Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising

Taku Nonomura; Hisaichi Shibata; Ryoji Takaki

doi:10.1371/journal.pone.0209836

Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising

PLoS One. 2019 Feb 21;14(2):e0209836. doi: 10.1371/journal.pone.0209836. eCollection 2019.

Authors

Taku Nonomura^{1

2}, Hisaichi Shibata³, Ryoji Takaki³

Affiliations

¹ Department of Aerospace Engineering, Graduate School of Engineering, Tohoku University, Sendai, Miyagi, Japan.
² Presto, JST, Sendai, Miyagi, Japan.
³ Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Kanagawa, Japan.

Abstract

A new dynamic mode decomposition (DMD) method is introduced for simultaneous system identification and denoising in conjunction with the adoption of an extended Kalman filter algorithm. The present paper explains the extended-Kalman-filter-based DMD (EKFDMD) algorithm which is an online algorithm for dataset for a small number of degree of freedom (DoF). It also illustrates that EKFDMD requires significant numerical resources for many-degree-of-freedom (many-DoF) problems and that the combination with truncated proper orthogonal decomposition (trPOD) helps us to apply the EKFDMD algorithm to many-DoF problems, though it prevents the algorithm from being fully online. The numerical experiments of a noisy dataset with a small number of DoFs illustrate that EKFDMD can estimate eigenvalues better than or as well as the existing algorithms, whereas EKFDMD can also denoise the original dataset online. In particular, EKFDMD performs better than existing algorithms for the case in which system noise is present. The EKFDMD with trPOD, which unfortunately is not fully online, can be successfully applied to many-DoF problems, including a fluid-problem example, and the results reveal the superior performance of system identification and denoising.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms*
Hydrodynamics
Signal Processing, Computer-Assisted*
Signal-To-Noise Ratio*
Software*

Grants and funding

This work was supported by PREST, JST (JPMJPR1678). URL: https://www.jst.go.jp/kisoken/presto/en/index.html. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.