Data-driven Sensor Placement for Fluid Flows

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.