Application of Gaussian Process Regression to Koopman Mode Decomposition for Noisy Dynamic Data
This work addresses the challenge of analyzing noisy dynamic data in nonlinear time-series analysis, specifically for power grid applications, but it appears incremental as it adapts an existing method to handle noise.
The authors tackled the problem of performing Koopman Mode Decomposition on noisy finite-time data by developing a numerical algorithm based on Gaussian process regression, and they applied it to estimate oscillatory modes in a multi-machine power grid's swing dynamics to evaluate its effectiveness.
Koopman Mode Decomposition (KMD) is a technique of nonlinear time-series analysis that originates from point spectrum of the Koopman operator defined for an underlying nonlinear dynamical system. We present a numerical algorithm of KMD based on Gaussian process regression that is capable of handling noisy finite-time data. The algorithm is applied to short-term swing dynamics of a multi-machine power grid in order to estimate oscillatory modes embedded in the dynamics, and thereby the effectiveness of the algorithm is evaluated.