基于B样条的水泵复杂特性曲线拟合方法

为适应水泵复杂特性曲线中存在大挠度和非等距测点的情况，探索了基于三次均匀B样条的曲线拟合方法。通过局部预测的方法引入新的型值点以克服曲线尖点拟合的困难。根据离散数据点连线的几何形状进行分段，基于最小二乘法分步优化节点的横坐标和纵坐标，得到了最优逼近的B样条拟合曲线。通过实例计算表明，该方法可以高精度地将全区域范围的水泵试验数据拟合成光滑的特性曲线，并能够消除因试验随机误差所引起的曲线扰动。

Fitting method for pump complex characteristic curve based on B-spline

A fitting method for pump complex characteristic curve with large deflections and non-equidistant data points based on cubic uniform B-spline is presented. New virtual data points are introduced when any spire point is detected in the curve, which is divided into several sections with simple shapes The optimal knots ordinates and abscissas within the specified distribution ranges are searched employing sequential optimization method in the least square sense. It is proved in the examples that the new method works well in precisely building the pump test data in wide area into smooth curve without disturbance caused by the random test error.