We present spectral analysis modal methods (SAMMs) to perform POD in the frequency domain using non-time-resolved particle image velocity (PIV) data combined with unsteady surface pressure measurements. In particular, time-resolved unsteady surface pressure measurements are synchronized with non-time-resolved planar PIV measurements acquired at 15 Hz in a Mach 0.6 cavity flow. Leveraging the spectral linear stochastic estimation (LSE) method of Tinney et al. (Exp Fluids 41:763–775, 2006), we first estimate the cross-correlations between the velocity field and the unsteady pressure sensors via sequential time shifts, followed by a Fast Fourier transform to obtain the pressure–velocity cross spectral density matrix. This leads to a linear multiple-input/multiple-output (MIMO) model that determines the optimal transfer functions between the input cavity wall pressure and the output velocity field. Two variants of SAMMs are developed and applied. The first, termed “SAMM-SPOD”, combines the MIMO model with the SPOD algorithm of Towne et al. (J Fluid Mech, https://doi.org/10.1017/jfm.2018.283, 2018). The second, called “SAMM-RR”, adds independent sources and uses a sorted eigendecomposition of the input pressure cross-spectral matrix to enable an efficient reduced-rank eigendecomposition of the velocity cross-spectral matrix. In both cases, the resulting rank-1 POD eigenvalues associated with the Rossiter frequencies exhibit very good agreement with those obtained using independent time-resolved PIV measurements. The results demonstrate that SAMMs provide a methodology to perform space-time POD without requiring a high-speed PIV system, while avoiding potential pitfalls associated with traditional time-domain LSE.

中文翻译：

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使用非时间分辨 PIV 的光谱分析模态方法 (SAMM)

我们提出了频谱分析模态方法 (SAMM)，使用非时间分辨粒子图像速度 (PIV) 数据结合不稳定表面压力测量在频域中执行 POD。特别是，时间分辨非定常表面压力测量与在 0.6 马赫腔流中以 15 Hz 获取的非时间分辨平面 PIV 测量同步。利用 Tinney 等人的谱线性随机估计 (LSE) 方法。(Exp Fluids 41:763–775, 2006)，我们首先通过顺序时移估计速度场和非稳态压力传感器之间的互相关，然后进行快速傅立叶变换以获得压力-速度交叉谱密度矩阵。这导致线性多输入/多输出 (MIMO) 模型确定输入腔壁压力和输出速度场之间的最佳传递函数。开发和应用了SAMM 的两种变体。第一个，称为“SAMM-SPOD”，将 MIMO 模型与 Towne 等人的 SPOD 算法相结合。(J Fluid Mech, https://doi.org/10.1017/jfm.2018.283, 2018)。第二个称为“SAMM-RR”，添加独立源并使用输入压力交叉谱矩阵的排序特征分解来实现速度交叉谱矩阵的有效降阶特征分解。在这两种情况下，所得的与 Rossiter 频率相关的 1 级 POD 特征值与使用独立时间分辨 PIV 测量获得的特征值非常吻合。