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The method not only improved the local optimal problem of GOA, but could also determine the bandwidth threshold and B-spline order of TVF-EMD adaptively. Firstly, a nonlinear decreasing strategy was introduced in this paper to adjust the decreasing coefficient of GOA dynamically. Then, energy entropy mutual information (EEMI) was introduced to comprehensively consider the energy distribution of the modes and the dependence between the modes and the original signal, and the EEMI was used as the objective function. In addition, TVF-EMD was optimized by IGOA and the optimal parameters matching the input signal were obtained. Finally, the feature frequency of the signal was extracted by analyzing the sensitive mode with larger kurtosis. The optimization experiments of 23 sets of benchmark functions showed that IGOA not only enhanced the balance between exploration and development, but also improved the global and local search ability and stability of the algorithm. The analysis of the simulation signal and bearing signal shows that the parameter-adaptive TVF-EMD method can separate the modes with specific physical meanings accurately. Compared with ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), TVF-EMD with fixed parameters and GOA-TVF-EMD, the decomposition performance of the proposed method is better. The proposed method not only improved the under-decomposition, over-decomposition and modal aliasing problems of TVF-EMD, but could also accurately separate the frequency components of the signal and extract the included feature information, so it has practical significance in mechanical fault diagnosis.<\/jats:p>","DOI":"10.3390\/s22197195","type":"journal-article","created":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T23:07:55Z","timestamp":1663888075000},"page":"7195","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Parameter-Adaptive TVF-EMD Feature Extraction Method Based on Improved GOA"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4218-105X","authenticated-orcid":false,"given":"Chengjiang","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China"},{"name":"The Laboratory of Pattern Recognition and Artificial Intelligence, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zenghui","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China"},{"name":"The Laboratory of Pattern Recognition and Artificial Intelligence, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haicheng","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China"},{"name":"The Laboratory of Pattern Recognition and Artificial Intelligence, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling","family":"Xing","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China"},{"name":"The Laboratory of Pattern Recognition and Artificial Intelligence, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunhua","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China"},{"name":"The Laboratory of Pattern Recognition and Artificial Intelligence, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5419-4777","authenticated-orcid":false,"given":"Xuyi","family":"Yuan","sequence":"additional","affiliation":[{"name":"Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ymssp.2018.03.004","article-title":"Adaptive iterative generalized demodulation for nonstationary complex signal analysis: Principle and application in rotating machinery fault diagnosis","volume":"110","author":"Feng","year":"2018","journal-title":"Mech. 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