改进的最小二乘法在水文分析计算中的应用

Application of Improved Least Square Method in Hydrological Analysis Calculation

在水文分析计算中,经常涉及到变量之间的线性或非线性拟合,而在拟合各种特性曲线时,通常应用以实测资料与拟合曲线间的误差平方和最小作为目标函数的方法———最小二乘法,但这种方法忽视了所有实测点应与拟合曲线间的相对误差尽量不超过某一百分比的原则,为了达到上述要求,提出了非线性的加权最小二乘法及线性相关方程的最小距离平方和法,探讨改进了传统的最小二乘法达到优化的效果。最小距离平方和法与常用的图解法相比,本法所得成果较为客观;与传统的单方向(x或y方向)最小二乘回归法相比,所求线性方程不会因坐标系的选取而改变。最后应用算例进行了初步讨论。

Linearity and non-linearity simulation are used in hydrological calculation.Least square method is of-ten applied to simulate curve generally,but this method ignores that the relative errors should be less than certain percent between fact sur vey point and simulated curve.In order to improve it's precision,weight least square method(WLSM)for non-linearity and least distance square method(LDSM)for linearity relative equation are provided to improve traditional least square method.Comparing to traditional method,LDSM's result is more practicality;relative to traditional one orientation method,its linear equation is not changed by the selection of coordinate system.A case study is applied to discuss it primarily.