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

arXiv: https://arxiv.org/abs/2107.11999 · HTML: https://mlsanity.com/paper/2107.11999/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 34 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 2 of 2)

- [Sparsity-promoting dynamic mode decomposition](https://mlsanity.com/paper/1309.4165/) (2013)
- [Dynamic mode decomposition for compressive system identification](https://mlsanity.com/paper/1710.07737/) (2017)

## Built on by (most cited first, 4 of 4)

- [Time-series image denoising of pressure-sensitive paint data by projected multivariate singular spectrum analysis](https://mlsanity.com/paper/2203.07574/) (2022)
- [Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMD](https://mlsanity.com/paper/2408.06607/) (2024)
- [Variational Mode Decomposition-Based Nonstationary Coherent Structure Analysis for Spatiotemporal Data](https://mlsanity.com/paper/2312.12113/) (2023)
- [Neuronal Temporal Filters as Normal Mode Extractors](https://mlsanity.com/paper/2401.03248/) (2024)

## Abstract (arXiv)

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.