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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。
In order to reduce the model error, reduce the complexity and improve the real-time performance of aero-engine steady-state modeling, a steady-state model modeling method based on pure B-spline function is proposed. This function is a linear combination of local polynomial basis functions. Therefore, solving this function is a linear regression problem. By using generalized least squares method to solve B coefficients, the computational efficiency and model accuracy can be improved. Finally, steady-state models of two-dimensional and four-dimensional turbofan engines based on this algorithm are established and compared with the steady-state model of least-squares support vector machine with multiple input and multiple output reduction iteratively under the same modeling sample. The simple B-spline modeling method not only inherits the advantages of the B-spline algorithm such as low complexity, small amount of stored data and good real-time performance, but also avoids the shortcomings that least-squares support vector regression can not fit large sample data, Fitting better than least square support vector machine.