Modal Analysis of Spatiotemporal Data via Multivariate Gaussian Process Regression
Open Access
- Author:
- Song, Jiwoo
- Graduate Program:
- Aerospace Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- June 15, 2023
- Committee Members:
- Daning Huang, Thesis Advisor/Co-Advisor
Edward Smith, Committee Member
Amy Pritchett, Program Head/Chair - Keywords:
- Modal analysis
Gaussian process
System identification
Correlation - Abstract:
- Modal analysis has become an essential tool to understand the coherent struc- ture of complex flows. The classical modal analysis methods, such as dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD), rely on sufficient amount of data that is regularly sampled in time. However, often one needs to deal with sparse temporarily irregular data, e.g., due to experimental measurements and simulation algorithm. To overcome this limitation, we propose a novel modal analysis technique using multi-variate Gaussian process regression (MVGPR). This thesis first establishes the connection between MVGPR and the existing modal analysis techniques, DMD and SPOD, from a linear system identification perspective. Next, leveraging this connection, this thesis develop a MVGPR-based modal analysis technique that addresses the aforementioned challenges. The capability of MVGPR is endowed by its judiciously designed kernel structure for correlation function, that emulates the linear dynamics. Subsequently, the proposed MVGPR method is benchmarked against DMD and SPOD on a range of examples, from academic and synthesized data to unsteady airfoil aerodynamics. The results demonstrate MVGPR as a promising alternative to conventional modal analysis methods, especially in the scenarios of scarce data and temporal irregularity.