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.

翻译：模态分析已成为理解复杂流场相干结构的重要工具。经典模态分析方法如动态模态分解（DMD）和谱本征正交分解（SPOD）依赖于时间规则采样的充足数据。然而，受实验测量和仿真算法等因素影响，常需处理稀疏且时间不规则的数据。为克服数据稀缺与不规则采样的局限，我们提出了一种基于多元高斯过程回归（MVGPR）的新型模态分析技术。首先从线性系统辨识视角建立MVGPR与现有DMD、SPOD模态分析技术之间的关联，进而利用该关联发展出能解决上述局限性的MVGPR模态分析方法。MVGPR的能力源于其基于假设线性动力学推导的相关函数核结构的精巧设计。最后，从学术与合成数据到非定常翼型气动力学等系列案例中，将所提MVGPR方法与DMD和SPOD进行基准测试。结果表明，特别是在数据稀疏且时间不规则的场景下，MVGPR是经典模态分析方法的有效替代方案。