Identifying Dynamic Modes of Separated Flow Subject to ZNMF-Based Control from Surface Pressure Measurements

Deem, Eric A.; Cattafesta, Louis N.; Zhang, Hao; Rowley, Clarence W.; Hemati, Maziar S.; Cadieux, Francois; Mittal, Rajat

doi:10.2514/6.2017-3309

Cited by 8 publications

(16 citation statements)

References 35 publications

(54 reference statements)

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“…Starting from the 13th eigenvalueμ 13 ≈ µ 6,0 = γ 6 δ 0 = (0.9) 6 (0.8) 0 = 0.531441, the error dramatically increases, which implies that the remaining eigenfunctions cannot be accurately identified using EDMD with this choice of observables. This is expected, as monomials up to degree 5 can not represent the eigenfunction ϕ 6,0 (x) = x 6 1 . This comparison gives us confidence in the reliability of the accuracy criterion.…”

Section: Validating the Accuracy Criterionmentioning

confidence: 97%

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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: Validating the Accuracy Criterionmentioning

confidence: 97%

“…The average separation bubble length is L sep = 0.2c. More information regarding the separation system and the flat plate model can be found in [6]. PIV velocity data is sampled at f s = 1600 Hz, with a resolution of 319 × 62 pixels.…”

Section: Canonical Separated Flowmentioning

confidence: 99%

Evaluating the accuracy of the dynamic mode decomposition

Zhang

Dawson

Rowley

et al. 2020

Journal of Computational Dynamics

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“…The microphones are placed at the centerline of the plate, between x/c = 0.70 and 0.94, with a spacing of 0.02. More details regarding this microphone array can be found in [28]. These 13 microphone signals provide the data we use for online DMD.…”

Section: Pressure Fluctuations In a Separation Bubblementioning

confidence: 99%

“…Prior to applying online DMD, the microphone signals are conditioned to remove external contaminating sources. This process is described in [28]. We collect pressure data for a total time of T = 10 sec.…”

Section: Pressure Fluctuations In a Separation Bubblementioning

confidence: 99%

Online Dynamic Mode Decomposition for Time-Varying Systems

Zhang

Rowley

Deem³

et al. 2019

SIAM J. Appl. Dyn. Syst.

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134

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Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time evolves. This work provides an efficient method for computing DMD in real time, updating the approximation of a system's dynamics as new data becomes available. The algorithm does not require storage of past data, and computes the exact DMD matrix using rank-1 updates. A weighting factor that places less weight on older data can be incorporated in a straightforward manner, making the method particularly well suited to time-varying systems. A variant of the method may also be applied to online computation of "windowed DMD", in which only the most recent data are used. The efficiency of the method is compared against several existing DMD algorithms: for problems in which the state dimension is less than about 200, the proposed algorithm is the most efficient for realtime computation, and it can be orders of magnitude more efficient than the standard DMD algorithm. The method is demonstrated on several examples, including a time-varying linear system and a more complex example using data from a wind tunnel experiment. In particular, we show that the method is effective at capturing the dynamics of surface pressure measurements in the flow over a flat plate with an unsteady separation bubble.

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“…A large portion of the turbulent flow controllers are derived from a reduced-order model, using previous knowledge of the physics of the flow. The physical analysis of the flow can yield simple models leading to efficient control laws [48,16]. The second option is system identification using experimentally obtained black-box models (seeks to build an input-output model of the flow from empirical observations).…”

Section: Introductionmentioning

confidence: 99%

Sliding mode control applied to a square-back Ahmed body

Chovet

Feingesicht

Plumjeau

et al. 2020

European Journal of Mechanics - B/Fluids

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We consider the first closed-loop separation control experiment on an Ahmed body using a robust, modelbased strategy called "sliding mode control" (SMC). The goal is to reduce and further maintain the aerodynamic drag of the square-back Ahmed body flow at Re h = 9 × 10 4 (based on the body height). This study also investigates the practical feasibility of this approach which shows a great promise for industrial applications. The flow is manipulated by a slotted jet placed on the top trailing edge, combined with a predefined angle direction, and sensed by a drag balance. Base pressure and lift measurements are also obtained in real-time. The interaction between the air jet actuator and the mean near-wake flow are depicted by means of Particle Image Velocimetry. In order to compare this closed-loop strategy we first present two open-loop ones. Continuous blowing is initially used to directly influence the recirculation area and hence achieve a reduction in the drag. Approximately a drag reduction of 8% is accomplished making this approach the "optimal case" control strategy. However, because steady blowing mechanisms lead to the highest energy consumption scheme, this strategy will only serve as the first open-loop control reference. The second open-loop strategy involves three periodic forcing frequencies, St A = 0.0765, 0.135 & 0.405. The influence of these frequencies on the near-wake, and its further drag modification, will be further examined. The proposed sliding mode control (closed-loop strategy) is applied to the same Ahmed body configuration and compared to the open-loop cases. It will be designed on the basis of a simplified input-output model which was recently defined for another flow control application. Last, a second experiment is conducted so to show the disturbance rejection of the controller, corroborating the robustness and efficiency of this control approach. Its limitations and difficulties on an experimental setup are also discussed. SMC is able to reduce and maintain the drag to a desire set-point regardless external flow perturbations. Our control strategy was recently used in another context (flow reattachement on a wing) with the same robustness. These successes make guess it is applicable to multiple experimental and industrial contexts.

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Identifying Dynamic Modes of Separated Flow Subject to ZNMF-Based Control from Surface Pressure Measurements

Cited by 8 publications

References 35 publications

Evaluating the accuracy of the dynamic mode decomposition

Evaluating the accuracy of the dynamic mode decomposition

Online Dynamic Mode Decomposition for Time-Varying Systems

Sliding mode control applied to a square-back Ahmed body

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