Statistical analysis and method to quantify the impact of measurement uncertainty on dynamic mode decomposition

Document Type

Conference Proceeding

Publication Date

1-1-2024

Abstract

We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate through the dynamic mode decomposition. While we focus on the first and second moments, the analytical expressions we derive are general and can be extended to higher-order moments. Furthermore, the proposed numerical method for propagating uncertainty is agnostic of specific dynamic mode decomposition formulations. Of particular relevance, the estimated second moments provide confidence bounds that may be used as a metric of trustworthiness, that is, how much one can rely on a finite-dimensional linear operator to represent an underlying dynamical system. We perform numerical experiments on two canonical systems and verify the estimated confidence levels by comparing the moments with those obtained from Monte Carlo simulations.

Identifier

86000560767 (Scopus)

ISBN

[9798350316339]

Publication Title

Proceedings of the IEEE Conference on Decision and Control

External Full Text Location

https://doi.org/10.1109/CDC56724.2024.10886110

e-ISSN

25762370

ISSN

07431546

First Page

4373

Last Page

4379

Grant

DE-AC36-08GO28308

Fund Ref

National Renewable Energy Laboratory

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