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

Taku Nonomura1,2, Hisaichi Shibata3, Ryoji Takaki3

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A novel extended Kalman filter-based dynamic mode decomposition (EKFDMD) method enables simultaneous system identification and denoising. This advanced technique offers superior performance, especially in the presence of system noise, for various degrees of freedom problems.

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Area of Science:

  • Engineering
  • Data Science
  • Signal Processing

Background:

  • Dynamic Mode Decomposition (DMD) is a powerful tool for analyzing complex dynamical systems.
  • Traditional DMD methods can struggle with noisy data and high-dimensional systems.
  • Online algorithms are desirable for real-time system analysis.

Purpose of the Study:

  • To introduce a new dynamic mode decomposition (DMD) method for simultaneous system identification and denoising.
  • To develop an online algorithm suitable for small degrees of freedom (DoF) datasets.
  • To extend the applicability of the method to many-DoF problems.

Main Methods:

  • Development of the extended Kalman filter-based DMD (EKFDMD) algorithm.
  • Integration of truncated Proper Orthogonal Decomposition (trPOD) with EKFDMD for many-DoF problems.
  • Numerical experiments on noisy datasets with varying DoFs.

Main Results:

  • EKFDMD provides accurate eigenvalue estimation and effective online denoising for small DoF systems.
  • The EKFDMD algorithm demonstrates superior performance compared to existing methods, particularly with system noise.
  • EKFDMD combined with trPOD successfully addresses many-DoF problems, including fluid dynamics, with excellent system identification and denoising.

Conclusions:

  • EKFDMD offers a robust solution for simultaneous system identification and denoising.
  • The combination of EKFDMD and trPOD extends its utility to complex, high-dimensional systems.
  • This approach significantly advances the analysis of noisy dynamical systems.