{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T22:50:41Z","timestamp":1778107841501,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,9,23]],"date-time":"2019-09-23T00:00:00Z","timestamp":1569196800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003471","name":"Harbin Engineering University","doi-asserted-by":"publisher","award":["51879056"],"award-info":[{"award-number":["51879056"]}],"id":[{"id":"10.13039\/501100003471","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The normal operation of high-pressure common rail injector is one of the important prerequisites for the healthy and reliable operation of diesel engines. Therefore, this paper studies the high-precision fault diagnosis method for injectors. Firstly, this paper chooses VMD to adaptively decompose the common rail fuel pressure wave. The biggest difficulty in VMD decomposition is the need to manually set the internal combination parameters K and \u03b1. In order to overcome this shortcoming, this paper proposes an improved fruit fly search. The variational mode decomposition method of the algorithm, with the energy growth factor e as the objective function, can adaptively decompose the multi-component signal into superimposed sub-signals. In addition, based on the analytic hierarchy process and dispersion entropy, hierarchical dispersion entropy is proposed to obtain a comprehensive and accurate complexity estimation of time series. Then, a fault diagnosis scheme for high-pressure common rail injector based on IFOA-VMD and HDE is proposed. Finally, using the engineering test data, the method is compared with other methods. The proposed method appears, based on the numerical examples, to be better from both a computational and classification accuracy point of view.<\/jats:p>","DOI":"10.3390\/e21100923","type":"journal-article","created":{"date-parts":[[2019,9,23]],"date-time":"2019-09-23T11:02:00Z","timestamp":1569236520000},"page":"923","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Fault Diagnosis Method for High-Pressure Common Rail Injector Based on IFOA-VMD and Hierarchical Dispersion Entropy"],"prefix":"10.3390","volume":"21","author":[{"given":"Enzhe","family":"Song","sequence":"first","affiliation":[{"name":"Institute of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun","family":"Ke","sequence":"additional","affiliation":[{"name":"Institute of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chong","family":"Yao","sequence":"additional","affiliation":[{"name":"Institute of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quan","family":"Dong","sequence":"additional","affiliation":[{"name":"Institute of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Yang","sequence":"additional","affiliation":[{"name":"Institute of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.ymssp.2017.03.026","article-title":"Discriminative non-negative matrix factorization (DNMF) and its application to the fault diagnosis of diesel engine","volume":"95","author":"Yang","year":"2017","journal-title":"Mech. 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