参变量样条函数磨光法在水轮机特性曲线拟合中的应用

Polishing method of parametric variable spline function applied to fitting of characteristic curves of turbine

水轮机选型设计时,必须大量查取水轮机特性曲线,而这些曲线大多是图形曲线,使用时必须对这些水轮机特性曲线进行数字化。此外,水轮机特性曲线大多为封闭曲线,而大多数曲线拟合方法均使用分段拟合,方法复杂且效果不佳。因此,曲线拟合方法的选择就至关重要。参变量样条函数磨光法不但具有直观性,而且有较高的逼近性、光滑度、保凸性及整体性好等特点,对封闭曲线的拟合效果更为明显。据此详细研究了三次参变量样条函数磨光法的曲线拟合,进而应用于水轮机特性曲线的拟合。

During type selection and design of hydraulic turbine, the selection on method for the fitting of the characteristic curves of turbine is quite important; for which the polishing method of parametric variable spline function is not only intuitive, but also has the merits such as higher approachability, smoothness, convexity-preserving property and better integration etc. ; furthermore, the fitting effect is more obvious for the closed-curves. Therefore, the polishing method of cubic parametric variable spline function for the curve-fitting is studied in detail, and then is applied to the fitting of cubic parametric variable spline function for the curve-fitting is studied in detail, and then is applied to the fitting of the characteristic curves of turbine as well.