Abstract A key step to improve data-driven reduced-order simulations is to compute a transfer function that predicts the time evolution of the reduced-order modes accurately. We demonstrate a couple of useful techniques to achieve this objective: One is to pre-process time-series of reduced-order modes with a low-pass filter, e.g. a polynomial filter and B-spline, and the other is to compute a data-driven transfer function from multiple past time-steps, corresponding to a high-order temporal scheme. These techniques are exercised with POD modes generated from time-resolved planar PIV data. A fully separated flow past the NACA0012 airfoil at the angle of attack of 30∘ and R e = 1000 is measured in a water tunnel, and non-periodic unsteady flow is analyzed in two dimensions. From the first 1000 frames, transfer functions are calculated based on minimization of different cost functions, which define least-squares errors in the predicted POD modes at the next time step; subsequently, their prediction capabilities are evaluated during the following 1000 frames based on the accuracy of the predicted POD modes at the next time steps. The multistep schemes can reduce the root-mean-square errors of the predicted mode coefficients by up to 10% without a low-pass filter. Combining a low-pass filter with the second-order temporal scheme can further reduce the errors by 7%, and introduction of an L1-norm constraint for the mode coefficients decreases it by extra 2%. In contrast, nonlinear transfer functions with more degrees of freedom deteriorate the prediction during time duration outside of the sampling period even relative to the linear prediction.

中文翻译：

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改进非定常流动的数据驱动降阶模拟的几种技术

摘要 改进数据驱动降阶仿真的关键步骤是计算传递函数，该函数可以准确预测降阶模式的时间演变。我们展示了一些有用的技术来实现这个目标：一种是使用低通滤波器（例如多项式滤波器和 B 样条）对降阶模式的时间序列进行预处理，另一种是计算数据来自多个过去时间步长的驱动传递函数，对应于高阶时间方案。这些技术使用从时间分辨平面 PIV 数据生成的 POD 模式。在水洞中测量了攻角为 30∘ 和 Re = 1000 时经过 NACA0012 翼型的完全分离的流动，并在二维上分析了非周期性非定常流动。从前 1000 帧开始，传递函数是基于不同成本函数的最小化计算的，这些成本函数定义了下一时间步预测 POD 模式中的最小二乘误差；随后，根据预测的 POD 模式在接下来的时间步长的准确性，在接下来的 1000 帧中评估它们的预测能力。多步方案可以在没有低通滤波器的情况下将预测模式系数的均方根误差减少多达 10%。将低通滤波器与二阶时间方案相结合可以进一步减少 7% 的误​​差，并且为模式系数引入 L1 范数约束使其额外减少 2%。相比之下，即使相对于线性预测，具有更多自由度的非线性传递函数也会在采样周期之外的持续时间内恶化预测。