Kazuyuki Nakakita

Yuya Ohmichi, Kohmi Takahashi, Kazuyuki Nakakita

Time-series data, such as unsteady pressure-sensitive paint (PSP) measurement data, may contain a significant amount of random noise. Thus, in this study, we investigated a noise-reduction method that combines multivariate singular spectrum analysis (MSSA) with low-dimensional data representation. MSSA is a state-space reconstruction technique that utilizes time-delay embedding, and the low-dimensional representation is achieved by projecting data onto the singular value decomposition (SVD) basis. The noise-reduction performance of the proposed method for unsteady PSP data, i.e., the projected MSSA, is compared with that of the truncated SVD method, one of the most employed noise-reduction methods. The result shows that the projected MSSA exhibits better performance in reducing random noise than the truncated SVD method. Additionally, in contrast to that of the truncated SVD method, the performance of the projected MSSA is less sensitive to the truncation rank. Furthermore, the projected MSSA achieves denoising effectively by extracting smooth trajectories in a state space from noisy input data. Expectedly, the projected MSSA will be effective for reducing random noise in not only PSP measurement data, but also various high-dimensional time-series data.

Yuya Ohmichi, Yosuke Sugioka, Kazuyuki Nakakita

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.