基于多元正交函数的非线性快速气动建模  

Nonlinear rapid aerodynamic modeling based on multivariate orthogonal functions

作　　者：高鑫[1] 连峰[1] 孔轶男[2] 陈功[2] 张光华[1] 王文正 GAO Xin;LIAN Feng;KONG Yinan;CHEN Gong;ZHANG Guanghua;WANG Wenzheng(Xi’an Jiaotong University,Xi’an 7100049,China;China Aerodynamics Research and Development Center,Mianyang 621000,China;School of Aeronautics and Astronautics,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]西安交通大学,西安710049 [2]中国空气动力研究与发展中心,绵阳621000 [3]电子科技大学航空航天学院,成都611731

出　　处：《空气动力学学报》2023年第6期81-88,I0002,共9页Acta Aerodynamica Sinica

摘　　要：多项式响应面模型是气动系数建模中常用的一种模型。实时采集的气动数据有较强的线性相关性,使用常规最小二乘回归方法估计模型参数时,由于回归矩阵的病态性导致估计误差较大。提出一种基于多元正交函数的多项式响应面建模方法,将回归矩阵进行QR分解后迭代实时数据,可以有效避免回归矩阵病态问题,提高多项式响应面模型的精确度;引入模型预测方差(PSE)与决定系数R^(2),简化模型结构,避免了模型的过度拟合。基于F-16风洞试验部分气动数据,利用仿真程序对风洞数据进行样条函数插值,得到完整的实验数据集,用以验证实验算法。采用多元正交函数建模方法分别建立目标飞行器的6个无量纲气动力系数模型,并对建模过程中的实时性进行分析。建模结果表明,基于多元正交函数建立的多项式响应面模型对实时数据有较好的预测效果;同时,建模过程中各环节的时间消耗均是毫秒级的,满足实时建模的要求,说明该方法可以实时地建立目标飞行器的非线性气动力系数模型。The polynomial response surface model(RSM)is a standard model in aerodynamic coefficient modeling.Real-time collected aerodynamic data are strongly correlated.Estimating the parameters of RSM by conventional least-square regression methods will yield significant errors since the regression matrix is ill-posed.A polynomial RSM based on multivariate orthogonal functions proposed here can overcome such a shortcoming and improve RSM's accuracy by iterating real-time data on the R matrix of the QR decomposed regression matrix.Moreover,RSM is further simplified by introducing Predicted Squared Error(PSE)and the R^(2)coefficient to eliminate negligible items so that the over-fitting of the model is avoided.Part of the aerodynamic data of an F-16 wind tunnel test is interpolated with the spline function to obtain complete experimental data.The real-time data acquisition process is simulated by inputting data one by one to verify the effectiveness and real-time performance of the experimental algorithm.The multivariate orthogonal function modeling method is used to establish six models of dimensionless aerodynamic coefficients of the target aircraft,and the real-time performance of the modeling process is analyzed.Results show that the polynomial RSM based on multivariate orthogonal functions has a good predictive capability for real-time data.Meanwhile,the time consumption of each step in the modeling process is milliseconds,indicating that the method can establish the real-time modeling of the nonlinear aerodynamic coefficients of target aircraft.

关 键 词：多元正交函数 非线性建模 QR分解 最小二乘回归 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程] O241[理学—计算数学]