全局连续的分段最小二乘曲线拟合方法

Global Continuous Curve Fitting Method of Piecewise Least Square Fitting with Global Continuity

针对传统最小二乘的曲线拟合方法不适合单一应用在具有复杂结构的试验观测数据中,本文提出一种满足全局连续性约束的多分段区间的最小二乘数据拟合方法。通过把每个相邻分段点上要求拟合连续的约束条件转化成一个矩阵等式Zα=0,建立一个只包含线性等式约束的最小二乘模型mαin‖Xα-y‖2,最后通过应用拉格朗日的乘数方法推导出最小二乘解α。本文的拟合方法在分段点上具有良好的拟合效果并满足全局连续,模型系数求解具有简单的显式表达式,易于编程数值计算。

The application of traditional least square method is limited when the experiment data are of heterogeneous structure. This paper presents a novel constrained least square method for solving the piecewise local curve fitting problem with global continuity constraint. In particular, the continuity constraint among the segment points was converted to the matrix equality Za = O. Therefore, the least square model min‖Xa-y‖2 was proposed with the linear equality constraint to address the problem. Here, the solution of the a least square model was seriously derived in a simple explicit form via the Lagrange muhiplier method, which can be easily programmed in numerical calculation. The experimental results show that the method proposed here provided a ＂best＂ fit for the data and the global continuity on the segment points.