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  • ÀúÀÚTaku Nonomura, Hisaichi Shibata, Ryoji Takaki Àú
  • ÃâÆÇ»ç¾ÆÁø
  • ÃâÆÇÀÏ2020-07-12
  • µî·ÏÀÏ2020-12-21
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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 manydegreeof-
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.

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Á¦ 2Æí : ¿¬±¸³í¹®
Extended-Kalman-filter-based dynamic mode decomposition for
simultaneous system identification and denoising

1. Introduction 51
2. Previous methods compared in the present study 53
3. Extended Kalman filter DMD 57
4. Numerical Experiments and discussion 61
5. Complexity and computational cost 87
7. References 95

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