Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Data

TL;DR

This paper introduces a stable dynamic mode decomposition method using truncated total least squares to improve noise robustness in pressure-sensitive paint data analysis, demonstrating enhanced stability and accuracy over existing methods.

Contribution

The paper proposes a novel T-TLS DMD algorithm with regularization, improving stability and eigenvalue accuracy in noisy pressure measurement data analysis.

Findings

T-TLS DMD is less affected by noise in eigenvalues.

T-TLS DMD captures flow patterns clearly despite noise.

Regularization improves DMD stability and accuracy.

Abstract

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.