{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T19:42:50Z","timestamp":1779306170530,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T00:00:00Z","timestamp":1680480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62073213"],"award-info":[{"award-number":["62073213"]}]},{"name":"National Natural Science Foundation of China","award":["52205111"],"award-info":[{"award-number":["52205111"]}]},{"name":"National Natural Science Foundation of China Youth Fund","award":["62073213"],"award-info":[{"award-number":["62073213"]}]},{"name":"National Natural Science Foundation of China Youth Fund","award":["52205111"],"award-info":[{"award-number":["52205111"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Federated learning is an effective means to combine model information from different clients to achieve joint optimization when the model of a single client is insufficient. In the case when there is an inter-client data imbalance, it is significant to design an imbalanced federation aggregation strategy to aggregate model information so that each client can benefit from the federation global model. However, the existing method has failed to achieve an efficient federation strategy in the case when there is an imbalance mode mismatch between clients. This paper aims to design a federated learning method guided by intra-client imbalance degree to ensure that each client can receive the maximum benefit from the federation model. The degree of intra-client imbalance, measured by gain of a class-by-class model update on the federation model based on a small balanced dataset, is used to guide the designing of federation strategy. An experimental validation for the benchmark dataset of rolling bearing shows that a 23.33% improvement of fault diagnosis accuracy can be achieved in the case when the degree of imbalance mode mismatch between clients is prominent.<\/jats:p>","DOI":"10.3390\/e25040606","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T02:32:27Z","timestamp":1680489147000},"page":"606","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Federated Learning Based Fault Diagnosis Driven by Intra-Client Imbalance Degree"],"prefix":"10.3390","volume":"25","author":[{"given":"Funa","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Logistic Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Logistic Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chaoge","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Logistic Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiong","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Logistic Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,3]]},"reference":[{"key":"ref_1","first-page":"801","article-title":"Fault diagnosis based on the quality effect of learning algorithm for manufacturing systems","volume":"233","author":"Djelloul","year":"2019","journal-title":"Proc. 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