Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

This work considers the optimal sensor placement problem for a general nonlinear system using the eigenvalues of the observability Gramian in the cost function. The problem is formulated as a mixed-integer convex optimization problem. Using the empirical observability Gramian, the input data to this optimization problem are computed from a simulation of the nonlinear system with no analytical model required. A piecewise linear approximation to the observability Gramian is proposed using special ordered sets of type two, allowing a coarser sensor location mesh and thus fewer binary variables and shorter solution times compared with standard gridded approaches. The solution methodology is applied to vortex estimation in the wake of a flapping airfoil using velocity sensors on the surface of the airfoil, which is modeled using unsteady potential flow and a Joukowski conformal mapping. Resulting optimal sensor sets are found near the trailing edge in pairs on the upper and lower surface. Although the observab...