On Relationship of Koopman Eigenvalues and Frequencies in Dynamic Mode Decomposition

TL;DR

This paper investigates how Koopman eigenvalues relate to frequencies in Dynamic Mode Decomposition, addressing nonuniqueness issues and proposing modifications, demonstrated on a supersonic jet oscillation example.

Contribution

It introduces modifications to DMD to ensure unique frequency estimation from Koopman eigenvalues.

Findings

Modified DMD improves frequency estimation accuracy.

Application to supersonic jet mode demonstrates practical effectiveness.

Addresses nonuniqueness in Koopman eigenvalue-based frequency calculation.

Abstract

The frequency estimation from the Koopman eigenvalues (phase angles) obtained via Dynamic Mode Decomposition (DMD) is addressed. Since the calculations of the frequencies from the phase angles are nonunique, the modifications of DMD for uniqueness restoration are considered. The nonlinear oscillating mode of supersonic jet, impinging the flat plate, is used as a toy problem.