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
Hauptverfasser: Iwasaki, Yuto, Sasaki, Yasuo, Nagata, Takayuki, Kaneko, Sayumi, Nonomura, Taku
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 15.01.2025
Schlagworte:
Denoising
Dynamic mode decomposition
Expectation–maximization algorithm
Linear dynamical system
System identification
Linear dynamical system
System identification
Dynamic mode decomposition
Expectation–maximization algorithm
Denoising
ISSN:0888-3270
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Zusammenfassung: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.
ISSN:0888-3270
DOI:10.1016/j.ymssp.2024.111864