Reconstruction of airfoil surface pressure by Kalman filter

Real-time reconstructing a complete picture of the flow field around aircraft by limited measurements is fundamental to real-time control. This paper proposes a method for real-time reconstruction of unsteady airfoil surface pressure based on the compressed sensing and Kalman filter. The method mainly consists of offline database construction and online real-time perception. Firstly, the full-field sampling of airfoil surface pressure is carried out by particle image velocimetry, pressure-sensitive paint, and computational fluid dynamics (CFD). The dimensionality of the measured full-field pressure data is reduced by the proper orthogonal decomposition, yielding a database containing the dominant coherent flow structures and the state transition relationships among the modal time coefficients. Secondly, based on the compressed sensing, the time coefficients of each dominant mode are preliminarily obtained by solving the optimization problem under the L₁-norm using the measurements of discrete pressure sensors and the dominant pressure modes. Finally, the state transition relationships among modal time coefficients obtained offline are put into the Kalman filter for prediction. The modal time coefficients obtained online are further corrected by the Kalman filter. CFD simulation results are used as validation to evaluate the performance of this method. Results show that the reconstruction error of this method is 64.79% lower than that of using compressed sensing only.