Modal analysis has become an essential tool to understand the coherent
structure of complex flows. The classical modal analysis methods, such as
dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition
(SPOD), rely on a sufficient amount of data that is regularly sampled in time.
However, often one needs to deal with sparse temporally irregular data, e.g.,
due to experimental measurements and simulation algorithm. To overcome the
limitations of data scarcity and irregular sampling, we propose a novel modal
analysis technique using multi-variate Gaussian process regression (MVGPR). We
first establish the connection between MVGPR and the existing modal analysis
techniques, DMD and SPOD, from a linear system identification perspective.
Next, leveraging this connection, we develop a MVGPR-based modal analysis
technique that addresses the aforementioned limitations. The capability of
MVGPR is endowed by its judiciously designed kernel structure for correlation
function, that is derived from the assumed 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 classical modal
analysis methods, especially in the scenario of scarce and temporally irregular
data.

通过多元高斯过程回归（MVGPR）方法，克服稀缺和时间不规则数据限制，提出了一种新颖的模态分析技术，能够代替传统的模态分析方法如动态模态分解（DMD）和谱正交分解（SPOD）。MVGPR 的核函数结构基于线性动态的相关函数假设，通过与 DMD 和 SPOD 的联系，该方法在学术研究、合成数据和非稳态翼型气动等范例下得到了验证，展示了 MVGPR 作为一种有前景的替代方法。