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

By Scott T. M. Dawson, Maziar S. Hemati, Matthew O. Williams, Clarence W. Rowley. Experiments in Fluids, 2014

354 citations recorded by the source corpus.

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: (1) a direct correction of the identified bias using known noise properties, (2) combining the results of performing DMD forwards and backwards in time, and (3) 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 the recent literature.

Subfields: Control and Systems Engineering, Geophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cf5aa0ec5ac54f3235e83403087c6053f9d83658

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

In Geophysics

In Statistical and Nonlinear Physics

Citations in the corpus

Generalizing Koopman Theory to Allow for Inputs and Control (2016, neutral): “The theory also allows for critical enabling theoretical augmentations that can take advantage of compression and sparsity [22, 7, 16], multiresolution/multiscale phenomenon [27], denoising [9, 18], data fusion [52], extended and kernel DMD [51, 50], and control [36].”
Modal Analysis of Fluid Flows: Applications and Outlook (2019, positive): “DMD has been observed to exhibit sensitivities [39] and has been shown to yield biased results [40,41] when the snapshot data”
Model Reduction for Flow Analysis and Control (2017, background): “Although it has been observed empirically that DMD can be sensitive to noisy data (Duke et al. 2012b, Pan et al. 2015), recent work has explained this sensitivity and presented modifications to the algorithm to make its outputs more robust to noisy data (Hemati et al. 2015, Dawson et al. 2016).”
Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition (2020, methodology): “The TDMD procedure consists of a preprocessing step that removes the asymmetric treatment of measurement noise inherent in the formulation of DMD provided above (Hemati et al. 2017; Dawson et al. 2016).”
De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets (2015, background): “Under favorable noise conditions [11], the resulting bias due to noise will not alter the dynamical interpretation of particular modes.”