基于卡尔曼滤波方法的流场重构参数化研究  

Research on Parameterization of Flow Field Reconstruction Based on Kalman Filtering Method

作　　者：刘余丹 周楷文 温新 Liu Yudan;Zhou Kaiwen;Wen Xin(School of Mechanical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学机械与动力工程学院,上海200240

出　　处：《气动研究与试验》2025年第2期31-40,共10页Aerodynamic Research & Experiment

摘　　要：针对一种基于卡尔曼滤波器的流场实时重构方法展开了参数化研究。该方法的基本思想为:利用有限的离散压力/速度测量数据,对流场进行实时重构。方法分为线下与线上两个部分。在线下阶段,对流场进行全场采样,并对所测得的流场数据做本征正交分解进行降维,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。在线上阶段,基于压缩感知,利用离散测量数据与主导模态,通过求解L1范数下的凸最优化问题,对各主导模态的时间系数进行初步求解。然后,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;将线上所求得的各模态时间系数放入卡尔曼滤波器,作为其观测值进行矫正。最后,针对卡尔曼滤波器参数对重构效果的影响进行了分析。A parameterization analysis on real-time flow field reconstruction method based on compressed sensing and Kalman filter is put forward.The method is divided into two parts:offline and online.In the offline step,full-field sampling is carried out,and the measured flow field data is reduced by proper orthogonal decomposition to establish the modal database containing the dominant coherent flow structure and the state transition relationship between the modal time coefficients.In the online step,based on compressed sensing,using discrete measurement data and dominant modes,the time coefficients of each dominant mode are calculated by solving the convex optimization problem under the L1 norm.Then,the state transition relationship between the modal time coefficients obtained offline is put into the Kalman filter as its system model for prediction.The modal time coefficients obtained online are put into the Kalman filter as the observed values to be corrected.Finally,the paper analyzes the influence of Kalman filter parameters on the reconstruction effect.

关 键 词：压缩感知 卡尔曼滤波器 动态模态分解 流场重构 数据融合 

分 类 号：O355[理学—流体力学]