Application of the dynamic mode decomposition to experimental data

By Peter J. Schmid. 2011

349 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/061d652a32ceb6d7efd11b1f92c8427eaf91fa4b

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition (2014, methodology): “It has subsequently been used to gain dynamic insight on a wide range of problems arising in ﬂuid mechanics (e.g., Schmid et al., 2011; Schmid, 2011; Jardin and Bury, 2012) and other ﬁelds (e.g., Grosek and Kutz, 2014).”
Optimal mode decomposition for unsteady flows (2013, methodology): “It is shown that the resulting optimization problem reduces, in a special case, to the recently developed technique of DMD (Schmid 2010, 2011) and hence provides an extension to DMD.”
Model Reduction for Flow Analysis and Control (2017, methodology): “…of a NACA 0015 airfoil with Gurney flap (PIV) Schmid et al. (2011) Schlieren snapshots of a helium jet; PIV snapshots of an acoustically forced jet Schmid (2011) Passive tracer in flame simulation and axisymmetric water jet experiment Seena & Sung (2011) Turbulent cavity flow (DNS) Duke et al.…”
Dynamic Mode Decomposition with Control (2014, background): “DMD has already been applied to a significant number of applications in the fluid dynamics community [33], [35], [14], [2], [39], [37] and is expanding to a variety of other applications like background subtraction in video processing [15].”
Multi-scale proper orthogonal decomposition of complex fluid flows (2018, methodology): “The second DMD algorithm considered, herein denoted as sDMD, avoids the calculation of the Companion matrix and projects the problem onto a space of much lower dimension (Schmid 2011), in which hopefully only a few eigenvectors are relevant.”
De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets (2015, background): “…studies have also encountered DMD’s sensitivity to measurement errors (e.g., sensor noise), which has led to a host of approaches aimed at mitigating noise-related eﬀects via various forms of rank-reduction, ensemble averaging, cross-validation, and windowing [2, 18, 19, 20, 21, 22, 23, 24, 25].”
Higher Order Dynamic Mode Decomposition (2017, methodology): “DMD itself was developed by Schmid [48], and has become a useful tool for postprocessing massive spatiotemporal data in numerical and experimental fluid mechanics [49, 50, 51, 52, 32] and other fields [28, 40].”
Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses (2012, methodology): “In this case, we apply the SVD-based DMD algorithm of Schmid (2010) and use select Ritz values as the initial condition for the iterator.”
On dynamic mode decomposition: Theory and applications (2013, background): “For instance, DMD has been applied in the study of the wake behind a flexible membrane [8], the flow around high-speed trains [9], instabilities in annular liquid sheets [10], shockwave-turbulent boundary layer interactions [11], detonation waves [12], cavity flows [8,13], and various jets [3,8,14,1”
Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction (2012, methodology): “Dynamic mode decomposition Dynamic mode decomposition is a technique that allows for a modal analysis of a data sequence, without resorting to a numerical solver or an underlying model (Schmid 2010, 2011).”
Generalizing Koopman Theory to Allow for Inputs and Control (2016, background): “In a very short period of time since, DMD theory has been applied with great success to a broad set of domain sciences including complex fluid flows [45, 43, 44, 13, 2, 48, 47], foreground/background separation in video streams [14], epidemiology [37], and neuroscience [3].”