Dynamic mode decomposition based on expectation–maximization algorithm for simultaneous system identification and denoising
The present study proposes a novel dynamic mode decomposition (DMD) that can simultaneously estimate the reduced-order model, the original signal, and the system/observation noise model only from the noisy data. An expectation–maximization (EM)-algorithm DMD (EMDMD) combines DMD and the parameter ad...
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| Veröffentlicht in: | Mechanical systems and signal processing Jg. 223; S. 111864 |
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| Sprache: | Englisch |
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15.01.2025
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| Abstract | The present study proposes a novel dynamic mode decomposition (DMD) that can simultaneously estimate the reduced-order model, the original signal, and the system/observation noise model only from the noisy data. An expectation–maximization (EM)-algorithm DMD (EMDMD) combines DMD and the parameter adjustment of the linear dynamical system (LDS) based on the EM algorithm. The initial parameters based on the linearity of the reduced-order data are set by using DMD. Subsequently, the log-likelihood of the complete data is maximized by adjusting the LDS parameters while separating the noise. The proposed algorithm is applied to the benchmark data of the short-fat and tall-skinny data matrices with different noise and the time-series velocity fields of the flow around a circular cylinder and the separated flow around an airfoil. The performance of EMDMD in terms of system identification and noise separation from the noisy data is evaluated, and the EMDMD shows the highest system identification and noise separation performance in all data. |
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| AbstractList | The present study proposes a novel dynamic mode decomposition (DMD) that can simultaneously estimate the reduced-order model, the original signal, and the system/observation noise model only from the noisy data. An expectation–maximization (EM)-algorithm DMD (EMDMD) combines DMD and the parameter adjustment of the linear dynamical system (LDS) based on the EM algorithm. The initial parameters based on the linearity of the reduced-order data are set by using DMD. Subsequently, the log-likelihood of the complete data is maximized by adjusting the LDS parameters while separating the noise. The proposed algorithm is applied to the benchmark data of the short-fat and tall-skinny data matrices with different noise and the time-series velocity fields of the flow around a circular cylinder and the separated flow around an airfoil. The performance of EMDMD in terms of system identification and noise separation from the noisy data is evaluated, and the EMDMD shows the highest system identification and noise separation performance in all data. |
| ArticleNumber | 111864 |
| Author | Iwasaki, Yuto Kaneko, Sayumi Nonomura, Taku Nagata, Takayuki Sasaki, Yasuo |
| Author_xml | – sequence: 1 givenname: Yuto orcidid: 0000-0002-2142-5791 surname: Iwasaki fullname: Iwasaki, Yuto email: yuto.iwasaki.t5@dc.tohoku.ac.jp – sequence: 2 givenname: Yasuo orcidid: 0000-0003-0450-2764 surname: Sasaki fullname: Sasaki, Yasuo – sequence: 3 givenname: Takayuki orcidid: 0000-0003-3644-4888 surname: Nagata fullname: Nagata, Takayuki – sequence: 4 givenname: Sayumi orcidid: 0009-0002-4014-7034 surname: Kaneko fullname: Kaneko, Sayumi – sequence: 5 givenname: Taku orcidid: 0000-0001-7739-7104 surname: Nonomura fullname: Nonomura, Taku |
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| Cites_doi | 10.1007/s00348-010-0911-3 10.1017/S0022112010001217 10.1063/1.4863670 10.3934/jcd.2014.1.391 10.1137/M1124176 10.1088/1361-6463/aa6a80 10.1063/1.5092166 10.1063/1.4996024 10.1007/s00332-012-9130-9 10.1007/s12650-022-00836-9 10.1115/1.3662552 10.1007/BF02288367 10.1103/PhysRevE.96.033310 10.1007/s00162-017-0432-2 10.1371/journal.pone.0209836 10.2514/3.3166 10.1063/1.5031816 10.2514/1.J059239 10.1007/s00348-019-2755-9 10.1146/annurev-fluid-030121-015835 10.1109/ACCESS.2022.3193157 10.1007/s00348-016-2127-7 |
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| Keywords | Linear dynamical system System identification Dynamic mode decomposition Expectation–maximization algorithm Denoising |
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| SubjectTerms | Denoising Dynamic mode decomposition Expectation–maximization algorithm Linear dynamical system System identification |
| Title | Dynamic mode decomposition based on expectation–maximization algorithm for simultaneous system identification and denoising |
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