The conventional modal analysis techniques face difficulties in handling nonstationary phenomena, such as transient, nonperiodic, or intermittent phenomena. This paper presents a variational mode decomposition–based nonstationary coherent structure (VMD-NCS) analysis that enables the extraction and analysis of coherent structures in the case of nonstationary phenomena from high-dimensional spatiotemporal data. The VMD-NCS analysis decomposes the input spatiotemporal data into intrinsic coherent structures (ICSs) that represent nonstationary spatiotemporal patterns and exhibit coherence in both spatial and temporal directions. Furthermore, unlike many conventional modal analysis techniques, the proposed method accounts for the temporal changes in the spatial distribution with time. The performance of the VMD-NCS analysis was validated based on the transient growth phenomena in the flow around a cylinder. It was confirmed that the temporal changes in the spatial distribution, depicting the transient growth of vortex shedding where fluctuations arising in the far-wake region gradually approach the near-wake region, were represented as a single ICS. Furthermore, in the analysis of the quasi-periodic flow field around a pitching airfoil, the temporal changes in the spatial distribution and the amplitude of vortex shedding behind the airfoil, influenced by the pitching motion of the airfoil, were captured as a single ICS. Additionally, the impact of two parameters that control the number of ICSs () and the penalty factor related to the temporal coherence (), was investigated. The results revealed that has a significant impact on the VMD-NCS analysis results. In the case of a relatively high , the VMD-NCS analysis tends to extract more periodic spatiotemporal patterns resembling the results of dynamic mode decomposition. In the case of a small , it tends to extract more nonstationary spatiotemporal patterns.

中文翻译：

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基于变分模态分解的时空数据非平稳相干结构分析


传统的模态分析技术在处理非平稳现象（例如瞬态、非周期或间歇现象）时面临困难。本文提出了一种基于变分模式分解的非平稳相干结构（VMD-NCS）分析，能够在非平稳现象的情况下从高维时空数据中提取和分析相干结构。 VMD-NCS 分析将输入时空数据分解为内在相干结构 (ICS)，这些结构表示非平稳时空模式并在空间和时间方向上表现出相干性。此外，与许多传统的模态分析技术不同，所提出的方法考虑了空间分布随时间的时间变化。 VMD-NCS 分析的性能基于圆柱体周围流动的瞬态增长现象进行了验证。经证实，空间分布的时间变化，描述了涡旋脱落的瞬时增长，其中远尾流区域中产生的波动逐渐接近近尾流区域，被表示为单个ICS。此外，在对俯仰翼型周围的准周期流场进行分析时，受翼型俯仰运动影响的翼型后方涡脱落的空间分布和振幅的时间变化被捕获为单个ICS。此外，还研究了控制 ICS 数量 () 和与时间相干性相关的惩罚因子 () 的两个参数的影响。结果表明，对VMD-NCS分析结果有显着影响。 在 相对较高的情况下，VMD-NCS 分析倾向于提取更多周期性的时空模式，类似于动态模式分解的结果。在 较小的情况下，它倾向于提取更多非平稳时空模式。