基于单纯B样条的航空发动机机载稳态模型研究

Research on Simplex B-Splines Algorithm in on-Board SteadyState Modeling of Turbofan Engines

为了减小航空发动机稳态建模的模型误差、降低复杂度及提升其实时性,提出了一种基于单纯B样条函数的航空发动机稳态模型建模方法。该函数是局部多项式基函数的线性组合,因此求解该函数为线性回归问题,通过运用广义最小二乘方法来求解B系数,从而提高计算效率和提高模型精度。最后建立了基于该算法的二维和四维涡扇发动机稳态模型,并分别与相同建模样本条件下的多输入多输出约简迭代最小二乘支持向量机稳态模型进行了比较,表明了单纯B样条建模方法不仅继承了B样条的算法复杂度低、存储数据量小和实时性好等优点,同时避免了最小二乘支持向量回归机不能拟合大样本数据的缺点,且拟合效果优于最小二乘支持向量机。

The method based on the Simplex B-spline function has been proposed to reduce the fitting error and complexity,which can also improve the real-time characteristics in steady-state modeling of an aero-engine. As the function is comprised of local polynomial basis functions,linear regression and generalized least squares method can be applied to solve the B coefficients. In this way,the computing efficiency and the accuracy of the model are significantly improved. At last,the model verification results with this new method are compared with that of muti-input muti-output recursive reduced least squares support vector regression（MRR-LSSVR） in two-and four-dimensional steady-state modelling of the turbofan engine,respectively. It shows that the new modeling method has a lower complexity,less data capacity and higher performance of instantaneity. Furthermore,it can overcome the shortcomings of MRR-LSSVR that cannot well be applied for large sample sets.Moreover,while fitting discrete samples,it will be better than MRR-LSSVR.