Schubert Yannick, Sieber Moritz, Oberleithner Kilian, Martinuzzi Robert
Laboratory for Flow Instabilities and Dynamics, Technische Universität Berlin, Berlin, Germany.
Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB Canada.
Theor Comput Fluid Dyn. 2022;36(3):517-543. doi: 10.1007/s00162-022-00609-y. Epub 2022 May 23.
This work presents a robust method that minimises the impact of user-selected parameter on the identification of generic models to study the coherent dynamics in turbulent flows. The objective is to gain insight into the flow dynamics from a data-driven reduced order model (ROM) that is developed from measurement data of the respective flow. For an efficient separation of the coherent dynamics, spectral proper orthogonal decomposition (SPOD) is used, projecting the flow field onto a low-dimensional subspace, so that the dominating dynamics can be represented with a minimal number of modes. A function library is defined using polynomial combinations of the temporal modal coefficients to describe the flow dynamics with a system of nonlinear ordinary differential equations. The most important library functions are identified in a two-stage cross-validation procedure (conservative and restrictive sparsification) and combined in the final model. In the first stage, the process uses a simple approximation of the derivative to match the model with the data. This stage delivers a reduced set of possible library function candidates for the model. In the second, more complex stage, the model of the entire flow is integrated over a short time and compared with the progression of the measured data. This restrictive stage allows a robust identification of nonlinearities and modal interactions in the data and their representation in the model. The method is demonstrated using data from particle image velocimetry (PIV) measurements of a circular cylinder undergoing vortex-induced vibration (VIV) at . It delivers a reduced order model that reproduces the average dynamics of the flow and reveals the interaction of coexisting flow dynamics by the model structure.
这项工作提出了一种稳健的方法，该方法可将用户选择的参数对通用模型识别的影响降至最低，以研究湍流中的相干动力学。目的是从基于相应流场测量数据开发的数据驱动降阶模型（ROM）中深入了解流动动力学。为了有效地分离相干动力学，使用了谱正交分解（SPOD），将流场投影到低维子空间上，以便用最少数量的模态来表示主导动力学。使用时间模态系数的多项式组合定义一个函数库，用非线性常微分方程组来描述流动动力学。在两阶段交叉验证过程（保守和限制性稀疏化）中识别最重要的库函数，并将其组合到最终模型中。在第一阶段，该过程使用导数的简单近似来使模型与数据匹配。此阶段为模型提供了一组减少的可能库函数候选。在第二个更复杂的阶段，对整个流动的模型进行短时间积分，并与测量数据的进展进行比较。这个限制性阶段允许在数据中稳健地识别非线性和模态相互作用及其在模型中的表示。使用来自在 处经历涡激振动（VIV）的圆柱体的粒子图像测速（PIV）测量数据演示了该方法。它提供了一个降阶模型，该模型再现了流动的平均动力学，并通过模型结构揭示了共存流动动力学的相互作用。
