基于卡尔曼滤波的翼型表面压力实时重构方法

Reconstruction of airfoil surface pressure by Kalman filter

为实现基于稀疏数据的翼型表面压力实时重构,提出了一种基于压缩感知与卡尔曼滤波器的数据融合方法,该方法主要包括线下建立数据库和线上实时感知两部分。首先,在线下通过粒子图像测速技术、压敏漆、计算流体力学等方法对翼型表面压力进行全场采样,并采用本征正交分解对所测得的全场压力数据进行降维,建立含有主导相干流动结构的模态数据库以及各模态时间系数之间的状态转换关系。其次,在线上基于压缩感知,利用离散压力传感器所测量数据与压力场主导模态,通过求解L1范数下的最优化问题,对各主导模态的时间系数进行初步求解。最后,将线下所得各模态时间系数之间的状态转换关系放入卡尔曼滤波器,作为其系统模型进行预测;将线上所求得各模态时间系数放入卡尔曼滤波器,作为其观测值进行校正。以CFD模拟翼型压力作为验证数据,对该方法的性能进行评估,结果显示:该方法与仅采用压缩感知进行重构对比,升力重构误差从18.15%减小至6.39%。

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.