Optimal sensor placement for fluid flows is an important and challenging problem. In this study, we propose a completely data-driven and computationally efficient method for sensor placement. We use adjoint-based gradient descent to find the sensor location that minimizes the trace of an approximation of the estimation error covariance matrix. The proposed methodology can be used in conjunction with any reduced-order modeling technique that provides a linear approximation of the fluid dynamics. Moreover, the objective function can be augmented for different applications, which we illustrate by proposing a control-oriented objective function. We demonstrate the performance of our method for reconstruction and prediction of the complex linearized Ginzburg–Landau equation in the globally unstable regime. We also construct a low-dimensional observer-based feedback controller for the flow over an inclined flat plate that is able to suppress the wake vortex shedding in the presence of system and measurement noise.

流体流动的最佳传感器放置是一个重要且具有挑战性的问题。在这项研究中，我们提出了一种完全数据驱动且计算效率高的传感器放置方法。我们使用基于伴随的梯度下降来找到最小化估计误差协方差矩阵近似轨迹的传感器位置。所提出的方法可以与提供流体动力学线性近似的任何降阶建模技术结合使用。此外，目标函数可以针对不同的应用进行扩充，我们通过提出一个面向控制的目标函数来说明这一点。我们展示了我们的方法在全局不稳定状态下重建和预测复杂线性化 Ginzburg-Landau 方程的性能。