Research and Development Program of Zhejiang Province","award":["52005032"],"award-info":[{"award-number":["52005032"]}]},{"name":"Key Research and Development Program of Zhejiang Province","award":["72271025"],"award-info":[{"award-number":["72271025"]}]},{"name":"Key Research and Development Program of Zhejiang Province","award":["2022C01010"],"award-info":[{"award-number":["2022C01010"]}]},{"name":"Key Research and Development Program of Zhejiang Province","award":["2023A1515011532"],"award-info":[{"award-number":["2023A1515011532"]}]},{"name":"Key Research and Development Program of Zhejiang Province","award":["2024A1515010132"],"award-info":[{"award-number":["2024A1515010132"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["52005032"],"award-info":[{"award-number":["52005032"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["72271025"],"award-info":[{"award-number":["72271025"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2022C01010"],"award-info":[{"award-number":["2022C01010"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2023A1515011532"],"award-info":[{"award-number":["2023A1515011532"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2024A1515010132"],"award-info":[{"award-number":["2024A1515010132"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Planetary gear transmission mechanisms (PGTMs) are widely used in mechanical transmission systems due to their compact structure and high transmission efficiency. To implement the reliability design and optimization of a PGTM, a novel multi-objective dynamic reliability optimization approach is proposed. First, a multi-objective reliability optimization model is established. Furthermore, considering the strength degradation of gears during service, a dynamic reliability analysis is conducted based on the theory of nonlinear fatigue damage accumulation. In addition, to improve computing efficiency, a random forest surrogate model based on the particle swarm optimization algorithm is proposed. Finally, an adaptive multi-objective evolutionary algorithm based on decomposition (AMOEA\/D) is designed to optimize the mechanism, along with an adaptive neighborhood updating strategy and a hybrid crossover operator. The feasibility and superiority of the proposed approach are verified through an NGW planetary gear reducer. The results show that the proposed surrogate model can reduce the calculation cost and has high accuracy. The AMOEA\/D algorithm can improve transmission efficiency, reduce gear volume and ensure reliability at the same time. It can provide guidance for actual gear production.<\/jats:p>","DOI":"10.3390\/axioms13080560","type":"journal-article","created":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T04:29:57Z","timestamp":1723782597000},"page":"560","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Novel Multi-Objective Dynamic Reliability Optimization Approach for a Planetary Gear Transmission Mechanism"],"prefix":"10.3390","volume":"13","author":[{"given":"Shuiguang","family":"Tong","sequence":"first","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"},{"name":"School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoyan","family":"Yan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"},{"name":"School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3895-0717","authenticated-orcid":false,"given":"Lechang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianmiao","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"},{"name":"School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"105520","DOI":"10.1016\/j.mechmachtheory.2023.105520","article-title":"Influence of ring gear flexibility on the fatigue reliability of planetary gear systems in heavy helicopters","volume":"191","author":"Li","year":"2024","journal-title":"Mech. 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