{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T03:38:36Z","timestamp":1774928316113,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T00:00:00Z","timestamp":1559433600000},"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":["5187051969"],"award-info":[{"award-number":["5187051969"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A data-driven adaptive iterative learning (IL) method is proposed for the active control of structural vibration. Considering the repeatability of structural dynamic responses in the vibration process, the time-varying proportional-type iterative learning (P-type IL) method was applied for the design of feedback controllers. The model-free adaptive (MFA) control, a data-driven method, was used to self-tune the time-varying learning gains of the P-type IL method for improving the control precision of the system and the learning speed of the controllers. By using multi-source information, the state of the controlled system was detected and identified. The square root values of feedback gains can be considered as characteristic parameters and the theory of imprecise probability was investigated as a tool for designing the stopping criteria. The motion equation was driven from dynamic finite element (FE) formulation of piezoelectric material, and then was linearized and transformed properly to design the MFA controller. The proposed method was numerically and experimentally tested for a piezoelectric cantilever plate. The results demonstrate that the proposed method performs excellent in vibration suppression and the controllers had fast learning speeds.<\/jats:p>","DOI":"10.3390\/sym11060746","type":"journal-article","created":{"date-parts":[[2019,6,3]],"date-time":"2019-06-03T02:08:40Z","timestamp":1559527720000},"page":"746","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5011-2674","authenticated-orcid":false,"given":"Liang","family":"Bai","sequence":"first","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Western Youyi Street 127, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yun-Wen","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Western Youyi Street 127, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ning","family":"Li","sequence":"additional","affiliation":[{"name":"College of Sciences, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Feng","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Western Youyi Street 127, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Western Youyi Street 127, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1049\/iet-cta.2010.0388","article-title":"Convergence characteristic of proportional-type iterative learning control in the sense of Lebesgue-p norm","volume":"6","author":"Ruan","year":"2012","journal-title":"IET Control Theory A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.mechatronics.2018.03.003","article-title":"Trajectory tracking using online learning LQR with adaptive learning control of a leg-exoskeleton for disorder gait rehabilitation","volume":"51","author":"Ajjanaromvat","year":"2018","journal-title":"Mechatronics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1875","DOI":"10.1007\/s12206-019-0340-z","article-title":"Research on flexible dynamics of a 6-DOF industrial robot and residual vibration control with a pre-adaptive input shaper","volume":"33","author":"Xu","year":"2019","journal-title":"J. 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