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介绍了一种基于多变量正交多项式的全局非线性气动系数建模方法。首先由离散数据点生成多变量正交函数;然后根据建立的最小平方误差预测准则,对正交函数进行筛选,保留下来的正交函数均可以分解成普通的独立变量多项式,最后的模型可以看作是多变量幂级数展开系列中的选择性保留项。将该方法应用于某高超声速飞行器的阻力系数建模;将所建模型和仿真数据进行分析比较,其误差小于3%,能够满足工程应用要求。
A global nonlinear aerodynamic coefficient modeling method based on multivariate orthogonal polynomials is introduced. Firstly, the multivariate orthogonal function is generated from the discrete data points. Then the orthogonal function is screened according to the established least square error prediction criterion. All the orthogonal functions preserved can be decomposed into ordinary independent variable polynomials. The final model can be seen It is a selective reservation in the series of multivariate power series expansion. The method is applied to the drag coefficient modeling of a hypersonic vehicle. The proposed model and the simulation data are compared and analyzed, and the error is less than 3%, which can meet the engineering application requirements.