scholarly journals Time-resolved denoising using model order reduction, dynamic mode decomposition, and kalman filter and smoother

2020 ◽  
Vol 7 (2) ◽  
pp. 469-487
Author(s):  
Mojtaba F. Fathi ◽  
◽  
Ahmadreza Baghaie ◽  
Ali Bakhshinejad ◽  
Raphael H. Sacho ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Model Order ◽  
Time Resolved ◽  
Mode Decomposition

Model Order Reduction for a Piecewise Linear System Based on Dynamic Mode Decomposition

2021 ◽  
Author(s):  
Akira Saito
Keyword(s):  
Model Order Reduction ◽  
Piecewise Linear ◽  
Order Reduction ◽  
Galerkin Projection ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Linear Boundary ◽  
Model Order ◽  
Linear Boundary Condition ◽  
Mode Decomposition

Abstract This paper presents a data-driven model order reduction strategy for nonlinear systems based on dynamic mode decomposition (DMD). First, the theory of DMD is briefly reviewed and its extension to model order reduction of nonlinear systems based on Galerkin projection is introduced. The proposed method utilizes impulse response of the nonlinear system to obtain snapshots of the state variables, and extracts dynamic modes that are then used for the projection basis vectors. The equations of motion of the system can then be projected onto the subspace spanned by the basis vectors, which produces the projected governing equations with much smaller number of degrees of freedom (DOFs). The method is applied to the construction of the reduced order model (ROM) of a finite element model (FEM) of a cantilevered beam subjected to a piecewise-linear boundary condition. First, impulse response analysis of the beam is conducted to obtain the snapshot matrix of the nodal displacements. The DMD is then applied to extract the DMD modes and eigenvalues. The extracted DMD mode shapes can be used to form a reduction basis for the Galerkin projection of the equation of motion. The obtained ROM has been used to conduct the forced response calculation of the beam subjected to the piecewise linear boundary condition. The results obtained by the ROM agree well with that obtained by the full-order FEM model.

scholarly journals Dynamic mode decomposition using a Kalman filter for parameter estimation

AIP Advances ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 105106 ◽  
Author(s):  
Taku Nonomura ◽  
Hisaichi Shibata ◽  
Ryoji Takaki
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mode Decomposition

scholarly journals Extracting Reproducible Time-Resolved Resting State Networks Using Dynamic Mode Decomposition

2019 ◽  
Vol 13 ◽  
Author(s):  
James M. Kunert-Graf ◽  
Kristian M. Eschenburg ◽  
David J. Galas ◽  
J. Nathan Kutz ◽  
Swati D. Rane ◽  
...  
Keyword(s):  
Resting State ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Resting State Networks ◽  
Time Resolved ◽  
Mode Decomposition

scholarly journals Extracting Reproducible Time-Resolved Resting State Networks using Dynamic Mode Decomposition

2018 ◽  
Author(s):  
James M. Kunert-Graf ◽  
Kristian M. Eschenburg ◽  
David J. Galas ◽  
J. Nathan Kutz ◽  
Swati D. Rane ◽  
...  
Keyword(s):  
Resting State ◽  
Dynamic Properties ◽  
Brain Regions ◽  
Dynamic Mode Decomposition ◽  
Single Subject ◽  
Dynamic Mode ◽  
Resting State Networks ◽  
Time Resolved ◽  
Mode Decomposition ◽  
Human Connectome Project

AbstractResting state networks (RSNs) extracted from functional magnetic resonance imaging (fMRI) scans are believed to reflect the intrinsic organization and network structure of brain regions. Most traditional methods for computing RSNs typically assume these functional networks are static throughout the duration of a scan lasting 5–15 minutes. However, they are known to vary on timescales ranging from seconds to years; in addition, the dynamic properties of RSNs are affected in a wide variety of neurological disorders. Recently, there has been a proliferation of methods for characterizing RSN dynamics, yet it remains a challenge to extract reproducible time-resolved networks. In this paper, we develop a novel method based on dynamic mode decomposition (DMD) to extract networks from short windows of noisy, high-dimensional fMRI data, allowing RSNs from single scans to be resolved robustly at a temporal resolution of seconds. We demonstrate this method on data from 120 individuals from the Human Connectome Project and show that unsupervised clustering of DMD modes discovers RSNs at both the group (gDMD) and the single subject (sDMD) levels. The gDMD modes closely resemble canonical RSNs. Compared to established methods, sDMD modes capture individualized RSN structure that both better resembles the population RSN and better captures subject-level variation. We further leverage this time-resolved sDMD analysis to infer occupancy and transitions among RSNs with high reproducibility. This automated DMD-based method is a powerful tool to characterize spatial and temporal structures of RSNs in individual subjects.

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