{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T19:24:41Z","timestamp":1776108281046,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T00:00:00Z","timestamp":1555459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Deep learning is an effective feature extraction method widely applied in fault diagnosis fields since it can extract fault features potentially involved in multi-sensor data. But different sensors equipped in the system may sample data at different sampling rates, which will inevitably result in a problem that a very small number of samples with a complete structure can be used for deep learning since the input of a deep neural network (DNN) is required to be a structurally complete sample. On the other hand, a large number of samples are required to ensure the efficiency of deep learning based fault diagnosis methods. To solve the problem that a structurally complete sample size is too small, this paper proposes a fault diagnosis framework of missing data based on transfer learning which makes full use of a large number of structurally incomplete samples. By designing suitable transfer learning mechanisms, extra useful fault features can be extracted to improve the accuracy of fault diagnosis based simply on structural complete samples. Thus, online fault diagnosis, as well as an offline learning scheme based on deep learning of multi-rate sampling data, can be developed. The efficiency of the proposed method is demonstrated by utilizing data collected from the QPZZ- II rotating machinery vibration experimental platform system.<\/jats:p>","DOI":"10.3390\/s19081826","type":"journal-article","created":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T07:58:09Z","timestamp":1555487889000},"page":"1826","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":47,"title":["Transfer Learning Based Fault Diagnosis with Missing Data Due to Multi-Rate Sampling"],"prefix":"10.3390","volume":"19","author":[{"given":"Danmin","family":"Chen","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China"},{"name":"School of Software, Henan University, Kaifeng 475004, China"}]},{"given":"Shuai","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"}]},{"given":"Funa","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475004, China"},{"name":"Department of Electrical Automation, Shanghai Maritime University, Shanghai 201306, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-1-4615-5149-2_1","article-title":"Robust model-based fault diagnosis for dynamic systems","volume":"Volume 3","author":"Chen","year":"1999","journal-title":"The International Series on Asian Studies in Computer and Information Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3757","DOI":"10.1109\/TIE.2015.2417501","article-title":"A survey of fault diagnosis and fault-tolerant techniques-Part I: Fault diagnosis with model-based and signal-based approaches","volume":"62","author":"Gao","year":"2015","journal-title":"IEEE Trans. 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