Dynamic mode decomposition based on expectation–maximization algorithm for simultaneous system identification and denoising

• Published in: Mechanical systems and signal processing Vol. 223; p. 111864
• Main Authors: Iwasaki, Yuto, Sasaki, Yasuo, Nagata, Takayuki, Kaneko, Sayumi, Nonomura, Taku
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.01.2025
• Subjects: 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
• DOI: 10.1016/j.ymssp.2024.111864

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.