Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Data
In this study, we investigated the stability of dynamic mode decomposition (DMD) algorithms to noisy data. To achieve a stable DMD algorithm, we applied the truncated total least squares (T-TLS) regression and optimal truncation level selection to the TLS DMD algorithm. By adding truncation regularization to the TLS DMD algorithm, T-TLS DMD improves the stability of the computation while maintaining the accuracy of TLS DMD. The effectiveness of the T-TLS DMD was evaluated by the analysis of the wake behind a cylinder and practical pressure-sensitive paint (PSP) data for the buffet cell phenomenon. The results showed the importance of regularization in the DMD algorithm. With respect to the eigenvalues, T-TLS DMD was less affected by noise, and accurate eigenvalues could be obtained stably, whereas the eigenvalues of TLS and subspace DMD varied greatly due to noise. It was also observed that the eigenvalues of the standard and exact DMD had the problem of shifting to the damping side, as reported in previous studies. With respect to eigenvectors, T-TLS and exact DMD captured the characteristic flow patterns clearly even in the presence of noise, whereas TLS and subspace DMD were not able to capture them clearly due to noise.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification
Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A diversity of regression techniques have be…
regressionUncertainty QuantificationApplication of Gaussian Process Regression to Koopman Mode Decomposition for Noisy Dynamic Data
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 a…
regressionTime SeriesTime Series AnalysisComprehensive Robust Dynamic Mode Decomposition from Mode Extraction to Dimensional Reduction
We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD …
Asymptotically Stable Data-Driven Koopman Operator Approximation with Inputs using Total Extended DMD
The Koopman operator framework can be used to identify a data-driven model of a nonlinear system. Unfortunately, when the data is corrupted by noise, the identified model can be biased. Additionally, depending on the cho…
A Spectral Method for Stable Bispectrum Inversion with Application to Multireference Alignment
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the…