De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets
| Autor: | Louis N. Cattafesta, Eric A. Deem, Maziar S. Hemati, Clarence W. Rowley |
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| Rok vydání: | 2017 |
| Předmět: |
Fluid Flow and Transfer Processes
Computer science General Engineering Computational Mechanics Probability and statistics Biasing Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Particle image velocimetry 0103 physical sciences Dynamic mode decomposition Snapshot (computer storage) Spectral analysis Total least squares 010306 general physics Algorithm Subspace topology |
| Zdroj: | Theoretical and Computational Fluid Dynamics. 31:349-368 |
| ISSN: | 1432-2250 0935-4964 |
| Popis: | The dynamic mode decomposition (DMD)—a popular method for performing data-driven Koopman spectral analysis—has gained increased popularity for extracting dynamically meaningful spatiotemporal descriptions of fluid flows from snapshot measurements. Often times, DMD descriptions can be used for predictive purposes as well, which enables informed decision-making based on DMD model forecasts. Despite its widespread use and utility, DMD can fail to yield accurate dynamical descriptions when the measured snapshot data are imprecise due to, e.g., sensor noise. Here, we express DMD as a two-stage algorithm in order to isolate a source of systematic error. We show that DMD’s first stage, a subspace projection step, systematically introduces bias errors by processing snapshots asymmetrically. To remove this systematic error, we propose utilizing an augmented snapshot matrix in a subspace projection step, as in problems of total least-squares, in order to account for the error present in all snapshots. The resulting unbiased and noise-aware total DMD (TDMD) formulation reduces to standard DMD in the absence of snapshot errors, while the two-stage perspective generalizes the de-biasing framework to other related methods as well. TDMD’s performance is demonstrated in numerical and experimental fluids examples. In particular, in the analysis of time-resolved particle image velocimetry data for a separated flow, TDMD outperforms standard DMD by providing dynamical interpretations that are consistent with alternative analysis techniques. Further, TDMD extracts modes that reveal detailed spatial structures missed by standard DMD. |
| Databáze: | OpenAIRE |
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