Improving Separation Control with Noise-Robust Variants of Dynamic Mode Decomposition

Hemati, Maziar S.; Deem, Eric A.; Williams, Matthew O.; Rowley, Clarence W.; Cattafesta, Louis N.

doi:10.2514/6.2016-1103

Cited by 41 publications

(58 citation statements)

References 25 publications

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“…In addition, it stands out by having a small mode error. The DMD mode associated with shear layer frequency is plotted in Figure 9(c), and it agrees with the mode identified in previous work [12].…”

Section: Canonical Separated Flowsupporting

confidence: 89%

Evaluating the accuracy of the dynamic mode decomposition

Zhang

Dawson

Rowley

et al. 2020

Journal of Computational Dynamics

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Dynamic mode decomposition (DMD) gives a practical means of extracting dynamic information from data, in the form of spatial modes and their associated frequencies and growth/decay rates. DMD can be considered as a numerical approximation to the Koopman operator, an infinite-dimensional linear operator defined for (nonlinear) dynamical systems. This work proposes a new criterion to estimate the accuracy of DMD on a mode-by-mode basis, by estimating how closely each individual DMD eigenfunction approximates the corresponding Koopman eigenfunction. This approach does not require any prior knowledge of the system dynamics or the true Koopman spectral decomposition. The method may be applied to extensions of DMD (i.e., extended/kernel DMD), which are applicable to a wider range of problems. The accuracy criterion is first validated against the true error with a synthetic system for which the true Koopman spectral decomposition is known. We next demonstrate how this proposed accuracy criterion can be used to assess the performance of various choices of kernel when using the kernel method for extended DMD. Finally, we show that our proposed method successfully identifies modes of high accuracy when applying DMD to data from experiments in fluids, in particular particle image velocimetry of a cylinder wake and a canonical separated boundary layer. *

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Section: Canonical Separated Flowsupporting

confidence: 89%

Evaluating the accuracy of the dynamic mode decomposition

Zhang

Dawson

Rowley

et al. 2020

Journal of Computational Dynamics

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“…11 Various studies have recently been conducted in this field. With regard to DMD for noisy datasets, noise-corrected DMD (ncDMD), 12 for-ward/backward DMD (fbDMD), 12 and total least-squares DMD (tlsDMD), [12][13][14] have been proposed. A previous study showed that tlsDMD and fbDMD have the best performance for DMD mode estimation.…”

Section: Introductionmentioning

confidence: 99%

Dynamic mode decomposition using a Kalman filter for parameter estimation

2018

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A novel dynamic mode decomposition (DMD) method based on a Kalman filter is proposed. This paper explains the fast algorithm of the proposed Kalman filter DMD (KFDMD) in combination with truncated proper orthogonal decomposition for many-degree-of-freedom problems. Numerical experiments reveal that KFDMD can estimate eigenmodes more precisely compared with standard DMD or total leastsquares DMD (tlsDMD) methods for the severe noise condition if the nature of the observation noise is known, though tlsDMD works better than KFDMD in the low and medium noise level. Moreover, KFDMD can track the eigenmodes precisely even when the system matrix varies with time similar to online DMD, and this extension is naturally conducted owing to the characteristics of the Kalman filter. In summary, the KFDMD is a promising tool with strong antinoise characteristics for analyzing sequential datasets. arXiv:1804.00143v3 [physics.flu-dyn]

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“…Open-loop flow control strategies based on various actuator technologies [3]-such as plasma actuators [4][5][6], fluidic oscillators [7][8][9][10][11], and synthetic jets [12][13][14][15][16]-have been shown to effectively alter separated flows, and in some cases to even yield complete reattachment. In [17], oscillatory forcing was found to improve control authority for separation control.…”

Section: Introductionmentioning

confidence: 99%

Data-driven selection of actuators for optimal control of airfoil separation

Bhattacharjee

Klose

Jacobs

et al. 2020

Theor. Comput. Fluid Dyn.

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We present a systematic approach for determining the optimal actuator location for separation control from input-output response data, gathered from numerical simulations or physical experiments. The Eigensystem Realization Algorithm is used to extract state-space descriptions from the response data associated with a candidate set of actuator locations. These system realizations are then used to determine the actuator location among the set that can drive the system output to an arbitrary value with minimal control effort. The solution of the corresponding minimum energy optimal control problem is evaluated by computing the generalized output controllability Gramian.We use the method to analyze high-fidelity numerical simulation data of the

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Improving Separation Control with Noise-Robust Variants of Dynamic Mode Decomposition

Cited by 41 publications

References 25 publications

Evaluating the accuracy of the dynamic mode decomposition

Evaluating the accuracy of the dynamic mode decomposition

Dynamic mode decomposition using a Kalman filter for parameter estimation

Data-driven selection of actuators for optimal control of airfoil separation

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