On the accuracy of dynamic mode decomposition in estimating instability of wave packet

Pan, Chong; Xue, Dong; Wang, Jinjun

doi:10.1007/s00348-015-2015-6

Cited by 20 publications

(11 citation statements)

References 36 publications

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“…The effects of noise on the accuracy of the DMD procedure was systematically investigated in the empirical study of Duke et al (2012), for the case of a synthetic waveform inspired by canonical periodic shear flow instabilities. More recently, Pan et al (2015) have extended this type of analysis to more complex data with multiple frequencies, as might be found in typical fluids systems. The present work builds upon these previous studies by analytically deriving an expression that explicitly shows how DMD should be affected by noise, for the case where the noise is assumed to be sensor noise that is uncorrelated with the dynamics of the system.…”

Section: Introductionmentioning

confidence: 99%

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition

Dawson

Hemati

Williams³

et al. 2016

Exp Fluids

282

241

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Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD's usefulness is limited by its ability to extract real and accurate dynamical features from noise-corrupted data. Here we show analytically that DMD is biased to sensor noise, and quantify how this bias depends on the size and noise level of the data. We present three modifications to DMD that can be used to remove this bias: (i) a direct correction of the identified bias using known noise properties, (ii) combining the results of performing DMD forwards and backwards in time, and (iii) a total least-squares-inspired algorithm. We discuss the relative merits of each algorithm, and demonstrate the performance of these modifications on a range of synthetic, numerical, and experimental datasets. We further compare our modified DMD algorithms with other variants proposed in recent literature.

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Section: Introductionmentioning

confidence: 99%

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition

Dawson

Hemati

Williams³

et al. 2016

Exp Fluids

282

241

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show abstract

“…For the datasets analyzed in this work, no appreciable difference between the two formulations is observed, and only the results with the classical DMD using the propagator in (7) are presented. For alternative formulations of the reduced propagators, the reader is referred to Pan et al (2015), Penland (1996), Schmid (2010), Tu et al (2014), while an interesting higherorder extension of the linear propagator is proposed in Clainche and Vega (2017a,b), Martinez et al (2017). Finally, writing the diagonalization of the reduced propagator asS = QΛQ −1 , the (complex) spatial structure from these decompositions can be computed as Φ D =Φ P Q.…”

Section: Frequency-based Formalism: the Dmd And The Opdmentioning

confidence: 99%

Multiscale proper orthogonal decomposition (mPOD) of TR-PIV data—a case study on stationary and transient cylinder wake flows

Mendez

Hess

Watz

et al. 2020

Meas. Sci. Technol.

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Data-driven decompositions of Particle Image Velocimetry (PIV) measurements are widely used for a variety of purposes, including the detection of coherent features (e.g., vortical structures), filtering operations (e.g., outlier removal or random noise mitigation), data reduction and compression. This work presents the application of a novel decomposition method, referred to as Multiscale Proper Orthogonal Decomposition (mPOD, Mendez et al 2019) to Time-Resolved PIV (TR-PIV) measurement. This method combines Multiresolution Analysis (MRA) and standard Proper Orthogonal Decomposition (POD) to achieve a compromise between decomposition convergence and spectral purity of the resulting modes. The selected test case is the flow past a cylinder in both stationary and transient conditions, producing a frequency-varying Karman vortex street. The results of the mPOD are compared to the standard POD, the Discrete Fourier Transform (DFT) and the Dynamic Mode Decomposition (DMD). The mPOD is evaluated in terms of decomposition convergence and time-frequency localization of its modes. The multiscale modal analysis allows for revealing beat phenomena in the stationary cylinder wake, due to the three-dimensional nature of the flow, and to correctly identify the transition from various stationary regimes in the transient test case.

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“…Tu [16] demonstrated the utility of this approach by presenting novel sampling strategies that increase computational efficiency and mitigated the effects of noise, respectively. Pan [17] used a linear combination of a sinusoidal unstable wave and its high-order harmonics as a prototype to take an error analysis of DMD algorithm. The result shows that the superimposition of finer structures with less energy dominance might damage the estimation accuracy of the primary structures' growth rate.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…where i denotes the amplitude of the ith mode, which represents the mode contribution to the initial snapshotv 1 . Substituting formula (17) and (18) into formula (16), the flow field at any time instant can be predicted as…”

mentioning

confidence: 99%

Study on Flow Characteristics in Volute of Centrifugal Pump Based on Dynamic Mode Decomposition

2019

Mathematical Problems in Engineering

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To investigate the unsteady flow characteristics and their influence mechanism in the volute of centrifugal pump, the Reynolds time-averaged N-S equation, RNG k-ε turbulence model, and structured grid technique are used to numerically analyze the transient flow-field characteristics inside the centrifugal pump volute. Based on the quantified parameters of flow field in the volute of centrifugal pump, the velocity mode contours and oscillation characteristics of the mid-span section of the volute of centrifugal pump are obtained by dynamic mode decomposition (DMD) for the nominal and low flow-rate condition. The research shows that the first-order average flow mode extracted by DMD is the dominant flow structure in the flow field of the volute. The second-order and third-order modes are the most important oscillation modes causing unsteady flow in the volute, and the characteristic frequency of the two modes is consistent with the blade passing frequency and the 2x blade passing frequency obtained by the fast Fourier transform (FFT). By reconstructing the internal flow field of the volute with the blade passing frequency for the nominal flow-rate condition, the periodic variation of the unsteady flow structure in the volute under this frequency is visually reproduced, which provides some ideas for the study of the unsteady structure in the internal flow field of centrifugal pumps.

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On the accuracy of dynamic mode decomposition in estimating instability of wave packet

Cited by 20 publications

References 36 publications

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition

Multiscale proper orthogonal decomposition (mPOD) of TR-PIV data—a case study on stationary and transient cylinder wake flows

Study on Flow Characteristics in Volute of Centrifugal Pump Based on Dynamic Mode Decomposition

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